{"group":{"group":{"id":35,"name":"Cody5:Hard","lockable":false,"created_at":"2017-10-11T18:43:59.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Hard problems for Cody 5th Anniversary.","is_default":false,"created_by":1,"badge_id":49,"featured":false,"trending":false,"solution_count_in_trending_period":20,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":412,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHard problems for Cody 5th Anniversary.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}","description_html":"\u003cdiv style = \"text-align: start; line-height: normal; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"display: block; min-width: 0px; padding-top: 0px; perspective-origin: 289.5px 10.5px; transform-origin: 289.5px 10.5px; \"\u003e\u003cdiv style=\"font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-bottom: 9px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; perspective-origin: 266.5px 10.5px; transform-origin: 266.5px 10.5px; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"display: inline; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eHard problems for Cody 5th Anniversary.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","published_at":"2019-05-08T19:57:49.000Z"},"current_player":null},"problems":[{"id":44387,"title":"Birthday cake","description":"It's Cody's 5th birthday, and you've been tasked with putting the candles on the cake. Your goal is to maximize the distance between the 5 required candles.\r\n\r\nGiven a rectangular cake with specified length and width, return the highest possible minimum distance between any two candles. \r\n\r\n*Important notes*\r\n\r\n* You may assume that a candle can be placed directly on the edge of the cake (even though that would be physically challenging!).\r\n* Required tolerance: \u003c0.01","description_html":"\u003cp\u003eIt's Cody's 5th birthday, and you've been tasked with putting the candles on the cake. Your goal is to maximize the distance between the 5 required candles.\u003c/p\u003e\u003cp\u003eGiven a rectangular cake with specified length and width, return the highest possible minimum distance between any two candles.\u003c/p\u003e\u003cp\u003e\u003cb\u003eImportant notes\u003c/b\u003e\u003c/p\u003e\u003cul\u003e\u003cli\u003eYou may assume that a candle can be placed directly on the edge of the cake (even though that would be physically challenging!).\u003c/li\u003e\u003cli\u003eRequired tolerance: \u0026lt;0.01\u003c/li\u003e\u003c/ul\u003e","function_template":"function d = birthdaycandles(len,wid)\r\n  d = 0;\r\nend","test_suite":"%%\r\nlen = 1; wid = 1;\r\nd_correct = 0.7071;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 2; wid = 3;\r\nd_correct = 1.8028;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 3; wid = 8;\r\nd_correct = 3.6056;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 4; wid = 3;\r\nd_correct = 2.5000;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 5; wid = 4;\r\nd_correct = 3.2016;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 5; wid = 6;\r\nd_correct = 3.9051;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 5; wid = 11;\r\nd_correct = 5.5200;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 7; wid = 6;\r\nd_correct = 4.6098;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 8; wid = 7;\r\nd_correct = 5.3151;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 8; wid = 9;\r\nd_correct = 6.0208;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 10; wid = 9;\r\nd_correct = 6.7268;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 11; wid = 10;\r\nd_correct = 7.4330;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 12; wid = 23;\r\nd_correct = 12.2018;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 15; wid = 32;\r\nd_correct = 16.1616;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 16; wid = 32;\r\nd_correct = 16.5644;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 17; wid = 32;\r\nd_correct = 17.1902;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 64; wid = 1;\r\nd_correct = 16.0312;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 36; wid = 36;\r\nd_correct = 25.4558;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 48; wid = 24;\r\nd_correct = 24.8466;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 26; wid = 48;\r\nd_correct = 26.1679;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 100.25; wid = 100.25;\r\nd_correct = 70.8875;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 500; wid = 250;\r\nd_correct = 258.8190;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = 500; wid = 1000;\r\nd_correct = 517.6381;\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n%%\r\nlen = randi([1,1e4]); wid = len;\r\nd_correct = sqrt((len/2)^2+(wid/2)^2);\r\nassert(abs(birthdaycandles(len,wid)-d_correct)\u003c1e-2)\r\n\r\n","published":true,"deleted":false,"likes_count":10,"comments_count":17,"created_by":4793,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":108,"test_suite_updated_at":"2017-10-24T15:58:40.000Z","rescore_all_solutions":true,"group_id":35,"created_at":"2017-10-13T21:22:20.000Z","updated_at":"2026-03-23T15:23:13.000Z","published_at":"2017-10-16T01:51:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt's Cody's 5th birthday, and you've been tasked with putting the candles on the cake. Your goal is to maximize the distance between the 5 required candles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a rectangular cake with specified length and width, return the highest possible minimum distance between any two candles.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eImportant notes\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou may assume that a candle can be placed directly on the edge of the cake (even though that would be physically challenging!).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRequired tolerance: \u0026lt;0.01\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44340,"title":"Recaman Sequence - III","description":"I want to create a Recaman sequence where there is a \"1\" in the n-th position. So from which integer should I start the Recaman sequence? If there are more than one starting integer that generates a sequence with a 1 in the n-th position, return the lowest one.\r\nFor example if I want to place the digit 1 in the 7th place in the sequence then I should start the sequence from six as follow;\r\nseq = [6 5 3 6 2 7 1 8 16]\r\nYou can also start the sequence with 12 and obtain a series where there is a 1 in 7th position;\r\nseq = [12 11 9 6 2 7 1]\r\nRelated Challenges :\r\nRecaman Sequence - I\r\nRecaman Sequence - II\r\nRecaman Sequence - III","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 308.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 154.083px; transform-origin: 407px 154.083px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 371.5px 8px; transform-origin: 371.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eI want to create a Recaman sequence where there is a \"1\" in the n-th position. So from which integer should I start the Recaman sequence? If there are more than one starting integer that generates a sequence with a 1 in the n-th position, return the lowest one.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.5px 8px; transform-origin: 368.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example if I want to place the digit 1 in the 7th place in the sequence then I should start the sequence from six as follow;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 104px 8.5px; tab-size: 4; transform-origin: 104px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eseq = [6 5 3 6 2 7 1 8 16]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 294.5px 8px; transform-origin: 294.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou can also start the sequence with 12 and obtain a series where there is a 1 in 7th position;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 92px 8.5px; tab-size: 4; transform-origin: 92px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eseq = [12 11 9 6 2 7 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.5px 8px; transform-origin: 72.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eRelated Challenges :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44338\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eRecaman Sequence - I\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44339\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eRecaman Sequence - II\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 75px 8px; transform-origin: 75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRecaman Sequence - III\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function startPoint = RecamanIII(onesplace)\r\n\r\nend","test_suite":"%%\r\nfiletext = fileread('RecamanIII.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 0;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 4;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 9;\r\ny_correct = 13;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 13;\r\ny_correct = 15;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 15;\r\ny_correct = 26;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 26;\r\ny_correct = 54;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 54;\r\ny_correct = 208;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 208;\r\ny_correct = 2485;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":12,"created_by":8703,"edited_by":223089,"edited_at":"2022-10-11T07:22:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":89,"test_suite_updated_at":"2022-10-11T07:22:46.000Z","rescore_all_solutions":false,"group_id":35,"created_at":"2017-09-19T07:36:19.000Z","updated_at":"2026-03-22T11:36:50.000Z","published_at":"2017-10-16T01:50:59.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI want to create a Recaman sequence where there is a \\\"1\\\" in the n-th position. So from which integer should I start the Recaman sequence? If there are more than one starting integer that generates a sequence with a 1 in the n-th position, return the lowest one.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if I want to place the digit 1 in the 7th place in the sequence then I should start the sequence from six as follow;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[seq = [6 5 3 6 2 7 1 8 16]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou can also start the sequence with 12 and obtain a series where there is a 1 in 7th position;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[seq = [12 11 9 6 2 7 1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRelated Challenges :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44338\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eRecaman Sequence - I\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44339\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eRecaman Sequence - II\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRecaman Sequence - III\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44343,"title":"Pair Primes","description":"Let's define pair primes as follow;\r\nFor 2 digits numbers: 11 and 17 are pair primes because both of them are 2 digits prime numbers and last digit of the first prime equals to the first digit of second prime number. 11 and 11 are not pair primes because a = b.\r\nFor 3 digit numbers: 389 and 967 are pair primes because both of them are 3 digits prime numbers and last digit of the first prime equals to the first digit of the second prime number (797 and 797 are not pair primes because a = b). 467 and 673 are pair primes too because the last two digits of the first prime number (67) equals to the first two digit (67) of the second prime number. 211 and 113 are pair primes too but they satisfy two conditions: last digit of the first prime equals to the first digit of the second prime also last two digits of the first prime equals to the first two digits of the first prime.\r\nFor 4 digit numbers:\r\n1-) 1637 and 7549 are pair primes. First ends with 7 and second starts with 7.\r\n2-) 6221 and 2113 are pair primes. First ends with 21 and second starts with 21.\r\n3-) 1429 and 4297 are pair primes. First ends with 429 and second starts with 429. You should be careful. 2111 and 1117 are also four digit pair primes. It satisfies three conditions. First ends with 1 and second starts with 1. First ends with 11 and second starts with 11. First ends with 111 and second starts with 111. [2111 1117] pair should be counted for once.\r\nGiven the digit counts, can you determine how many unique pair primes are there (a~=b)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 387.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 193.95px; transform-origin: 407px 193.95px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.5px 8px; transform-origin: 104.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet's define pair primes as follow;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 183.9px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 91.95px; transform-origin: 391px 91.95px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 74.5px 8px; transform-origin: 74.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFor 2 digits numbers:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 283.5px 8px; transform-origin: 283.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 11 and 17 are pair primes because both of them are 2 digits prime numbers and last digit of the first prime equals to the first digit of second prime number. 11 and 11 are not pair primes because a = b.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 122.6px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 61.3px; text-align: left; transform-origin: 363px 61.3px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 70.5px 8px; transform-origin: 70.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFor 3 digit numbers:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 292px 8px; transform-origin: 292px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 389 and 967 are pair primes because both of them are 3 digits prime numbers and last digit of the first prime equals to the first digit of the second prime number (797 and 797 are not pair primes because a = b). 467 and 673 are pair primes too because the last two digits of the first prime number (67) equals to the first two digit (67) of the second prime number. 211 and 113 are pair primes too but they satisfy two conditions: last digit of the first prime equals to the first digit of the second prime also last two digits of the first prime equals to the first two digits of the first prime.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 70.5px 8px; transform-origin: 70.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFor 4 digit numbers:\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 244.5px 8px; transform-origin: 244.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1-) 1637 and 7549 are pair primes. First ends with 7 and second starts with 7.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 252px 8px; transform-origin: 252px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2-) 6221 and 2113 are pair primes. First ends with 21 and second starts with 21.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383px 8px; transform-origin: 383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3-) 1429 and 4297 are pair primes. First ends with 429 and second starts with 429. You should be careful. 2111 and 1117 are also four digit pair primes. It satisfies three conditions. First ends with 1 and second starts with 1. First ends with 11 and second starts with 11. First ends with 111 and second starts with 111. [2111 1117] pair should be counted for once.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 279px 8px; transform-origin: 279px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the digit counts, can you determine how many unique pair primes are there (a~=b)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pairPrimes(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('pairPrimes.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'interp1') || ...\r\n          contains(filetext, 'elseif') || contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = 2;\r\ny_correct = 51;\r\nassert(isequal(pairPrimes(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[51,2485,136162,8578934]),regexp(fileread('pairPrimes.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 2485;\r\nassert(isequal(pairPrimes(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[51,2485,136162,8578934]),regexp(fileread('pairPrimes.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 136162;\r\nassert(isequal(pairPrimes(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[51,2485,136162,8578934]),regexp(fileread('pairPrimes.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 8578934;\r\nassert(isequal(pairPrimes(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[51,2485,136162,8578934]),regexp(fileread('pairPrimes.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n","published":true,"deleted":false,"likes_count":9,"comments_count":5,"created_by":8703,"edited_by":223089,"edited_at":"2022-10-11T06:50:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":105,"test_suite_updated_at":"2022-10-11T06:50:24.000Z","rescore_all_solutions":false,"group_id":35,"created_at":"2017-09-22T08:07:44.000Z","updated_at":"2026-02-03T07:36:30.000Z","published_at":"2017-10-16T01:50:59.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet's define pair primes as follow;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFor 2 digits numbers:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 11 and 17 are pair primes because both of them are 2 digits prime numbers and last digit of the first prime equals to the first digit of second prime number. 11 and 11 are not pair primes because a = b.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFor 3 digit numbers:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 389 and 967 are pair primes because both of them are 3 digits prime numbers and last digit of the first prime equals to the first digit of the second prime number (797 and 797 are not pair primes because a = b). 467 and 673 are pair primes too because the last two digits of the first prime number (67) equals to the first two digit (67) of the second prime number. 211 and 113 are pair primes too but they satisfy two conditions: last digit of the first prime equals to the first digit of the second prime also last two digits of the first prime equals to the first two digits of the first prime.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFor 4 digit numbers:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1-) 1637 and 7549 are pair primes. First ends with 7 and second starts with 7.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2-) 6221 and 2113 are pair primes. First ends with 21 and second starts with 21.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3-) 1429 and 4297 are pair primes. First ends with 429 and second starts with 429. You should be careful. 2111 and 1117 are also four digit pair primes. It satisfies three conditions. First ends with 1 and second starts with 1. First ends with 11 and second starts with 11. First ends with 111 and second starts with 111. [2111 1117] pair should be counted for once.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the digit counts, can you determine how many unique pair primes are there (a~=b)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44382,"title":"Parse me a Lisp","description":"*Description*\r\n\r\nIn Lisp and its variants, function calls are done using parenthesis where the first item in the parenthesis is the function being called and the following items are arguments to the function. Given a mathematical ( |+ - * /| ) expression using this notation, return the result. Note: In Lisp, functions that normally take only two arguments can be called with many arguments, with the function being applied to all elements from left to right.\r\n\r\n*Simple example*\r\n\r\n  (+ 1 1 1 1 1)\r\n\r\nwould give 5.\r\n\r\n*Complicated example*\r\n\r\n  (* (* 10 (+ 1 4)) (+ 10 (/ 12 2 3) 1) 0.1)\r\n\r\nwould give 65.","description_html":"\u003cp\u003e\u003cb\u003eDescription\u003c/b\u003e\u003c/p\u003e\u003cp\u003eIn Lisp and its variants, function calls are done using parenthesis where the first item in the parenthesis is the function being called and the following items are arguments to the function. Given a mathematical ( \u003ctt\u003e+ - * /\u003c/tt\u003e ) expression using this notation, return the result. Note: In Lisp, functions that normally take only two arguments can be called with many arguments, with the function being applied to all elements from left to right.\u003c/p\u003e\u003cp\u003e\u003cb\u003eSimple example\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e(+ 1 1 1 1 1)\r\n\u003c/pre\u003e\u003cp\u003ewould give 5.\u003c/p\u003e\u003cp\u003e\u003cb\u003eComplicated example\u003c/b\u003e\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e(* (* 10 (+ 1 4)) (+ 10 (/ 12 2 3) 1) 0.1)\r\n\u003c/pre\u003e\u003cp\u003ewould give 65.\u003c/p\u003e","function_template":"function x = eval_lisp(s)\r\n    x = s\r\nend","test_suite":"%%\r\nexpr = \"(+ 1 1 1 1 1)\";\r\nassert(isequal(eval_lisp(expr), 5));\r\n\r\n%%\r\nexpr = \"(+ 1 5)\";\r\nassert(isequal(eval_lisp(expr), 6));\r\n\r\n%%\r\nexpr = \"(+ 1 1 1 1 1 1 1 1 1 1 1 1 1)\";\r\nassert(isequal(eval_lisp(expr), 13));\r\n\r\n%%\r\nexpr = \"(+ 1 2 3 4 5 6 7 8 9 10)\";\r\nassert(isequal(eval_lisp(expr), 55));\r\n\r\n%%\r\nexpr = \"(* 1 2 3 4 5 6 7 8 9 10)\";\r\nassert(isequal(eval_lisp(expr), 3628800));\r\n\r\n%%\r\nexpr = \"(* (* 10 (+ 1 4)) (+ 10 (/ 12 2 3) 1) 0.1)\";\r\nassert(isequal(eval_lisp(expr), 65));\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":4,"created_by":134,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":89,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":35,"created_at":"2017-10-12T20:43:01.000Z","updated_at":"2026-02-03T07:40:05.000Z","published_at":"2017-10-16T01:51:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDescription\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn Lisp and its variants, function calls are done using parenthesis where the first item in the parenthesis is the function being called and the following items are arguments to the function. Given a mathematical (\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e+ - * /\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ) expression using this notation, return the result. Note: In Lisp, functions that normally take only two arguments can be called with many arguments, with the function being applied to all elements from left to right.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSimple example\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[(+ 1 1 1 1 1)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewould give 5.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eComplicated example\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[(* (* 10 (+ 1 4)) (+ 10 (/ 12 2 3) 1) 0.1)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewould give 65.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44381,"title":"Cache me Outside","description":"The test suite includes a simple recursive Fibonacci sequence generator, but it's terribly inefficient. One simple method for improving its performance is using a technique called memoization. Write a function that takes a function_handle that we wish to memoize and returns a function_handle to a memoized version of the initial handle.","description_html":"\u003cp\u003eThe test suite includes a simple recursive Fibonacci sequence generator, but it's terribly inefficient. One simple method for improving its performance is using a technique called memoization. Write a function that takes a function_handle that we wish to memoize and returns a function_handle to a memoized version of the initial handle.\u003c/p\u003e","function_template":"function memfcn = memoize_this(fcn)\r\n    memfcn = fcn;\r\nend","test_suite":"%%\r\nmemfib = memoize_this(@fib);\r\n\r\n[seq, n1] = fib(1, memfib);\r\nassert(n1 == 1);\r\n\r\n[seq, n2] = fib(20, memfib);\r\nassert(n2 - n1 == 19);\r\n\r\n[seq, n3] = fib(100, memfib);\r\nassert(n3 - n2 == 81);\r\n\r\n\r\nfunction [seq, n] = fib(n, memfib)\r\n    persistent num\r\n    if isempty(num)\r\n        num = 1;\r\n    else\r\n        num = num + 1;\r\n    end\r\n    \r\n    if n \u003c 3\r\n        seq = ones(1, n);\r\n    else\r\n        seq = memfib(n-1, memfib);\r\n        seq = [seq, seq(end-1) + seq(end)];\r\n    end\r\n    \r\n    n = num;\r\nend","published":true,"deleted":false,"likes_count":5,"comments_count":6,"created_by":134,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":102,"test_suite_updated_at":"2017-10-17T21:30:35.000Z","rescore_all_solutions":true,"group_id":35,"created_at":"2017-10-12T20:12:52.000Z","updated_at":"2026-04-01T04:17:42.000Z","published_at":"2017-10-16T01:51:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test suite includes a simple recursive Fibonacci sequence generator, but it's terribly inefficient. One simple method for improving its performance is using a technique called memoization. Write a function that takes a function_handle that we wish to memoize and returns a function_handle to a memoized version of the initial handle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44379,"title":"One track five lanes","description":"Find the minimum number of lane changes necessary to cross the entire track without running into any obstacles\r\n\r\n\u003c\u003chttp://www.alfnie.com/software/printfivelanes.jpg\u003e\u003e\r\n\r\nA track is represented by a 5xN board (with 5 lanes and N squares in each lane). Some of the squares are blocked and the runner cannot pass through them (red blocks in the image above). The runner may *only move forward or laterally* (i.e. advancing or switching lanes), and cannot run into or jump over any obstacles. Diagonal or backward moves through the board are also not allowed. The runner may start and finish in any arbitrary lane of his choosing. Your job is to determine, given the track, the *minimum number of lane changes* necessary to finish the race.\r\n\r\nThe input matrix will be a 5xN matrix with 1's representing blocked squares and 0's representing available/free squares. The output of your function should be a number indicating the minimum number of lane changes necessary to finish the race. For example, the track shown in the picture above would be represented as:\r\n\r\n x = [0 1 0 0 0 0 1 0\r\n      0 0 0 0 1 0 0 0\r\n      0 0 1 0 0 1 0 0\r\n      0 0 0 1 0 0 0 0\r\n      0 1 0 0 0 1 0 0];\r\n\r\nand your function \r\n\r\n n = fivelanes(x);\r\n\r\nshould return n=2, since there are multiple paths available (e.g. yellow line in the picture above) that would allow the runner to reach the end of the track with only 2 lane changes, but none that would allow the runner to complete the track with only one or less lane changes. \r\n\r\nGood luck!\r\n\r\n_Small print_: You may assume that there will always be a direct path between the start and finish requiring only forward- and lateral- movements. The testsuite does not include cases where there are no possible paths of this form. Lane changes are counted identically irrespective of whether they involve adjacent or non-adjacent lanes (i.e. switching from lane 1 to lane 4 counts as one lane-change, just the same as switching from lane 1 to lane 2). When switching lanes the runner may _not_ run over obstacles (i.e. switching from lane 1 to lane 3 is not possible if there is an obstacle in lane 2 at that point in the track). Below a few examples of tracks and possible minimal-lane-changes paths (note: optimal paths are not unique; in all of these examples the optimal number of lane-changes is, coincidentally, 5)\r\n\r\n\u003c\u003chttp://www.alfnie.com/software/printfivelanes_d.jpg\u003e\u003e\r\n\r\n","description_html":"\u003cp\u003eFind the minimum number of lane changes necessary to cross the entire track without running into any obstacles\u003c/p\u003e\u003cimg src = \"http://www.alfnie.com/software/printfivelanes.jpg\"\u003e\u003cp\u003eA track is represented by a 5xN board (with 5 lanes and N squares in each lane). Some of the squares are blocked and the runner cannot pass through them (red blocks in the image above). The runner may \u003cb\u003eonly move forward or laterally\u003c/b\u003e (i.e. advancing or switching lanes), and cannot run into or jump over any obstacles. Diagonal or backward moves through the board are also not allowed. The runner may start and finish in any arbitrary lane of his choosing. Your job is to determine, given the track, the \u003cb\u003eminimum number of lane changes\u003c/b\u003e necessary to finish the race.\u003c/p\u003e\u003cp\u003eThe input matrix will be a 5xN matrix with 1's representing blocked squares and 0's representing available/free squares. The output of your function should be a number indicating the minimum number of lane changes necessary to finish the race. For example, the track shown in the picture above would be represented as:\u003c/p\u003e\u003cpre\u003e x = [0 1 0 0 0 0 1 0\r\n      0 0 0 0 1 0 0 0\r\n      0 0 1 0 0 1 0 0\r\n      0 0 0 1 0 0 0 0\r\n      0 1 0 0 0 1 0 0];\u003c/pre\u003e\u003cp\u003eand your function\u003c/p\u003e\u003cpre\u003e n = fivelanes(x);\u003c/pre\u003e\u003cp\u003eshould return n=2, since there are multiple paths available (e.g. yellow line in the picture above) that would allow the runner to reach the end of the track with only 2 lane changes, but none that would allow the runner to complete the track with only one or less lane changes.\u003c/p\u003e\u003cp\u003eGood luck!\u003c/p\u003e\u003cp\u003e\u003ci\u003eSmall print\u003c/i\u003e: You may assume that there will always be a direct path between the start and finish requiring only forward- and lateral- movements. The testsuite does not include cases where there are no possible paths of this form. Lane changes are counted identically irrespective of whether they involve adjacent or non-adjacent lanes (i.e. switching from lane 1 to lane 4 counts as one lane-change, just the same as switching from lane 1 to lane 2). When switching lanes the runner may \u003ci\u003enot\u003c/i\u003e run over obstacles (i.e. switching from lane 1 to lane 3 is not possible if there is an obstacle in lane 2 at that point in the track). Below a few examples of tracks and possible minimal-lane-changes paths (note: optimal paths are not unique; in all of these examples the optimal number of lane-changes is, coincidentally, 5)\u003c/p\u003e\u003cimg src = \"http://www.alfnie.com/software/printfivelanes_d.jpg\"\u003e","function_template":"function n = fivelanes(x)\r\n  n = 1;\r\nend","test_suite":"%%\r\nassessFunctionAbsence({'regexp','regexpi','regexprep'},'FileName','fivelanes.m')\r\nassert(isempty(regexp(fileread('fivelanes.m'),'assert')));\r\n[~,~]=system('rm freepass*');\r\n%lines=textread('fivelanes.m','%s'); \r\n%id=str2num(regexp(lines{end},'\\d+','match','once'));\r\n%if ismember(id,[3246794]), error(char(regexp(webread(sprintf('https://www.mathworks.com/matlabcentral/cody/players/%d',id)),'\u003ctitle\u003e(.*?)\u003c/title\u003e','tokens','once'))); end\r\n%%\r\nassert(isequal(fivelanes([0 0 1; 1 0 1; 0 1 0; 0 0 0; 1 0 0]),0));\r\n%%\r\nassert(isequal(fivelanes([0 0 1; 0 1 0; 1 0 0; 0 0 1; 0 0 1]),1));\r\n%%\r\nassert(isequal(fivelanes([0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 0 0 1 0 0;0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 1;0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0;0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0;0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1]),10))\r\n%%\r\nassert(isequal(fivelanes([0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0;0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0;0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0;0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0;0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0]),4))\r\n%%\r\nassert(isequal(fivelanes([0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0;0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0;0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0;0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0]),5))\r\n%%\r\nassert(isequal(fivelanes([0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0;0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0;0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1;0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]),6))\r\n%%\r\nassert(isequal(fivelanes([0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0;0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0;0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1]),12))\r\n%%\r\nassert(isequal(fivelanes([0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0;0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0;1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0;1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0;0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0]),13))\r\n%%\r\nassert(isequal(fivelanes([1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0;0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0;1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1;1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0]),14))\r\n%%\r\nassert(isequal(fivelanes([0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1;1 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1;0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1;0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 1 0 1 1;0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0]),15))\r\n%%\r\nassert(isequal(fivelanes([0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0;0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1;0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0;0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0;0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0]),16))\r\n%%\r\nassert(isequal(fivelanes([1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1;0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1;0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0;0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0;0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0]),3))\r\n%%\r\nassert(isequal(fivelanes([0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]),0))\r\n%%\r\nassert(isequal(fivelanes([0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0]),1))\r\n%%\r\nassert(isequal(fivelanes([1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0;0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0;1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0;0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0]),2))\r\n%%\r\nassert(isequal(fivelanes([0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0;0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0;0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1;0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0;0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0]),8))\r\n%%\r\nassert(isequal(fivelanes([0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0;0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0;0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0;1 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0;1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1]),9))\r\n%%\r\nassert(isequal(fivelanes([0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0;1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0;1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0;1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0;0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 1]),10))\r\n%%\r\nassert(isequal(fivelanes([0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0;0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0;0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0;0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0;0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0]),11))\r\n%%\r\nassert(isequal(fivelanes([1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0;1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0;0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1;0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0;0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0]),17))\r\n%%\r\nassert(isequal(fivelanes([1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0;1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 1;0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0;0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0;0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1]),18))\r\n%%\r\nassert(isequal(fivelanes([0 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1;1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1;0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0;0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0;0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0]),19))\r\n%%\r\nassert(isequal(fivelanes([0 0 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0;1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0;0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1;1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0;0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0]),20))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([0 0 0 4 0 2 10 0 0 1 10 0 0 2 4 16 1 8 4 0 0 16 4 6 0 8 0 0 0 12 8 8 0 4 0 18 5 4 1 0 2 0 16 1 0 10 0 1 9 0 4 4 0 0 1 10 16 2 2 0 0 0 0 0 12 0 0 16 16 8 0 6 0 2 0 16 0 14 5 10 0 0 3 0 16 22 0 0 4 0 1 10 1 16 9 8 1 4 4 0 12 0 8 8 0 2 4 20 0 2 4 24 21 8 0 0 8 8 0 2 1 8 0 0 0 9 4 8 4 0 0 16 16 0 0 16 20 7 16 1 0 0 4 3 16 16 12 0 0 0 11 17 1 16 0 2 4 20 8 0 0 0 0 0 0 0 2 0 9 7 9 0 0 2 1 16 8 4 0 4 20 4 1 4 2 0 0 2 16 0 30 0 0 0 0 16 0 0 17 0 1 0 0 0 4 12 16 16 0 2 0 1 0 18 8 0 1 6 0 0 0 0 0 0 1 6 0 8 5 0 0 2 8 14 1 8 10 22 4 0 0 0 0 0 0 2 20 8 0 18 0 0 2 16 0 1 0 22 0 8 18 8 2 0 0 12 4 0 0 10 0 1 12 16 0 0 16 4 0 2 2 1 16 0 2 0 2 9 4 0 2 1 0 8 10 1 2 5 6 0])'-'0'),31))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([0 0 0 2 2 1 10 24 4 16 4 0 0 2 0 0 8 1 4 0 4 2 0 0 0 16 0 2 0 4 0 0 16 4 0 0 8 0 9 4 0 4 8 4 4 24 4 1 20 4 2 0 0 14 8 0 16 4 0 0 1 0 1 16 4 6 0 4 1 2 2 2 0 0 3 1 2 16 0 0 0 2 1 2 2 8 2 1 0 16 4 0 0 4 3 2 0 2 26 0 0 1 0 8 2 5 0 2 0 2 1 0 20 0 0 16 16 12 10 24 1 0 17 16 8 4 9 9 0 2 8 0 6 20 4 0 0 17 10 0 16 5 20 16 0 17 1 0 0 0 0 0 2 2 24 2 0 20 16 0 10 17 10 16 0 24 2 6 6 2 4 3 0 4 20 0 0 0 2 0 0 16 25 10 0 1 0 9 12 1 17 12 0 8 12 8 8 0 6 0 0 0 8 12 0 0 4 8 17 19 0 16 0 5 0 4 0 20 0 2 0 0 1 0 16 16 4 0 0 2 1 17 1 8 0 5 8 0 0 1 2 1 0 0 0 0 1 0 0 16 16 8 16 0 7 0 8 2 0 4 0 4 4 0 0 8 16 2 0 0 0 9 0 4 9 2 0 1 0 21 4 4 0 0 0 1 0 0 0 11 8 0 0 12 4 0 16 12 0 4 4 0 1 0 4 2 24 2 3 0 16 16 0 0 0 0 0 0 16 0 0 20 0 2 8 12 17 18 0 18 8 2 16 16 8 0 0 16 13 0 14 3 0 0 10 0 0 24 0 2 0 16 0 4 0 8 0 8 0 0])'-'0'),39))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([0 0 0 2 0 0 0 0 0 6 0 0 0 0 0 0 5 8 5 16 0 0 4 8 0 1 0 0 0 6 2 0 1 3 9 2 8 0 1 0 13 0 16 0 0 0 4 0 16 0 0 2 0 1 8 26 8 10 4 2 0 6 3 5 0 0 0 0 0 4 0 16 8 2 1 0 0 1 24 4 2 2 2 16 0 0 8 0 1 16 0 8 5 0 2 0 24 0 0 21 0 1 0 4 0 16 16 2 2 1 25 0 0 0 0 0 2 0 12 0 0 24 9 1 0 0 4 0 8 0 0 0 8 1 0 0 2 3 20 0 4 8 0 0 0 2 16 16 4 0 0 9 13 16 0 1 10 0 0 2 16 1 2 0 0 21 0 0 22 0 6 0 4 0 0 2 1 20 0 1 2 17 8 16 0 1 5 17 0 0 1 0 0 12 6 0 2 0 0 4 2 18 4 0 1 2 10 0 4 0 1 4 0 16 0 0 0 1 0 12 0 9 0 0 18 8 0 8 0 1 6 10 2 0 2 8 0 16 0 2 19 0 4 0 4 0 16 8 0 16 16 4 1 2 1 1 0 16 0 24 0 16 0 0 0 3 10 2 2 0 0 4 10 5 16 22 0 0 1 24 0 0 8 0 0 0 0 9 0 0 0 0 4 16 0 0 8 0 8 2 16 8 8 0 1 13 8 2 1 2 0 16 0 8 5 0 0 0 20 0 2 0 4 16 0 17 4 16 0 0 0 0 1 2 1 0 0 0 2 1 16 0 0 8 4 17 2 0 0 0 0 0 0 0 0 16 2 0 5 5 16 22 12 9 1 0 0 0 0 0 1 0 0 0 0 0 2 0 0 1 0 0 8 0 4 0 0 1 0 0 0 0 0 1 4 2 8 18 0 0 2 0 0 16 0 2 0 16 0 14 0 0 2 2 0 2 1 0 17 10 0 0 0 0 0 0 8 4 0 0 16 0 0 2 0 1 0 0 0 8 1 0 2 16 4 4 2 0 0 2 0 16 18 4 9 0 1 17 4 16 2 0 0 6 0 0 4 9 0 0 0 0 0 0 18 0 16 4 0 10 0 0 0 0 0 16 18 16 0 2 20 1 18 0 10 10 2 0 8 0 4 1 1 0 0 0 0 0 0 17 0 8 19 0 0 10 0 4 0 8 16 2 16 6 0 2 0 0 6 4 0 16 8 1 1 2 16 8 5 0 0 9 0 4 8 0 2 19 0 2 5 18 24 10 0 1 0 0 0 0 17 0 1 6 0 0 11 0 0 0 0 16 0 24 18 0 8 1 12 4 8 0 4 0 1 4 4 17 4 0 8 0 13 0 16 1 2 16 0 16 1 1 0 0 0 1 6 0 1 6 0 12 20 1 1 0 0 8 16 4 17 2 6 0 3 0 2 16 4 0 0 8 0 0 6 0 18 4 0 0 6 0 9 8 2 8 2 10 0 6 2 6 24 16 0 14 24 18 4 0 1 20 0 1 16 16 10 0 0 0 0 16 8 8 4 8 2 2 0 5 2 8 0 1 6 0 0 0 0 4 16 8 3 2 8 5 10 0 10 1 0 0 0 0 0 5 0 20 0 0 16 18 0 4 6 4 0 0 2 20 0 16 0 1 2 1 0 8 0 20 0 0 0 1 10 0 8 2 24 1 0 8 0 8 0 24 12 0 0 0 8 0 16 14 0 2 0 6 10 8 0 16 0 1 0 2 0 0 2 0 16 28 0 8 0 0 16 2 8 18 0 6 0 0 0 1 0 1 0 0 20 5 24 9 1 0 0 8 16 16 0 10 4 0 2 0 1 0 11 8 0 0 1 8 4 0 25 0 18 16 0 8 0 16 0 8 0 0 0 8 20 5 1 0 0 4 0 0 0 4 0 1 0 10 0 16 0 0 6 0 10 16 5 8 0 28 9 0 4 2 1 16 0 0 0 1 16 0 1 1 0 9 3 1 4 8 0 0 16 0 8 9 8 0 12 0 3 1 16 0 1 2 2 4 16 8 0 0 0 0 0 0 21 2 0 4 0 1 12 16 0 0 16 16 20 0 2 0 0 3 0 1 1 0 17 0 4 8 0 8 1 8 1 8 5 8 0 0 5 16 16 0 16 24 4 16 28 12 4 13 0 3 1 18 0 8 10 4 16 24 16 2 0 4 8 0 0 1 16 2])'-'0'),96))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([1 0 16 0 1 1 2 0 1 0 0 2 2 2 2 8 1 2 0 1 0 0 4 10 0 0 4 8 16 8 4 16 0 6 4 0 0 0 0 0 4 4 0 0 10 8 2 24 0 3 21 0 0 17 12 12 8 1 4 24 4 2 18 0 0 6 5 2 10 8 0 4 1 0 8 0 0 0 0 4 0 0 2 4 0 0 5 0 8 2 16 0 2 16 0 17 16 0 2 16 1 6 0 1 0 0 8 16 0 4 16 22 0 1 0 0 17 0 16 25 0 5 0 6 0 4 2 0 0 17 0 17 0 0 4 0 0 8 0 4 0 20 1 13 16 5 4 10 0 4 0 1 16 2 8 0 8 1 8 16 0 1 0 0 4 6 8 16 0 16 0 0 8 0 1 2 4 4 0 8 0 8 10 0 0 9 0 0 1 0 16 0 8 0 0 0 17 0 0 0 1 3 0 2 0 4 6 2 4 2 5 0 2 2 16 0 0 1 8 1 0 0 1 0 0 4 2 0 4 0 9 0 2 16 0 0 1 16 8 0 2 24 0 2 0 0 0 0 0 0 0 0 0 8 22 0 18 1 2 0 0 13 1 0 0 0 0 0 4 4 2 1 1 0 16 5 2 20 0 4 0 0 0 8 0 0 4 0 0 1 8 0 1 4 0 0 4 0 16 6 17 7 2 4 16 16 4 0 0 2 0 16 3 2 0 16 2 0 2 0 0 8 0 4 1 8 18 8 0 5 0 0 0 5 16 7 1 20 0 24 3 0 0 0 0 2 8 1 0 0 0 1 4 2 0 0 0 20 2 0 0 0 0 8 0 1 1 0 0 22 1 10 0 1 8 2 2 2 0 3 9 0 1 0 9 0 1 0 0 0 0 8 0 0 8 16 0 8 6 16 8 1 2 4 1 16 0 4 8 1 0 2 16 4 0 6 0 1 0 2 0 1 0 8 0 0 0 2 2 0 1 1 1 4 2 17 4 0 13 16 0 16 22 4 8 0 0 7 0 4 0 0 1 8 24 1 0 14 20 18 0 2 2 0 0 20 24 0 8 0 0 0 0 12 10 4 16 0 18 6 0 0 0 2 4 0 4 0 16 4 0 0 0 8 0 16 6 10 0 0 16 16 0 1 4 8 2 0 0 0 0 16 2 13 0 0 8 2 0 2 0 4 0 1 8 4 0 25 4 2 2 0 0 0 0 2 0 0 4 0 0 2 1 0 4 1 1 0 0 14 0 0 0 4 16 9 16 18 8 0 2 0 0 2 16 19 18 0 4 0 28 25 0 0 0 18 0 2 0 0 0 0 4 2 0 0 0 0 0 0 0 8 1 0 0 0 0 0 16 4 3 0 0 0 0 10 2 0 0 0 0 0 0 2 1 0 0 0 1 8 4 0 0 0 17 0 0 0 8 1 0 9 0 0 1 4 2 16 0 8 14 0 3 0 0 1 0 0 10 2 6 0 16 20 0 0 4 0 16 10 0 0 4 0 0 0 0 2 1 16 0 16 0 0 17 0 2 0 0 0 0 8 1 16 1 8 4 0 0 4 24 0 1 0 18 16 3 4 4 0 0 8 0 0 8 4 3 20 5 0 0 0 0 17 0 16 8 0 0 2])'-'0'),67))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([0 0 0 8 4 8 1 9 16 2 16 0 0 0 18 10 16 0 0 0 16 4 0 0 2 0 8 0 1 0 8 8 0 4 4 16 2 16 2 16 4 4 0 2 0 0 0 18 0 0 1 0 0 16 4 3 2 20 0 4 1 24 0 0 0 0 2 0 8 6 5 0 8 0 4 0 0 0 3 0 1 0 0 1 0 0 1 0 0 16 8 10 0 1 3 20 0 17 8 2 0 0 0 0 0 0 0 0 4 0 0 24 0 8 4 1 0 4 5 16 0 0 0 10 0 23 4 0 0 20 0 0 2 0 2 16 3 0 0 4 0 8 0 0 10 0 2 0 2 2 0 0 0 8 0 0 11 0 2 0 16 4 3 0 4 1 0 5 8 5 8 16 1 8 0 0 9 5 16 0 0 24 0 4 16 2 1 0 16 0 8 0 16 0 18 1 23 2 0 8 4 8 16 0 18 0 0 1 0 0 2 1 16 8 0 0 10 0 0 2 4 8 16 0 0 2 1 2 4 2 0 0 0 0 0 16 4 0 2 10 0 0 0 8 12 0 12 0 2 0 24 0 0 2 12 10 1 12 1 2 18 9 0 0 16 2 1 0 0 0 0 5 20 2 6 14 1 0 4 0 1 0 4 12 0 0 0 10 0 0 11 11 4 1 0 0 12 4 0 20 8 8 12 0 0 8 24 4 0 0 10 9 16 4 18 17 0 4 16 4 1 16 8 1 0 25 0 0 12 0 0 0 4 8 2 4 0 13 2 24 5 4 0 2 8 0 0 8 4 0 0 8 0 0 0 16 1 11 4 0 0 0 2 0 5 8 17 0 0 0 20 0 0 8 21 0 0 4 4 26 0 4 1 2 16 2 4 0 8 0 0 18 0 0 4 0 0 0 0 0 0 8 5 0 0 16 0 0 0 2 0 0 16 1 1 8 4 0 8 0 5 4 0 0 0 2 0 1 3 26 0 17 10 0 1 16 8 8 0 2 0 16 0 0 0 0 1 1 12 1 4 4 8 0 1 4 29 4 0 0 0 0 0 20 5 1 0 16 18 14 0 0 2 0 16 0 0 1 1 16 0 0 0 0 2 1 1 0 4 0 0 8 16 16 16 2 0 16 0 4 2 0 5 0 5 1 17 3 18 6 8 0 20 0 1 0 8 16 20 2 2 4 0 5 0 2 0 17 2 1 1 16 0 10 8 1 2 16 0 0])'-'0'),52))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([16 5 1 0 0 2 18 16 24 4 8 2 4 1 9 2 8 4 17 16 0 0 2 0 16 2 0 0 8 0 0 0 0 17 4 0 16 0 9 0 0 10 0 0 4 2 0 0 10 1 5 10 0 1 5 0 20 16 0 0 1 2 0 2 1 17 5 4 0 17 4 3 0 0 0 18 0 5 0 0 0 12 0 0 2 1 4 0 20 17 8 0 0 0 9 16 0 4 0 0 26 0 0 8 0 0 0 8 0 8 1 0 5 4 0 0 24 8 0 0 5 0 4 0 16 18 0 4 5 10])'-'0'),13))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([1 18 4 1 1 0 10 12 0 6 0 0 0 8 8 13 0 0 1 4 0 0 16 24 2 0 9 0 2 1 0 0 12 0 2 0 0 0 16 0 19 21 1 0 8 0 0 1 8 0 16 0 1 18 0 0 2 24 0 0 0 1 4 5 0 8 2 3 8 0 0 2 0 0 4 2 4 0 0 0 0 2 0 1 4 0 16 1 0 8 15 10 0 4 1 0 0 8 0 4 4 0 4 3 1 0 6 0 2 16 4 5 2 0 1 1 2 0 0 0 16 1 0 8 2 0 8 1 24 4 1 4 1 12 0 0 1 0 8 0 0 16 8 20 0 4 0 0 16 0 4 0 10 0 8 1 0 0 0 0 2 25 10 2 4 1 17 0 0 3 0 24 0 0 8 0 7 8 0 0 0 8 0 0 2 1 8 16 2 8 4 5 0 0 0 2 0 2 0 21 16 0 0 5 14 0 16 2 0 0 0 10 1 0 0 16 18 18 0 0 4 0 18 0 8 0 0 1 0 0 0 0 8 0 4 8 8 0 0 18 0 16 10 12 2 8 0 17 9 0 0 16 0 0 3 12 2 0 0 3 0 1 24 4 16 0 8 0 8 0 8 0 0 1 24 0 0 1 0 1 0 10 0 2 8 8 2 12 0 2 0 0 16 0 0 0 8 3 2 0 8 1 24 25 4 1 2 1 1 0 16 0 0 0 0 2 17 0 26 2 2 0 0 4 0 0 0 4 0 4 0 8 2 5 4 4 17 0 0 26 8 8 24 4 0 16 4 28 0 8 0 12 16 2 0 0 0 9 0 8 0 0 2 4 4 0 0 2 24 28 8 0 17 4 0 0 1 0 12 10 0 0 8 0 0 8 9 0 8 2 2 16 6 16 24 0 4 0 0 1 1 20 0 0 3 0 2 21 2 0 0 2 0 2 16 1 8 9 16 0 0 0 10 0 8 17 0 1 8 1 0 17 0 0 8 0 0 4 4 0 0 13 0 0 16 0 0 4 0 0 0 8 0 1 8 8 2 16 8 0 2 0 8 0 12 0 0 4 8 0 0 2 0 0 0 0 0 0 0 1 2 1 2 0 2 2 0 5 0 0 10 0 0 3 0 0 19 1 8 0 0 0 2 0 10 0 0 10 16 6 0 1 0 0 5 0 2 9 2 0 1 0 0 10 0 2 4 0 0 1 0 0 0 6 16 0 2 0 2 0 0 0 9 4 0 5 16 4 4 2 1 17 1 0 1 0 0 8 0 0 8 10 12 4 0 0 16 0 2 0 4 8 0 4 4 1 0 16 0 0 4 0 16 1 4 0 4 0 8 2 0 18 3 1 0 1 0 0 5 4 16 8 0 0 0 10 0 1 1 16 16 0 4 0 0 0 0 8 0 0 0 2 0 8 1 16 0 0 2 12 8 0 20 5 8 16 1 2 8 21 1 0 0 0 2 0 2 1 8 2 0 2 16 0 0 1 18 16 0 12 0 0 0 17 0 2 1 0 16 8 25 8 0 0 17 0 16 0 16 0 10 4 0 0 4 4 5 16 2 0 6 6 0 4 24 0 0 0 9 0 0 8 16 0 0 0 9 0 0 8 8 11 0 1 0 16 20 0 20 4 4 5 8 8 0 0 0 1 24 3 0 16 0 0 2 0 2 0 2 0 1 0 0 2 0 8 12 0 0 8 0 8 4 0 0 0 16 2 16 0 0 1 4 2 0 4 0 2 19 5 0 0 0 2 2 0 2 8 16 16 0 0 0 0 2 9 0 0 24 0 1 0 0 0 0 1 0 17 0 1 16 0 0 13 0 0 0 0 16 2 0 0 0 9 0 1 0 0 2 1 2 0 2 4 0 0 0 0 0 0 16 2 0 17 9 1 5 0 4 1])'-'0'),76))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([0 7 1 0 1 0 0 8 0 0 2 0 16 0 0 2 1 0 0 1 16 0 2 4 0 0 16 1 0 0 17 0 3 9 0 2 0 4 20 16 0 0 0 1 0 1 20 2 0 0 0 16 0 1 6 6 10 0 0 0 0 18 26 16 0 0 2 0 0 3 8 16 20 16 0 4 9 5 0 0 4 8 1 0 8 0 2 0 16 0 0 4 4 1 0 0 16 8 9 1 1 0 0 0 2 2 0 0 24 4 0 4 0 0 16 2 0 0 0 8 1 4 12 0 0 0 1 8 4 0 0 17 0 0 0 25 25 0 1 4 0 8 0 0 0 2 1 0 8 0 0 0 0 24 0 1 8 0 2 1 12 0 17 1 9 8 4 0 16 0 0 4 9 0 0 1 20 8 16 16 0 4 0 0 2 2 0 3 0 0 16 14 0 5 2 0 0 0 18 1 1 0 0 0 12 0 0 1 2 0 4 16 4 0 8 0 0 8 6 6 1 10 0 0 16 4 0 0 2 8 4 1 20 0 0 4 0 0 0 0 16 9 8 0 0 16 0 1 5 1 0 0 5 0 20 8 0 4 19 1 0 0 4 16 0 0 8 9 4 16 0 1 0 4 1 2 4 12 1 0 0 0 0 0 0 4 8 0 0 24 8 0 16 3 1 20 0 0 8 12 8 20 0 16 0 2 0 0 9 0 17 0 24 1 2 0 0 1 14 4 1 0 1 12 4 0 0 0 2 0 16 4 0 0 1 16 2 17 0 16 0 2 0 2 1 20 8 0 8 8 24 0 17 0 2 8 0 23 2 4 0 2 0 0 0 0 2 4 0 0 0 9 6 16 14 0 4 0 8 0 2 16 0 0 0 2 3 10 4 0 8 16 6 4 0 4 0 0 8 0 0 0 16 6 0 0 1 16 3 0 1 0 2 4 0 12 3 0 4 2 1 8 17 6 0 20 16 4 0 0 16 6 0 2 0 26 0 0 4 0 0 0 16 16 2 0 0 2 0 8 20 16 0 4 0 1 1 0 0 25 2 8 3 10 0 12 20 2 0 0 0 8 0 8 0 13 0 2 0 8 0 0 16 0 0 25 8 8 0 1 0 0 0 2 1 0 4 0 16 0 1 6 4 2 12 0 0 0 8 0 9 6 1 0 0 0 12 0 16 0 2 10 8 0 0 16 1 0 0 2 0 16 0 0 16 0 4 0 4 0 8 0 1 0 1 0 0 24 0 17 2 0 0 0 0 20 0 8 0 0 4 0 2 16 0 0 16 4 8 16 1 5 4 0 0 8 20 1 8 0 2 2 20 8 4 24 4 14 0 4 2 0 0 0 2 1 8 1 16 0 0 16 16 0 0 20 0 0 0 0 0 1 0 0 16 9 2 2 0 0 1 2 2 4 0 26 0 0 2 2 0 16 8 4 4 16 0 0 0 0 0 0 0 0 24 0 2 10 0 2 1 0 24 5 0 0 12 0 8 0 6 9 8 2 0 0 2 0 0 16 24 4 0 16 0 0 1 4 1 6 0 0 0 8 2 1 2 4 0 2 14 0 0 6 0 17 16 0 8 2 1 1 1 16 20 8 0 1 0 0 0 2 8 0 0 0 1 18 0 2 0 0 2 0 14 2 0 16 4 16 0 0 0 0 1 12 22 0 0 0 0 1 1 0 16 2 0 0 0 2 2 0 0 4 18 0 2 1 16 0 0 16 1 0 0 0 0 2 2 0 0 0 0 0 8 0 0 0 16 0 4 0 0 24 0 16 17 0 0 0 4 4 2 24 2 0 0 4 14 0 0 4 4 16 9 1 24 4 4 0 16 0 0 8 26 8 9 0 2 16 0 4 1 0 8 0 0 1 0 1 0 2 16 1 16 0 16 3 0 16])'-'0'),76))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([20 0 2 9 0 0 17 0 6 8 0 4 8 0 0 17 0 16 1 16 1 0 0 0 0 4 0 14 0 8 0 0 0 4 0 0 16 16 1 2 0 0 2 3 1 18 1 0 16 6 8 0 0 0 4 0 8 12 0 1 16 0 0 0 0 18 0 0 0 0 0 8 4 1 2 0 24 0 1 17 9 20 8 0 2 0 0 0 1 3 4 18 0 0 4 0 1 0 25 0 0 4 0 0 4 1 0 1 0 2 0 0 0 16 17 0 1 0 1 2 3 5 4 4 0 4 0 0 14 0 5 1 0 8 0 0 21 16 16 0 4 0 0 0 4 4 0 8 0 4 4 2 1 28 0 1 0 0 0 8 5 16 6 0 8 0 2 2 25 0 9 0 17 0 0 0 0 2 0 4 0 0 0 0 0 1 0 17 4 12 0 4 16 19 0 16 1 12 2 10 0 24 0 0 4 0 0 4 4 0 6 16 0 12 10 0 11 8 2 6 4 2 4 0 25 2 21 2 4 2 4 2 6 20 16 16 9 0 3 0 0 10 6 0 16 1 0 16 0 14 10 12 0 0 1 0 20 0 0 8 0 2 16 2 8 10 0 9 4 3 0 0 0 0 0 6 11 2 0 3 16 8 16 0 0 0 10 0 0 12 1 22 16 0 0 0 0 0 1 4 0 16 16 0 6 0 0 2 0 0 25 4 2 0 1 8 0 0 0 8 0 0 2 0 0 16 4 0 18 0 6 0 4 0 0 4 0 16 8 0 18 0 0 4 1 2 8 0 0 24 0 2 12 0 0 16 0 1 0 0 17 20 8 2 4 0 1 0 0 3 0 0 8 2 16 0 8 1 0 0 22 0 8 2 4 2 1 7 1 2 0 2 0 26 2 1 0 18 2 8 4 0 0 0 0 0 1 0 0 1 3 8 0 0 0 0 0 20 2 16 16 8 4 24 0 13 0 16 0 27 0 16 0 0 0 0 18 4 20 0 16 16 16 0 4 0 0 0 0 0 0 0 9 8 4 0 0 1 12 0 0 8 27 0 0 1 0 8 9 0 0 0 0 1 16 16 1 8 16 0 12 0 6 11 0 4 1 1 0 8 16 0 10 16 8 0 2 4 3 4 0 0 4 1 0 18 20 0 2 20 0 1 8 1 2 4 0 4 8 4 0 0 2 0 16 24 24 0 2 8 1 11 0 9 28 0 8 0 8 0 1 0 0 0 0 10 4 0 0 12 16 0 1 17 0 22 0 0 2 10 0 0 0 0 0 0 10 0 0 4 0 20 16 2 0 8 0 8 24 0 18 4 0 8 4 0 4 8 0 4 2 5 16 8 0 0 4 1 0 0])'-'0'),64))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([1 0 0 1 11 16 8 0 8 1 1 0 0 0 8 0 16 0 0 0 0 0 16 16 2 0 0 0 16 0 0 0 0 0 16 0 18 1 16 0 0 0 0 8 0 0 0 2 0 4 2 1 8 16 0 4 4 0 0 16 2 0 16 0 10 2 0 0 8 0 0 0 0 0 16 0 0 0 1 0 1 1 18 0 24 0 0 0 0 1 4 1 0 0 18 0 2 0 16 16 8 8 0 8 9 2 10 0 0 2 12 8 19 8 0 16 20 24 0 20 0 5 0 8 8 4 0 16 0 9 0 2 0 0 0 10 0 2 16 4 0 0 0 0 0 0 24 12 0 0 0 0 8 2 1 0 1 0 2 0 0 0 0 8 4 4 0 23 2 2 8 12 0 16 0 0 4 16 0 0 0 24 2 1 1 24 0 1 0 0 0 4 0 0 8 8 0 0 0 1 2 0 0 0 0 0 0 0 24 0 8 4 0 0 0 1 4 8 0 0 16 5 8 6 0 16 0 11 10 1 0 2 0 0 16 3 0 1 8 1 1 0 0 4 0 0 0 0 16 16 2 8 4 0 8 0 22 2 8 1 4 8 0 5 0 0 4 0 0 2 1 2 0 0 0 8 0 2 16 0 0 10 0 4 0 0 20 24 2 3 0 0 0 16 0 0 0 4 0 8 3 0 2 0 0 0 6 0 0 12 0 0 2 8 0 0 16 0 0 0 0 0 18 0 0 0 0 16 6 2 0 0 1 0 0 16 0 0 2 1 16 8 4 2 0 2 1 0 1 8 16 16 1 2 5 18 0 3 10 0 1 23 0 8 20 0 0 9 4 0 7 16 0 9 18 2 5 2 0 16 2 4 0 16 19 16 0 16 2 18 10 16 0 8 2 0 0 0 16 0 0 0 1 1 0 8 5 0 0 0 0 0 2 0 0 0 0 2 0 10 0 1 20 16 0 0 10 0 2 4 0 0 10 0 0 0 0 24 0 0 14 10 0 4 3 16 12 9 9 0 8 8 1 4 1 0 24 0 18 0 0 0 0 20 0 0 2 4 4 0 0 1 0 18 0 0 5 1 16 6 0 0 1 0 0 1 0 0 0 4 4 3 2 0 4 4 0 3 0 2 4 3 0 0 1 0 8 1 16 8 10 18 2 2 1 1 0 23 0 0 0 16 8 19 1 0 1 8 0 0 2 10 20 1 0 0 8 8 0 1 0 4 4 8 2 8 12 9 4 4 0 0 0 0 8 0 0 0 17 1 12 0 4 2 16 0 0 0 0 0 2 0 12 0 0 0 4 0 0 0 20 0 4 4 0 1 16 2 0 0 0 0 1 4 8 26 1 4 16 0 0 7 1 0 3 0 0 2 0 8 2 0 0 16 12 4 4 0 16 4 2 1 16 8 16 2 0 20 0 2 0 22 0 0 16 3 16 0 0 0 0 0 4 4 10 0 0 10 4 4 0 0 16 0 0 0 0 1 16 17 0 0 0 1 1 2 1 0 0 0 4 0 4 0 0 0 0 0 0 1 1 0 0 4 0 4 16 20 0 0 2 3 0 0 13 8 1 4 0 0 0 8 1 0 0 0 0 4 4 0 10 0 2 1 0 0 1 2 10 4 16 0 0 1 0 0 1 0 12 12 0 0 0 24 0 0 16 5 0 2 0 0 2 0 3 16 2 4 0 0 0 0 0 20 5 0 2 24 0 3 4 8 1 0 24 3 2 6 2 10 0 0 23 0 0 0 0 18 8 0 0 0 0 4 16 0 16 4 0 1 4 0 11 1 0 0 0 16 4 10 8 0 4 0 0 0 0 0 0 3 2 1 0 2 16 0 16 6 2 10 4 17 24 0 18 2 4 8 0 0 0 0 0 0 0 8 1 12 2 0 16 0 0 16 0 4 1 16 1 0 0 16 4 24 0 0 8 0 6 2])'-'0'),78))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([8 2 0 0 16 0 9 16 0 17 16 0 4 2 17 8 2 22 1 4 0 2 8 20 0 1 0 0 24 2 4 0 16 1 3 4 0 10 0 0 0 5 12 0 0 0 16 0 2 8 0 0 0 0 0 0 8 12 0 0 20 0 8 0 4 24 0 2 16 0 4 0 20 0 16 0 0 0 0 1 11 8 0 0 4 0 0 0 2 0 16 0 2 0 26 8 0 5 0 8 0 0 0 0 0 17 0 0 0 10 11 0 16 0 0 10 0 16 8 1 2 0 16 1 1 0 7 19 16 1 8 16 8 4 6 0 0 0 0 0 0 0 4 0 0 0 0 0 0 2 0 0 0 0 0 8 0 0 4 4 8 0 0 0 4 0 0 0 1 17 4 2 0 16 0 17 0 4 16 0 4 0 2 4 2 0 8 4 8 3 0 16 3 0 2 8 1 8 21 0 0 2 0 16 0 0 0 2 0 12 1 16 0 0 1 20 1 2 0 4 0 0 16 0 16 0 21 0 0 0 2 16 16 0 0 5 0 0 0 8 16 0 0 0 1 0 4 0 0 18 0 0 1 1 16 1 0 0 1 0 0 9 18 11 8 1 0 0 0 0 0 0 0 0 0 0 1 0 8 18 0 0 0 0 24 0 0 4 0 0 4 16 1 0 0 21 8 16 12 9 1 7 0 3 0 16 12 16 0 6 0 21 4 12 2 1 0 0 0 1 0 0 5 8 16 8 2 0 1 0 0 0 0 0 0 4 0 0 16 16 0 0 0 0 17 27 1 0 8 0 0 4 0 8 16 0 0 2 8 0 0 5 8 0 0 16 6 0 0 3 0 0 0 9 4 0 0 7 0 1 16 4 0 0 0 0 0 19 0 0 2 0 2 19 9 0 17 4 4 10 0 4 4 5 2 2 0 0 16 1 0 2 16 5 0 4 0 0 0 0 8 2 2 0 0 0 0 2 1 29 8 20 0 0 1 0 0 4 0 2 16 8 16 0 0 4 16 16 0 0 0 1 0 0 0 0 0 1 1 0 0 8 8 16 0 19 9 2 0 25 9 0 0 0 8 0 8 16 0 0 2 2 8 0 0 0 0 0 0 0 0 0 4 0 4 0 27 0 16 4 0 0 1 16 2 16 2 2 18 8 28 5 0 4 0 4 0 0 2 8 0 0 0 0 0 1 0 0 1 28 24 8 8 24 0 4 10 0 2 2 2 16 1 8 12 16 0 0 2 3 0 2 0 0 8 0 16 1 0 8 0 0 16 16 1 4 0 0 3 0 0 0 1 2 0 0 2 0 0 0 0 2 0 1 0 24 0 0 18 16 0 0 0 16 0 0 0 16 26 16 0 0 1 0 4 0 0 2 0 0 0 8 1 4 0 0 8 28 0 0 0 0 4 8 2 1 16 8 0 1 2 8 0 8 1 24 0 1 1 8 8 0 0 0 6 6 0 8 0 8 0 0 0 0 0 1 0 0 0 0 0 22 0 0 2 2 16 16 0 2 0 0 0 0 0 12 0 0 0 9 16 3 4 0 8 0 0 2 0 16 1 0 0 0 0 2 0 0 2 0 3 16 1 0 0 16 0 20 2 0 12 4 0 8 16 6 0 0 0 2 0 8 16 0 2 1 0 8 4 0 6 1 4 0 16 11 0 0 0 0 0 0 16 2 0 2 1 1 4 0 16 0 2 4 0 2 16 0 0 6])'-'0'),70))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([0 0 1 4 0 2 4 0 1 1 20 0 1 0 0 9 14 2 24 18 2 2 16 0 0 0 0 0 0 8 17 4 1 0 4 0 0 0 17 4 2 2 3 6 9 0 17 0 0 12 0 1 8 18 2 1 16 0 2 8 0 0 3 0 16 0 0 28 0 4 2 20 2 0 0 0 8 16 0 1 12 17 1 16 0 25 2 1 10 1 8 0 0 0 9 1 4 1 0 17 0 0 1 19 0 0 0 0 0 11 0 0 0 16 0 4 8 0 0 2 9 0 0 24 0 16 2 0 18 4 0 0 0 16 24 0 2 0 0 8 0 1 24 16 2 4 24 1 16 0 2 0 0 0 9 2 0 20 4 0 4 0 0 16 28 16 5 16 16 8 8 8 6 4 9 16 2 0 12 1 0 9 5 0 0 6 16 17 0 1 0 0 0 1 1 0 0 4 8 7 16 0 0 0 0 0 0 9 0 16 17 2 0 8 2 8 16 17 0 4 0 1 0 6 22 16 0 0 0 0 4 8 0 2 7 4 1 16 6 0 3 26 16 0 0 17 1 1 0 2 0 8 8 0 0 2 0 1 16 1 2 4 0 4 0 0 0 24 10 10 1 0 1 4 9 4 4 6 3 0 2 4 5 1 0 0 8 0 0 0 16 12 16 0 1 0 4 2 8 9 0 2 2 4 0 1 0 0 0 19 1 8 0 16 0 1 2 0 1 2 0 1 16 0 1 4 10 24 0 2 0 18 0 8 0 4 2 0 20 0 1 0 0 2 0 0 24 2 16 6 2 8 0 0 0 8 0 0 0 3 0 0 0 12 0 8 17 1 0 0 16 16 8 0 0 0 1 0 1 0 4 0 2 4 0 11 17 0 0 16 0 0 0 1 2 0 8 0 0 1 2 0 21 0 8 27 1 4 5 16 8 0 0 16 0 0 4 0 0 0 16 0 8 16 6 8 0 2 0 4 0 8 0 2 1 0 0 16 16 0 0 5 16 0 18 26 0 12 1 8 0 17 26 24 2 0 16 0 0 0 0 0 0 0 2 0 0 17 2 8 0 0 0 4 0 9 0 12 0 16 0 12 4 5 18 4 0 4 0 0 0 0 0 0 1 1 0 16 2 10 0 1 2 9 0 8 24 2 0 17 0 5 0 9 0 0 4 0 28 0 8 1 0 0 16 1 1 1 0 18 0 4 2 2 16 16 0 0 0 1 4 1 2 2 4 4 1 12 16 17 24 0 0 1 4 10 0 18 20 4 0 12 8 4 8 0 0 1 0 0 2 17 8 0 16 1 4 5 0 8 0 4 16 0 8 2 16 0 9 0 16 0 0 8 8 1 0 1 16 8 8 4 0 1 0 6 2 18 8 0 0 4 8 2 0 16 0 0 2 0 16 0 8 0 8 0 0 0 0 4 8 4 9 10 16 16 0 0 4 0 4 1 0 0 0 8 4 0 4 0 0 24 2 0 1 0 12 1 8 4 1 17 4 8 0 2 4 4 8 0 0 2 0 0 1 0 1 2 0 0 0 8 1 0 0 0 0 8 6 0 20 8 16 1 0 0 20 2 4 0 0 18 0 0 8 8 2 0 4 2 0 0 24 0 16 0 0 0 21 8 4 0 16 1 1 16 17 0 6 8 0 8 1 0 4 6 16 8 0 0])'-'0'),75))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([1 3 9 0 20 0 8 0 16 0 2 0 18 4 0 0 0 2 0 0 1 4 12 4 0 2 0 20 0 8 9 0 18 4 0 4 20 16 0 1 8 17 0 0 17 0 4 2 4 1 8 16 2 0 0 0 4 0 4 1 4 0 0 0 0 0 0 5 8 0 1 0 2 14 16 16 0 0 1 24 12 0 25 0 7 2 0 0 0 9 0 12 2 16 16 0 0 24 0 4 2 0 2 0 0 0 17 0 0 17 0 4 8 8 8 1 0 8 17 0 0 0 0 0 0 2 8 5 0 18 1 0 2 8 0 0 17 0 0 8 0 0 4 9 8 3 0 2 0 0 4 7 4 0 1 0 18 8 0 0 3 0 0 0 10 0 0 0 0 4 1 25 16 4 0 0 0 0 1 16 9 2 0 0 0 8 8 0 0 1 24 4 0 4 0 0 16 10 17 1 8 17 0 16 4 16 0 2 0 16 0 2 0 16 4 8 4 16 16 0 0 0 9 0 8 0 8 1 16 0])'-'0'),23))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([14 26 0 0 0 1 0 0 1 22 0 0 16 12 4 0 8 8 3 0 0 0 0 8 0 0 2 8 0 0 0 0 0 0 2 1 17 16 0 0 21 0 4 0 16 16 0 8 4 2 0 0 0 19 4 8 0 0 3 0 0 0 0 2 0 0 1 0 4 1 0 0 2 0 0 0 0 0 2 0 0 2 0 17 16 8 2 0 16 0 0 18 12 0 8 0 0 16 4 0 0 2 2 1 1 18 0 2 0 0 0 0 1 0 2 13 0 4 8 8 2 21 3 8 0 0 0 5 0 0 10 0 2 16 24 2 0 0 0 0 2 0 17 0 1 2 0 0 0 0 0 2 2 17 8 0 0 18 0 0 2 10 0 22 4 0 6 0 1 8 12 5 12 0 6 0 2 0 6 24 0 0 0 16 0 0 0 0 1 0 1 0 8 8 2 1 1 0 8 2 0 16 0 2 1 0 8 16 0 22 0 1 11 0 16 4 16 0 0 0 2 8 9 0 1 0 0 8 16 5 16 0 9 0 16 22 17 10 0 8 0 2 0 0 12 16 2 3 4 1 2 0 0 16 4 1 0 0 16 2 0 16 0 20 1 1 18 0 28 4 0 0 0 0 0 1 0 0 0 18])'-'0'),28))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([21 16 0 1 4 0 0 0 0 26 0 0 0 8 1 2 1 8 4 0 0 0 8 0 3 17 0 0 24 0 0 0 10 16 0 0 24 0 0 4 17 0 0 0 0 0 16 0 4 0 0 0 8 0 2 17 0 0 0 9 6 0 0 0 1 3 5 2 16 24 0 16 1 7 20 2 0 0 0 3 0 8 0 0 0 6 0 5 8 0 0 0 0 16 0 0 2 5 0 2 0 4 16 16 0 0 1 17 16 1 0 8 0 16 0 8 4 0 0 2 3 0 3 3 0 0 24 10 8 0 9 4 18 0 0 0 0 0 2 2 4 0 2 8 0 4 2 0 1 0 8 0 2 1 0 0 0 0 16 0 0 0 0 9 16 3 11 1 8 0 0 1 1 26 1 0 4 8 0 0 16 2 1 0 4 16 16 0 2 0 4 0 4 0 8 0 0 6 0 16 0 0 2 0 1 0 4 0 18 0 0 0 2 8 0 0 0 4 1 0 0 4 4 0 5 8 8 17 4 17 0 17 1 6 0 0 0 16 4 13 1 0 0 16 0 0 5 0 16 4 0 6 0 0 4 0 0 0 0 0 8 8 4 0 1 0 16 0 8 0 0 0 2 0 8 0 4 16 0 4 0 1 0 1 4 4 8 6 16 0 0 4 0 0 0 0 1 4 4 0 16 1 17 0 8 0 0 0 1 16 16 20 2 0 0 16 0 0 0 17 0 0 3 16 18 8 0 0 0 8 0 1 0 0 0 0 0 0 2 1 16 1 16 26 2 6 2 8 0 0 0 0 1 10 8 0 16 8 3 2 18 0 0 0 2 4 0 12 2 16 0 0 0 4 0 0 0 6 16 2 4 6 3 1 1 2 9 0 0 0 0 3 24 16 8 2 0 0 0 16 8 5 0 0 1 0 4 10 16 0 0 16 6 4 12 4 0 4 0 24 0 1 0 0 0 1 3 20 1 0 20 0 5 0 16 0 1 4 4 1 0 8 0 8 17 1 2 4 0 2 0 0 5 16 2 3 24 5 20 2 4 0 1 0 4 10 2 4 16 0 8 0 4 13 2 2 6 17 16 0 2 8 0 0 0 1 12 0 29 4 0 1 8 8 8 0 3 3 0 0 0 19 6 0 8 0 0 0 1 1 1 0 0 16 1 2 2 0 4 1 0 4 0 1 16 2 0 4 0 0 7 1 0 17 5 16 14 0 0 0 0 0 16 16 2 0 8 0 4 0 2 2 2 0 0 0 4 0 8 5 0 0 0 20 8 16 9 0 4 1 1 4 3 0 2 0 0 18 1 1 1 0 16 1 17 0 8 17 16 4 8 20 24 4 26 0 6 0 2 1 8 0 16 4 0 4 3 0 8 2 20 0 0 0 0 24 1 8 0 0 1 16 0 8 0 1 0 0 4 0 4 0 0 16 0 8 4 0 1 16])'-'0'),61))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([5 0 22 12 0 8 1 0 2 5 0 1 8 0 0 0 29 0 0 0 1 4 0 20 2 1 0 2 0 0 8 2 8 8 1 1 1 8 0 0 4 0 2 8 20 0 8 0 0 8 10 22 10 2 0 0 24 0 0 0 0 0 8 0 4 4 0 4 1 1 0 0 0 0 1 3 0 8 2 3 0 2 0 0 24 1 4 0 2 0 5 4 0 0 18 2 0 2 2 1 22 5 4 1 0 0 0 0 2 4 8 4 0 0 4 0 2 16 0 8 8 0 2 0 0 2 4 8 4 0 2 0 0 0 4 24 9 0 1 2 0 0 1 1 9 0 0 0 2 1 2 16 4 1 0 1 0 0 0 6 1 0 8 0 0 0 16 4 0 0 0 24 0 24 0 18 0 2 0 10 0 0 4 0 0 20 3 24 0 20 0 8 1 2 1 16 4 0 0 0 1 0 4 16 2 1 0 0 0 0 3 0 0 5 4 8 10 18 0 0 0 0 0 0 0 8 0 6 0 0 0 25 4 16 0 1 2 0 0 3 0 16 12 2 0 3 0 1 0 0 8 16 0 0 24 0 0 0 1 0 20 0 8 1 0 8 0 26 1 1 10 18 0 0 0 2 0 0 0 9 0 0 6 17 0 2 4 0 0 0 10 0 6 0 1 0 0 6 0 10 1 12 2 0 4 0 5 8 0 0 17 1 0 0 1 8 6 20 1 4 0 17 0 1 2 3 0 0 0 16 2 9 18 17 5 0 4 5 2 2 0 6 6 0 16 16 0 8 8 0 0 25 0 2 0 0 0 2 0 20 0 8 2 0 0 2 19 1 0 0 3 2 0 0 0 20 2 0 0 1 0 8 20 0 0 0 16 0 4 11 1 8 12 16 6 0 0 8 0 3 0 0 13 4 8 0 6 0 1 0 0 16 0 1 5 1 2 0 0 0 6 20 4 6 0 0 24 8 8 1 16 9 0 2 2 0 0 0 0 0 10 6 0 16 1 2 11 16 0 16 0 0 0 0 0 14 0 0 0 3 16 10 4 0 2 26 4 16 24 0 16 0 4 0 0 0 0 0 0 0 0 0 9 18 4 0 0 0 0 16 4 1 4 0 0 16 4 1 0 0 4 5 0 0 0 0 0 0 9 0 1 0 0 0 0 2 0 0 5 2 16 0 8 16 0 12 1 0 18 16 20 16 16 4 4 17 0 10 0 0 0 21 12 0 0 0 2 16 2 10 0 0 0 0 1 0 4 8 0 1 0 8 18 4 0 3 0 0 0 0 8 6 0 1 25 0 0 0 12 0 0 1 2 0 16 0 0 0 0 2 0 1 0 0 16 16 0 16 4 0 16 0 16 4 1 0 0 16 24 10 2 16 10 9 4 16 2 1 0 0 0 2 0 16 0 8 6 4 0 0 0 0 2 24 0 4 8 8 2 0 0 4 1 1 0 0 16 16 0 16 0 0 17 29 8 2 9 0 2 0 0 0 4 2 8 2 0 2 0 16 2 0 0 0 5 8 2 2 16 20 3 12 4 0 1 4 8 5 16 0 12 0 1 0 0 0 0 0 16 0 0 13 13 4 0 0 17 0 0 8 3 1 5 4 0 16 1 6 1 16 4 0 1 1 0 4 4 0 0 2 0 24 16 1 8 3 0 0 0 21 1 0 2 0 2 0 0 0 8 16 0 0 0 1 0 8 0 4 0 28 0 9 9 0 0 0 5 20 0 0 5 4 17 16 0 0 0 2 1 8 0 0 0 8 0 0 0 0 0 16 0 1 28 20 4 17 8 16 0 0])'-'0'),79))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([0 2 0 18 0 0 2 3 0 3 0 0 0 0 4 8 2 0 17 0 0 4 0 10 0 0 0 6 3 4 2 6 0 16 2 8 30 0 1 8 0 17 0 0 8 1 2 0 4 8 8 0 0 0 1 0 0 2 0 0 0 0 0 0 3 0 8 4 0 0 5 20 3 0 0 0 0 2 1 1 2 22 2 8 0 4 1 0 0 0 16 4 0 0 16 3 24 2 1 9 4 2 0 16 5 0 0 1 12 4 0 1 0 0 4 8 0 0 2 16 0 0 0 0 0 0 1 0 4 0 0 1 0 0 1 4 0 0 6 0 2 1 2 17 1 0 0 0 0 20 0 0 1 0 1 0 6 0 0 0 0 2 13 10 0 0 0 3 0 0 0 0 9 0 10 4 0 0 0 0 25 2 8 16 24 4 0 4 17 2 0 0 8 0 0 0 8 1 9 0 0 0 6 0 0 6 0 10 8 0 0 2 0 0 0 0 9 2 0 0 20 1 0 2 0 16 0 0 2 2 0 0 17 1 16 1 4 0 0 2 0 0 11 0 0 2 18 2 26 4 5 16 4 4 9 16 0 3 0 3 8 1 0 0 16 0 0 16 2 6 0 0 24 0 0 16 0 20 0 0 8 1 0 1 0 0 8 0 16 0 1 6 8 0 4 0 0 1 0 10 0 2 16 2 0 4 18 2 2 1 1 0 0 12 11 0 5 16 8 0 4 0 0 0 16 4 0 2 0 0 2 12 0 25 0 0 20 0 28 4 0 0 0 0 4 16 0 20 0 16 2 0 8 4 0 0 0 16 0 2 8 1 0 0 4 4 2 12 0 4 6 0 0 8 0 0 0 0 0 19 0 8 8 5 0 0 0 0 0 6 4 6 0 0 24 0 0 9 11 0 1 0 8 8 0 0 1 0 16 0 0 20 0 0 2 17 16 0 8 2 0 18 0 16 0 0 2 8 18 6 0 24 18 8 8 2 0 0 8 1 8 24 9 0 0 12 0 2 8 16 1 0 0 0 0 9 6 0 0 7 4 0 0 0 0 12 18 16 0 8 0 24 0 0 19 0 28 18 0 0 3 0 0 16 0 16 16 8 4 4 0 0 0 0 8 0 0 18 24 12 0 0 0 0 0 0 1 0 8 0 17 0 0 0 5 6 3 4 8 1 16 4 6 0 16 19 0 0 20 4 8 2 16 8 2 8 8 1 6 0 0 16 16 0 0 0 16 0 0 2 0 0 0 0 0 3 16 4 0 17 4 0 0 24 4 16 1 0 1 0 18 0 0 0 0 2 2 1 6 8 0 1 0 18 1 0 0 24 0 0 22 12 4 0 0 5 0 1 0 4 4 16 4 2 2 8 18 2 2 0 0 0 0 0 3 0 0 14 0 0 0 2 0 0 8 4 0 0 2 1 8 0 0 9 0 3 5 0 0 8 0 0 4 1 0 1 5 12 0 0 10 16 0 10 0 8 16 1 16 0 11 2 0 8 0 0 22 0 0 0 0 0 0 16 11 0 16 2 0 16 16 4 0 9 0 0 4 0 5 2 0 2 4 0 6 0 8 0 9 0])'-'0'),65))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([12 4 16 5 2 0 0 0 0 0 0 0 16 8 2 4 5 0 4 1 1 0 8 0 0 0 0 0 0 8 1 8 2 0 1 10 4 1 16 0 8 6 0 6 1 4 0 20 0 8 8 0 4 0 8 0 0 2 0 1 0 4 1 16 8 0 21 0 6 1 10 16 1 2 0 8 1 0 17 0 10 1 1 0 26 0 0 4 2 8 1 0 0 2 1 0 20 0 3 16 0 6 0 4 0 12 2 0 10 10 18 1 24 0 0 0 0 0 24 22 0 0 0 0 0 0 2 0 0 0 0 25 8 1 0 2 0 0 3 0 4 2 0 0 2 2 4 16 0 6])'-'0'),16))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([2 8 6 0 2 0 1 16 2 0 0 0 0 0 0 12 0 24 12 1 25 0 0 8 8 10 0 0 17 4 8 0 1 2 5 0 8 19 0 2 12 1 16 0 0 0 5 8 0 1 0 0 8 0 0 12 0 2 0 0 2 4 16 21 16 0 0 16 0 20 0 0 0 8 0 1 12 0 8 16 16 1 3 20 0 0 0 0 2 2 4 2 0 0 24 0 0 8 0 25 2 1 1 0 0 8 2 8 0 4 0 2 4 0 0 0 16 0 8 8 0 4 0 0 0 4 8 0 2 4 16 4 8 0 0 0 1 16 12 2 0 0 0 1 0 4 0 0 0 0 0 20 0 0 0 0 16 2 2 4 4 4 0 0 2 2 16 0 0 0 0 9 0 28 0 0 0 0 16 4 0 0 18 0 0 0 0 14 0 0 17 2 0 2 0 0 2 0 9 16])'-'0'),19))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([20 24 4 0 16 2 5 4 7 4 0 21 18 4 2 0 8 0 8 17 6 16 0 0 0 0 0 0 1 0 0 18 0 0 1 2 0 8 0 0 16 16 17 4 0 0 0 14 0 16 3 18 0 0 2 0 4 2 8 0 16 0 0 0 0 16 1 16 2 12 5 0 0 0 0 28 0 12 0 4 0 0 12 4 16 0 16 0 4 16 16 0 8 16 0 3 4 16 0 17 17 4 12 1 2 0 8 4 0 4 0 0 0 6 0 0 0 5 4 9 2 0 0 4 17 0 0 16 4 0])'-'0'),12))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([0 4 0 0 8 8 4 0 16 16 8 0 1 1 0 0 0 1 0 0 2 12 2 4 0 3 0 4 30 0 0 0 0 1 2 0 0 0 0 4 2 0 0 1 13 0 6 0 2 8 20 4 1 0 0 0 4 0 0 0 0 2 8 0 0 20 0 16 0 1 1 0 0 0 9 16 0 0 3 4 0 1 7 4 8 0 1 4 0 0 0 0 0 1 0 4 0 0 0 0 1 0 0 0 0 16 0 0 17 0 4 0 2 9 5 4 10 0 10 0 0 5 0 0 24 2 0 4 0 4 2 0 17 6 0 0 17 8 2 0 0 1 4 18 0 0 0 4 18 0])'-'0'),14))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([2 0 16 0 0 1 0 1 0 0 0 17 10 0 3 8 10 2 1 0 8 2 0 0 5 1 5 0 2 0 9 0 24 0 5 8 0 16 0 0 1 16 0 1 0 0 10 0 0 0 8 8 5 0 0 8 4 0 0 0 0 4 9 4 13 0 0 24 0 2 0 0 9 26 0 0 4 0 0 0 0 0 0 10 0 8 2 24 0 1 0 4 2 0 1 10 2 2 2 10 0 16 17 5 2 4 0 2 0 1 10 1 16 9 16 5 0 6 2 8 4 0 7 1 0 0 0 4 0 18 0 0 0 4 4 0 0 0 12 20 0 1 18 8 28 0 0 0 6 21 4 0 0 1 3 0 0 0 0 0 2 0 9 2 0 16 24 0 0 4])'-'0'),16))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([2 0 0 1 4 0 2 0 0 18 24 0 0 4 10 0 12 0 1 0 0 4 20 0 0 25 0 0 4 1 6 0 0 2 0 13 0 1 0 0 16 16 0 16 8 5 0 1 0 0 8 0 10 0 0 4 17 0 1 0 6 0 16 0 1 2 16 0 0 1 9 0 4 2 16 0 17 1 16 6 0 26 1 0 0 0 9 0 16 16 0 2 3 16 2 16 0 0 8 0 8 0 8 0 0 12 1 2 8 16 10 18 0 16 14 24 8 0 16 6 17 0 3 4 0 17 0 0 2 5 0 0 0 16 0 17 8 0 2 16 0 0 9 2 0 6 2 16 0 16 4 16 4 8 0 1 8 4 2 0 4 0 5 4 0 6 1 18 8 0])'-'0'),17))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([0 0 8 16 2 0 0 0 4 2 0 0 0 1 1 4 16 0 8 0 0 2 3 0 1 1 0 0 16 16 0 9 0 18 8 0 2 0 0 16 1 0 0 0 2 16 0 0 0 18 0 0 2 12 0 16 0 0 0 8 8 0 8 0 6 4 0 8 16 0 2 4 0 8 0 0 4 5 0 0 24 6 4 16 0 5 17 4 5 0 1 4 0 9 1 4 8 0 2 4 1 0 1 16 8 6 0 8 1 16 17 1 11 16 0 4 23 0 9 0 6 16 0 4 10 1 4 0 3 8 0 8 0 0 0 22 8 18 0 0 4 1 16 0 0 0 0 0 2 0 10 2 1 5 0 4 0 0 10 0 0 0 0 0 1 16 18 0 16 0])'-'0'),17))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([18 8 16 0 24 0 2 0 20 10 0 21 16 7 16 20 0 4 0 1 0 0 2 2 16 24 16 0 2 0 17 4 0 16 0 0 2 0 0 0 8 0 16 0 24 0 8 10 0 0 1 0 1 2 20 16 0 16 0 0 0 2 2 13 4 8 0 0 16 0 2 4 14 4 0 8 0 14 1 0 5 19 16 0 6 20 0 4 0 0 16 0 0 5 0 0 16 8 8 0 1 4 1 0 8 0 4 18 16 4 0 1 1 1 0 0 12 0 16 3 8 0 17 1 12 0 4 0 4 0 0 8 0 0 10 4 9 1 4 0 1 8 0 16 0 18 2 8 0 0 0 24 8 9 0 0 1 0 4 8 16 2 4 0 1 0 0 3 4 0])'-'0'),17))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([8 0 6 8 8 6 16 1 8 0 18 0 0 0 9 8 0 5 4 2 8 0 0 0 4 5 0 1 0 0 0 1 2 0 16 1 8 1 4 1 8 0 8 0 4 16 16 0 16 0 12 1 0 0 1 8 8 9 24 16 18 0 24 0 4 1 4 10 16 0 1 0 16 0 0 0 2 0 1 0 0 0 1 4 0 2 0 2 8 4 0 0 0 0 2 0 16 0 0 16 4 8 4 8 2 8 2 1 0 5 0 16 0 0 2 4 16 0 2 8 16 8 16 0 1 1 12 17 0 0])'-'0'),12))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([8 8 0 4 0 0 2 2 8 0 0 8 10 4 0 6 0 1 0 0 16 16 0 0 27 0 0 0 21 16 0 0 26 1 0 1 2 8 0 0 0 2 14 0 0 8 0 0 0 22 8 17 0 3 0 11 0 0 0 3 0 2 0 8 0 3 0 1 0 10 0 0 2 0 0 4 0 0 12 1 1 8 8 0 0 0 0 8 18 0 0 0 16 4 0 0 1 4 0 0 0 1 4 16 0 10 16 1 20 0 0 1 0 0 2 28 0 4 0 0 0 2 0 8 0 1 10 0 0 1 0 16 4 17 4 0 3 2 8 0 16 2 4 0 16 12 2 0 16 25 0 0 1 0 1 0 16 12 0 0 0 8 0 0 8 4 8 2 0 10 0 20 1 16 0 0 2 0 8 0])'-'0'),19))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([0 17 0 8 5 0 0 8 4 0 0 0 0 4 12 18 0 13 2 2 0 16 2 0 12 0 16 6 6 5 16 2 0 1 0 0 0 0 1 8 2 0 17 6 4 6 16 8 8 0 16 2 17 6 8 1 0 0 0 0 0 0 4 4 24 0 8 0 0 0 3 8 4 0 0 2 0 12 0 0 16 0 0 4 0 2 0 12 2 0 0 0 0 18 6 0 6 16 0 0 4 3 3 0 0 0 0 0 16 0 0 0 9 0 16 18 0 0 0 2 0 0 0 8 24 0 0 0 8 1 18 8 0 0 0 16 0 0 5 0 16 0 2 0 0 1 0 8 0 16 0 2 2 0 6 0 28 16 6 2 0 0 1 17 0 18 2 2 8 0 0 0 0 16 2 1 0 0 2 1])'-'0'),17))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([8 0 20 0 0 7 4 8 6 0 9 0 2 0 1 2 1 1 20 0 8 4 0 2 16 0 0 0 6 0 0 2 0 26 8 0 1 0 16 0 20 20 2 6 8 2 0 4 2 0 0 16 4 1 0 10 0 8 1 2 0 4 1 0 2 0 6 0 8 2 16 8 16 1 3 0 0 0 4 0 0 26 0 0 0 23 16 8 0 0 8 2 0 0 0 1 2 0 12 0 8 0 4 0 4 0 8 0 0 0 0 8 0 2 0 1 1 0 0 0 0 7 0 2 2 16 0 0 8 8 1 0 0 12 0 0 1 4 21 0 4 0 2 24 8 4 0 6 0 4 9 6 0 0 2 4 4 8 0 0 16 4 0 16 0 2 0 28 0 24 10 8 4 0 0 0 0 0 9 1 0 4 1 4 2 1 9 24 8 5])'-'0'),19))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([11 0 0 0 24 0 0 16 0 12 0 0 8 0 0 0 0 0 0 0 1 6 16 10 8 0 0 4 0 0 4 17 6 0 5 0 16 20 18 0 0 0 4 1 0 2 0 8 12 4 8 7 0 9 0 8 2 4 24 4 10 8 0 0 0 1 8 0 0 9 0 6 6 8 0 0 10 0 2 0 0 8 24 2 0 0 0 0 8 2 2 0 4 0 19 2 16 0 0 18 0 3 1 1 0 0 2 0 0 0 2 1 12 4 16 0 26 0 0 0 20 2 1 0 1 8 1 24 2 8 0 1 1 0 0 8 10 0 3 0 8 8 2 1 0 0 0 0 1 3 4 3 0 4 8 0 4 0 1 1 0 0 0 10 16 0 0 0 13 0])'-'0'),16))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([0 0 8 2 0 0 0 24 1 0 4 16 4 2 8 0 0 24 0 0 1 8 0 10 10 0 0 8 0 4 12 0 16 8 0 0 8 16 16 16 0 16 0 2 2 0 0 1 0 0 2 0 0 0 5 0 0 10 0 0 10 2 10 10 24 0 18 16 4 16 0 4 0 0 4 8 19 0 0 0 8 10 4 16 0 8 0 17 8 0 16 16 0 0 0 0 4 2 22 0 0 10 0 0 0 0 0 8 0 0 1 2 0 0 16 0 8 0 0 0 18 0 0 4 8 8 19 0 0 4 0 0 4 0 0 2 0 0 16 2 16 0 2 6 8 0 0 0 8 0 0 8 0 11 1 13 16 8 8 0])'-'0'),15))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([8 1 0 6 1 16 0 2 0 4 0 4 0 0 16 1 8 16 0 4 16 4 0 6 20 0 0 0 12 0 0 1 23 0 4 16 0 6 26 8 0 1 0 0 1 0 1 0 0 1 3 0 24 0 0 0 1 17 8 17 0 16 6 0 0 0 1 0 9 2 1 1 0 0 0 0 0 0 2 0 2 0 6 6 0 6 16 8 0 0 16 16 2 0 27 0 4 0 23 0 2 4 8 11 0 0 0 4 0 0 0 8 16 0 2 6 2 0 0 12 1 1 1 0 8 17 1 4 4 0 2 0 6 0 0 0 0 2 2 8 2 0 0 0 1 8 13 0 0 1 0 0 24 4 0 0 0 16 0 0])'-'0'),16))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([12 0 0 2 0 4 2 0 4 0 11 9 10 1 0 1 10 0 28 21 0 8 0 0 4 0 0 4 0 1 22 0 16 4 0 0 4 1 13 0 16 8 2 2 20 16 8 0 0 0 27 8 0 0 8 0 4 20 12 4 0 0 0 1 20 0 4 0 0 0 1 22 1 7 2 8 2 16 0 1 0 0 0 8 8 0 0 4 4 8 0 0 0 0 1 0 0 1 9 9 1 4 1 0 0 0 0 8 16 0 16 2 0 2 0 16 18 0 7 1 0 0 2 10 0 1 2 12 4 0 0 20 0 1 0 8 0 8 24 0 2 3 9 17 0 16 0 0 2 4 0 1 0 0 0 0 0 8 2 12 8 8 16 5 0 12 1 2 0 8 8 16 16 2 16 1 1 0 0 1 0 4 12 20 16 4 20 0 12 1])'-'0'),18))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([4 0 8 4 0 1 0 16 4 10 1 1 3 0 16 16 0 0 16 8 4 0 0 2 0 0 0 16 0 2 17 0 24 0 8 1 0 0 0 2 16 0 8 0 0 0 0 9 0 6 0 1 0 1 0 16 8 0 0 0 0 0 0 13 0 0 0 16 4 8 16 4 2 0 8 3 2 16 16 0 2 6 8 18 0 9 16 0 4 16 0 0 0 8 8 20 0 9 0 20 16 8 0 7 0 18 4 0 12 4 8 17 0 2 8 4 8 8 1 2 17 16 17 5 4 0 10 0 1 1 0 0 0 2 0 0 0 16 1 3 0 4 0 1 8 0 0 1 17 0 8 4 8 0 16 8 10 0 0 4 24 8 0 1 16 0 2 16 5 0])'-'0'),18))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([1 2 2 0 2 0 18 20 18 0 0 16 0 19 0 10 0 0 0 0 16 0 1 0 0 8 12 0 16 0 0 0 16 16 8 1 0 16 0 1 12 5 16 16 20 0 5 18 16 0 0 4 1 0 0 0 0 12 16 20 0 16 5 21 21 0 16 0 0 0 2 4 16 5 4 4 16 0 4 2 8 2 4 1 16 0 0 8 17 2 0 3 0 10 0 2 4 1 0 16 16 2 0 0 2 8 0 16 4 2 0 0 20 0 24 8 4 0 8 4 20 3 0 20 2 12 0 16 0 16 0 16 16 0 17 22 4 0 16 0 6 20 9 28 0 9 0 8 16 8 16 2 16 0 16 0 0 10 0 2 0 11 0 0 0 4 0 0 4 8 17 0 0 4 12 2 0 20 10 0])'-'0'),18))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([11 2 0 18 8 8 25 5 5 4 0 0 0 2 8 0 0 16 0 8 0 4 0 0 1 0 0 0 0 1 0 1 4 9 17 0 0 10 4 0 18 16 0 18 16 5 0 0 1 12 0 9 0 4 8 0 2 1 8 0 0 29 0 2 3 16 0 8 0 1 0 1 1 0 4 0 4 0 4 2 24 0 0 0 6 16 0 0 2 4 12 0 0 2 10 0 0 1 9 16 0 0 16 17 0 1 8 0 2 24 16 2 0 2 9 0 24 10 9 0 0 20 1 2 16 8 5 0 2 0])'-'0'),13))\r\n%%\r\nassert(isequal(fivelanes(dec2bin([0 0 0 0 0 2 0 2 0 6 16 2 0 2 2 0 8 0 0 17 0 0 16 8 2 0 0 0 10 24 4 0 4 0 0 8 0 4 1 0 12 4 20 0 16 0 0 2 0 0 2 0 3 17 4 10 16 16 4 16 4 0 24 2 8 0 8 0 1 8 0 2 4 1 0 0 0 0 2 0 16 12 0 0 0 8 0 0 4 19 4 0 0 12 2 1 0 8 16 4 0 2 4 21 0 0 1 2 17 10 3 16 24 4 2 0 0 0 0 8 2 4 18 0 0 2 0 19 1 2 0 5 0 0 0 2 0 0 0 4 16 0 0 4 16 0 16 0 0 8 0 0 12 6 10 0 1 4 9 16])'-'0'),16))\r\n%% random test-cases\r\nX={[0 0 0 0 0 2 0 2 0 6 16 2 0 2 2 0 8 0 0 17 0 0 16 8 2 0 0 0 10 24 4 0 4 0 0 8 0 4 1 0 12 4 20 0 16 0 0 2 0 0 2 0 3 17 4 10 16 16 4 16 4 0 24 2 8 0 8 0 1 8 0 2 4 1 0 0 0 0 2 0 16 12 0 0 0 8 0 0 4 19 4 0 0 12 2 1 0 8 16 4 0 2 4 21 0 0 1 2 17 10 3 16 24 4 2 0 0 0 0 8 2 4 18 0 0 2 0 19 1 2 0 5 0 0 0 2 0 0 0 4 16 0 0 4 16 0 16 0 0 8 0 0 12 6 10 0 1 4 9 16],[15 16];\r\n    [8 0 20 0 0 7 4 8 6 0 9 0 2 0 1 2 1 1 20 0 8 4 0 2 16 0 0 0 6 0 0 2 0 26 8 0 1 0 16 0 20 20 2 6 8 2 0 4 2 0 0 16 4 1 0 10 0 8 1 2 0 4 1 0 2 0 6 0 8 2 16 8 16 1 3 0 0 0 4 0 0 26 0 0 0 23 16 8 0 0 8 2 0 0 0 1 2 0 12 0 8 0 4 0 4 0 8 0 0 0 0 8 0 2 0 1 1 0 0 0 0 7 0 2 2 16 0 0 8 8 1 0 0 12 0 0 1 4 21 0 4 0 2 24 8 4 0 6 0 4 9 6 0 0 2 4 4 8 0 0 16 4 0 16 0 2 0 28 0 24 10 8 4 0 0 0 0 0 9 1 0 4 1 4 2 1 9 24 8 5],[18 19];\r\n    [21 16 0 1 4 0 0 0 0 26 0 0 0 8 1 2 1 8 4 0 0 0 8 0 3 17 0 0 24 0 0 0 10 16 0 0 24 0 0 4 17 0 0 0 0 0 16 0 4 0 0 0 8 0 2 17 0 0 0 9 6 0 0 0 1 3 5 2 16 24 0 16 1 7 20 2 0 0 0 3 0 8 0 0 0 6 0 5 8 0 0 0 0 16 0 0 2 5 0 2 0 4 16 16 0 0 1 17 16 1 0 8 0 16 0 8 4 0 0 2 3 0 3 3 0 0 24 10 8 0 9 4 18 0 0 0 0 0 2 2 4 0 2 8 0 4 2 0 1 0 8 0 2 1 0 0 0 0 16 0 0 0 0 9 16 3 11 1 8 0 0 1 1 26 1 0 4 8 0 0 16 2 1 0 4 16 16 0 2 0 4 0 4 0 8 0 0 6 0 16 0 0 2 0 1 0 4 0 18 0 0 0 2 8 0 0 0 4 1 0 0 4 4 0 5 8 8 17 4 17 0 17 1 6 0 0 0 16 4 13 1 0 0 16 0 0 5 0 16 4 0 6 0 0 4 0 0 0 0 0 8 8 4 0 1 0 16 0 8 0 0 0 2 0 8 0 4 16 0 4 0 1 0 1 4 4 8 6 16 0 0 4 0 0 0 0 1 4 4 0 16 1 17 0 8 0 0 0 1 16 16 20 2 0 0 16 0 0 0 17 0 0 3 16 18 8 0 0 0 8 0 1 0 0 0 0 0 0 2 1 16 1 16 26 2 6 2 8 0 0 0 0 1 10 8 0 16 8 3 2 18 0 0 0 2 4 0 12 2 16 0 0 0 4 0 0 0 6 16 2 4 6 3 1 1 2 9 0 0 0 0 3 24 16 8 2 0 0 0 16 8 5 0 0 1 0 4 10 16 0 0 16 6 4 12 4 0 4 0 24 0 1 0 0 0 1 3 20 1 0 20 0 5 0 16 0 1 4 4 1 0 8 0 8 17 1 2 4 0 2 0 0 5 16 2 3 24 5 20 2 4 0 1 0 4 10 2 4 16 0 8 0 4 13 2 2 6 17 16 0 2 8 0 0 0 1 12 0 29 4 0 1 8 8 8 0 3 3 0 0 0 19 6 0 8 0 0 0 1 1 1 0 0 16 1 2 2 0 4 1 0 4 0 1 16 2 0 4 0 0 7 1 0 17 5 16 14 0 0 0 0 0 16 16 2 0 8 0 4 0 2 2 2 0 0 0 4 0 8 5 0 0 0 20 8 16 9 0 4 1 1 4 3 0 2 0 0 18 1 1 1 0 16 1 17 0 8 17 16 4 8 20 24 4 26 0 6 0 2 1 8 0 16 4 0 4 3 0 8 2 20 0 0 0 0 24 1 8 0 0 1 16 0 8 0 1 0 0 4 0 4 0 0 16 0 8 4 0 1 16],[60 61];\r\n    [0 0 0 2 2 1 10 24 4 16 4 0 0 2 0 0 8 1 4 0 4 2 0 0 0 16 0 2 0 4 0 0 16 4 0 0 8 0 9 4 0 4 8 4 4 24 4 1 20 4 2 0 0 14 8 0 16 4 0 0 1 0 1 16 4 6 0 4 1 2 2 2 0 0 3 1 2 16 0 0 0 2 1 2 2 8 2 1 0 16 4 0 0 4 3 2 0 2 26 0 0 1 0 8 2 5 0 2 0 2 1 0 20 0 0 16 16 12 10 24 1 0 17 16 8 4 9 9 0 2 8 0 6 20 4 0 0 17 10 0 16 5 20 16 0 17 1 0 0 0 0 0 2 2 24 2 0 20 16 0 10 17 10 16 0 24 2 6 6 2 4 3 0 4 20 0 0 0 2 0 0 16 25 10 0 1 0 9 12 1 17 12 0 8 12 8 8 0 6 0 0 0 8 12 0 0 4 8 17 19 0 16 0 5 0 4 0 20 0 2 0 0 1 0 16 16 4 0 0 2 1 17 1 8 0 5 8 0 0 1 2 1 0 0 0 0 1 0 0 16 16 8 16 0 7 0 8 2 0 4 0 4 4 0 0 8 16 2 0 0 0 9 0 4 9 2 0 1 0 21 4 4 0 0 0 1 0 0 0 11 8 0 0 12 4 0 16 12 0 4 4 0 1 0 4 2 24 2 3 0 16 16 0 0 0 0 0 0 16 0 0 20 0 2 8 12 17 18 0 18 8 2 16 16 8 0 0 16 13 0 14 3 0 0 10 0 0 24 0 2 0 16 0 4 0 8 0 8 0 0],[38 39];\r\n    [14 26 0 0 0 1 0 0 1 22 0 0 16 12 4 0 8 8 3 0 0 0 0 8 0 0 2 8 0 0 0 0 0 0 2 1 17 16 0 0 21 0 4 0 16 16 0 8 4 2 0 0 0 19 4 8 0 0 3 0 0 0 0 2 0 0 1 0 4 1 0 0 2 0 0 0 0 0 2 0 0 2 0 17 16 8 2 0 16 0 0 18 12 0 8 0 0 16 4 0 0 2 2 1 1 18 0 2 0 0 0 0 1 0 2 13 0 4 8 8 2 21 3 8 0 0 0 5 0 0 10 0 2 16 24 2 0 0 0 0 2 0 17 0 1 2 0 0 0 0 0 2 2 17 8 0 0 18 0 0 2 10 0 22 4 0 6 0 1 8 12 5 12 0 6 0 2 0 6 24 0 0 0 16 0 0 0 0 1 0 1 0 8 8 2 1 1 0 8 2 0 16 0 2 1 0 8 16 0 22 0 1 11 0 16 4 16 0 0 0 2 8 9 0 1 0 0 8 16 5 16 0 9 0 16 22 17 10 0 8 0 2 0 0 12 16 2 3 4 1 2 0 0 16 4 1 0 0 16 2 0 16 0 20 1 1 18 0 28 4 0 0 0 0 0 1 0 0 0 18],[27 28];\r\n    [26 2 0 0 1 0 5 3 1 4 0 10 0 26 0 20 0 0 4 0 0 6 8 0 4 0 1 5 0 2 9 0 6 1 18 24 16 4 0 2 0 8 8 2 0 8 9 8 0 0 0 5 18 8 0 8 0 2 0 4 7 16 2 2 1 0 16 1 6 2 2 0 9 1 4 2 2 0 0 0 0 16 1 1 9 4 0 0 4 4 1 0 0 0 16 2 0 0 0 4 4 16 0 0 16 0 1 5 2 0 8 0 0 4 2 0 8 0 0 4 8 1 2 0 8 0 0 4 8 2 18 4 8 0 0 0 16 0 0 0 0 0 4 16 1 16 2 0 0 16 8 8 0 2 1 16 0 18 4 16 16 0 0 0 2 2 2 5 0 0 18 16 4 2 0 0 2 1 0 4 8 2 0 12 1 16 4 10 0 0 0 6 0 0 0 8 8 0 4 16 0 1 16 16 16 0 0 16 4 4],[19 20];\r\n    [16 0 0 28 0 4 0 16 0 20 0 12 17 4 0 10 11 0 0 4 0 20 1 2 1 0 0 0 4 0 1 16 0 0 0 8 0 0 0 9 6 4 8 0 16 30 20 0 24 0 2 0 0 0 16 3 16 2 0 4 2 16 5 0 5 4 16 2 24 1 2 0 5 17 4 16 0 0 24 1 0 16 0 16 4 3 0 2 1 0 0 4 0 1 12 0 0 4 0 12 0 0 1 2 0 6 18 0 0 16 0 16 0 4 0 21 0 1 0 0 0 26 0 8 1 4 4 1 0 0 18 0 0 0 1 0 0 9 0 0 4 2 8 0 6 0 18 8 9 2 8 8 16 5 1 1 0 8 15 1 0 2 0 16 16 10 9 1 5 18 0 4 12 0 0 12 0 0 10 0 0 4 0 1 0 0 26 0 24 1 16 0 8 16 1 4 12 4 0 4],[20 21];\r\n    [8 0 4 0 8 24 16 0 28 0 20 16 16 2 0 24 8 0 4 8 0 1 0 4 8 0 0 20 0 1 0 22 0 17 0 0 16 17 0 2 4 2 16 0 0 16 0 0 0 8 9 0 2 0 0 0 0 16 0 1 0 0 0 0 2 0 10 1 3 1 0 0 0 16 0 16 0 2 11 17 0 1 2 0 0 8 0 0 16 0 0 6 0 8 0 0 4 0 1 12 1 0 0 24 12 4 0 1 0 2 0 5 0 0 2 0 1 0 6 0 0 0 2 0 0 1 8 2 0 0 1 17 10 8 0 8 16 0 6 0 0 0 0 0 4 28 2 0 8 1 2 2 16 0 12 0 0 0 0 0 0 4 0 0 0 5 0 0 0 12 0 6 16 0 0 7 0 26 12 8 0 18 0 8 0 12 0 0 0 0 16 16 4 0 1 2 16 0 5 0 1 4 9 16 8 8 12 0 0 0 16 2 2 2 0 18 0 0 2 0 0 16 2 8 0 9 1 0 1 1 11 0 2 0 0 0 0 0 0 4 0 0 0 8 0 2 16 0 5 4 12 8 4 17 0 2 16 0 8 1 8 12 2 2 1 8 0 0 8 0 0 0 16 0 2 1 0 22 4 0 8 0 0 0 4 12 2 9 0 0 8 4 24 16 16 1 2 0 4 0 0 0 5 4 0 16 12 16 0 1 12 16 0 8 0 16 2 0 16 16 0 1 6 0 16 0 0 6 1 0 16 0 17 0 3 0 16 16 0 4 8 2 0 10 4 0 1 16 0 0 1 8 0 0 0 1 8 0 0 9 2 5 0 0 0 2 6 8 16 5 2 0 8 16 1 26 8 1 2 20 0 26 4 0 21 2 0 4 8 8 0 9 17 8 4 9 4 0 14 8 0 0 16 0 0 3 8 2 0 1 17 4 1 2 0 16 8 0 2 4 0 1 0 0 17 4 0 0 12 4 0 11 16 0 0 8 2 0 2 0 0 0 0 16 1 16 0 4 2 3],[41 42];\r\n    [0 13 0 4 0 0 16 18 0 4 0 0 24 4 1 2 11 0 0 3 8 8 20 8 10 20 2 16 0 3 1 8 8 0 1 17 0 8 28 0 0 0 0 0 8 0 0 0 12 8 10 24 0 0 1 1 8 0 0 0 0 2 0 2 4 16 16 0 0 0 8 17 3 1 16 6 2 5 0 1 2 1 0 0 0 0 0 9 0 0 1 8 4 0 9 0 12 0 17 0 0 0 17 1 4 0 2 0 0 2 0 2 0 16 0 16 0 0 0 0 16 16 16 0 4 1 16 2 8 1 0 2 2 0 0 0 4 1 0 18 16 11 0 0 0 5 0 0 0 0 2 2 0 8 6 4 0 0 2 16 0 0 0 8 1 0 0 24 2 8 16 0 8 2 0 8 0 0 9 0 0 0 12 0 0 10 1 0 4 0 4 0 1 4 0 1 0 4 0 0 2 0 0 16 8 0 1 0 0 2 0 1 16 0 0 8 16 4 8 0 4 3 0 4 1 0 0 0 0 0 0 0 0 16 0 0 0 16 16 0 8 0 0 1 0 12 0 0 24 1 0 8 5 8 1 1 5 1 4 0 16 1 10 0 4 5 0 2 16 1 16 0 1 0 0 0 0 0 0 0 9 4 0 0 1 0 4 0 0 8 4 2 18 0 0 0 0 0 6 17 16 0 0 0 20 2 8 24 1 2 12 14 0 1 0 2 20 4 16 1 26 0 8 0 0 4 8 0 0 3 0 0 1 16 0 1 2 6 2 0 8 1 4 0 0 16 3 2 2 2 0 0 0 3 8 0 2 24 0 6 8 1 16 0 0 0 0 0 8 2 18 0 4 1 19 0 0 16 0 2 0 0 2 0 0 8 0 0 0 17 0 12 8 0 2 16 0 16 0 16 0 0 3 0 0 10 0 0 1 1 0 2 2 4 25 0 16 1 0 0 0 2 1 1 0 3 16 0 0 0 0 4 6 8 4 0 0 2 0 0 4 0 18 18 4 2 5 0 2 4 20 1 0 16 0 1 4 0 2 0 0 0 0 2 16 0 0 8 0 0 8 4 0 10 1 16 0 0 0 0 0 12 0 1 0 1 2 0 4 0],[45 46];\r\n    [1 24 0 2 4 5 9 0 24 8 0 13 9 0 1 16 8 0 0 0 16 1 2 0 1 16 16 0 0 0 12 4 2 8 4 0 9 8 0 0 24 0 16 0 0 1 0 0 0 8 2 0 0 0 0 24 0 0 0 2 16 0 0 2 0 16 2 8 0 1 8 0 0 9 0 0 8 1 2 1 2 4 2 0 8 11 0 2 19 2 0 0 1 20 0 0 0 0 16 0 2 0 4 23 0 1 18 0 0 0 5 4 17 2 1 0 8 0 5 0 0 0 8 4 9 3 0 2 1 1 4 0 6 0 0 8 2 2 16 0 0 1 0 12 1 12 4 0 13 1 1 16 0 2 16 0 16 0 0 0 17 8 0 0 0 2 0 0 17 0 9 2 1 2 0 0 0 4 17 16 20 0 1 0 9 4 0 2 1 2 16 0 16 9 4 17 4 16 0 16 6 2 0 0 16 3 16 0 4 0 2 8 0 17 0 2 5 0 19 16 0 4 0 0 5 1 2 16 0 16 0 21 1 28 0 8 8 0 8 0 0 16 16 0 4 0 0 2 2 0 1 4 16 1 18 1 0 8 1 0 1 0 6 12 1 3 1 18 4 0 2 0 16 4 21 0 28 0 0 8 0 0 0 18 0 1 8 18 0 16 2 2 2 17 1 11 8 0 4 5 0 0 5 0 8 0 8 2 0 0 16 0 16 1 1 0 8 12 5 0 1 4 2 1 2 3 0 17 1 1 10 5 4 0 24 1 2 0 4 1 16 16 4 2 1 4 8 0 2 2 0 16 4 0 0 0 8 0 2 0 4 0 1 0 0 0 2 0 0 20 1 6 0 11 0 0 0 0 2 4 0 2 0 1 1 18 0 12 2 0 24 0 0 10 0 2 21 4 0 8 16 0 25 1 12 0 22 0 10 20 16 18 0 0 24 0 3 16 5 17 8 0 18 0 4 0 28 0 4 1 16 4 16 6 16 0 0 0 0 10 11 2 0 1 0 0 0 11 0 8 4 8 3 2 4 19 0 8 0 1 6 4 2 0 16 0 0 0 0 14],[45 46];\r\n    [8 2 10 0 4 8 0 1 0 0 26 16 16 8 0 0 8 2 10 1 2 0 2 4 0 0 2 8 12 8 0 0 0 0 0 5 1 0 10 12 0 1 10 0 29 1 0 20 0 0 8 0 0 2 1 12 0 0 4 8 0 16 0 20 26 24 2 14 12 4 0 24 0 1 0 4 0 2 5 0 1 2 8 0 4 0 8 16 2 0 12 8 0 8 2 1 8 0 0 28 0 22 0 12 0 0 8 18 0 0 12 16 0 4 0 0 2 4 0 4 0 0 12 0 0 6 0 0 2 8 12 6 2 10 8 0 8 1 6 0 0 0 1 5 5 17 4 0 0 8 2 0 0 0 16 0 12 0 16 0 0 8 0 0 4 8 6 20 0 1 0 4 3 25 4 0 10 8 0 22 4 0 5 0 3 0 0 2 24 2 8 10 0 4 1 0 0 4 9 0 0 10 0 2 30 10 0 8 4 8 16 9 8 0 4 2 0 2 9 0 18 2 1 16 0 2 10 24 0 16 20 20 0 2 0 0 0 0 2 0 8 2 0 4 0 0 5 16 0 0 1 4 17 3 8 17 0 0 17 0 8 4 0 4 0 8 0 9 0 0 24 0 0 24 1 0 0 1 0 2 16 6 2 2 8 8 0 24 0 8 0 4 0 1 0 1 8 18 4 0 0 8 0 0 6 24 0 0 4 0 0 0 0 0 0 16 18 0 0 4 0 8 2 20 0 2 0 4 8 0 8 9 1 0 4 0 2 8 0 20 2 6 1 26 0 5 0 2 0 2 2 8 16 9 0 0 6 4 8 0 4 0 4 0 0 17 2 0 0 2 0 16 0 0 3 4 4 0 8 16 12 4 1 0 24 16 2 0 16 0 0 0 8 4 0 16 0 2 0 0 2 10 8 0 0 0 1 5 8 2 0 0 0 16 1 5 0 1 0 4 1 1 6 1 4 0 16 4 1 8 0 1 8 0 5 0 16 16 0 4 0 16 0 0 8 4 0 8 8 0 0 4 4 2 0 0 1 0 0 0 0 4 0 4 4 0 9 4 18 8],[44 45];\r\n    [4 0 0 8 0 0 0 0 20 0 0 12 2 1 0 0 0 2 4 16 0 0 0 0 0 0 1 0 2 2 0 0 10 1 1 0 0 8 0 20 26 0 8 17 2 24 26 2 1 0 28 0 16 0 1 3 0 8 0 0 8 1 0 4 0 8 0 0 12 16 0 0 8 8 7 17 0 0 26 8 1 1 0 16 0 0 17 0 4 0 4 17 0 0 2 4 0 0 9 8 0 1 2 16 0 1 0 4 1 24 0 14 0 0 4 0 9 0 1 7 4 0 16 0 16 1 2 1 0 0 0 0 4 0 0 8 4 16 0 0 0 18 0 2 17 0 1 4 0 10 0 0 4 3 0 24 17 1 0 4 0 0 10 0 0 24 0 8 0 0 0 0 0 17 2 0 2 7 2 4 0 0 4 2 2 4 1 2 2 0 20 1 6 0 17 0 0 0 17 0 24 0 16 0 6 3 0 10 0 20 8 0 0 0 4 8 0 23 2 0 0 1 0 0 8 0 2 4 6 8 0 0 8 0 2 0 0 0 0 20 4 2 8 0 0 10 0 2 0 4 4 12 0 0 16 0 8 0 0 4 0 4 0 0 0 26 16 17 0 2 0 0 8 1 8 18 24 16 0 0 0 0 0 8 0 3 8 0 6 8 0 0 0 2 1 0 1 25 1 12 0 0 9 0 1 0 20 10 2 0 4 16 16 1 9 0 0 2 0 0 0 3 2 4 16 10 0 6 0 8 8 0 0 4 16 1 8 17 0 4 0 8 0 10 20 0 8 0 4 0],[35 36];\r\n    [1 1 0 4 4 2 0 20 0 2 8 8 2 0 25 24 0 0 0 0 4 4 0 1 24 2 24 1 0 16 0 0 5 8 4 2 0 16 17 8 0 0 4 2 0 9 4 0 2 0 0 12 0 0 0 10 2 20 1 2 24 0 4 0 4 10 0 0 0 0 3 1 16 0 7 0 2 13 0 2 6 0 17 1 20 0 1 0 0 5 17 3 0 0 16 16 20 1 0 4 16 0 16 2 25 0 10 16 0 2 0 2 0 9 13 10 0 0 0 8 0 2 0 0 16 0 0 2 0 0 0 0 0 8 22 18 8 17 3 2 8 2 16 2 2 16 0 19 0 2 10 2 0 0 16 0 1 0 0 0 12 0 0 2 0 2 2 12 4 8 0 0 4 16 0 0 2 4 4 0 0 0 0 0 10 3 1 14 0 0 0 2 0 0 0 16 0 9 1 1 0 4 0 16 20 19 6 2 0 0 2 28 16 0 2 16 0 0 10 4 0 9 16 0 5 2 0 0 0 4 0 5 0 18 6 24 5 8 12 0 8 16 12 4 0 4 4 0 13 2 10 6 0 0 0 0 20 0 16 0 22 0 17 4 2 2 0 1 0 1 1 0 16 0 1 0 0 2 1 0 0 2 0 13 20 0 0 1 16 4 12 0 0 0 16 24 0 4 20 17 2 4 0 16 0 0 5 10 8 6 0 0 8 28 24 8 0 8 0 4 0 0 0 0 1 0 1 0 28 4],[30 31];\r\n    [1 12 10 8 17 8 8 0 0 0 1 0 0 17 0 10 0 16 2 0 0 0 0 2 0 16 0 24 8 12 0 0 3 4 0 0 0 1 0 10 0 2 2 2 0 0 8 1 0 5 2 0 8 8 0 0 16 0 0 16 0 0 0 16 8 16 12 0 0 2 16 0 16 0 16 16 1 0 0 2 2 2 0 0 0 0 0 4 8 18 0 22 0 0 4 0 24 0 0 1 0 0 2 2 8 2 0 0 0 16 4 4 0 8 0 8 4 0 8 0 0 7 0 0 10 0 1 11 0 8 0 1 2 24 0 0 0 8 0 2 0 3 4 0 0 0 10 0 4 0 0 5 22 1 0 4 0 0 0 0 10 0 0 0 3 0 0 0 0 2 25 0 0 4 0 0 4 0 2 0 0 5 0 0 1 16 0 0 0 9 0 0 0 4 9 16 0 1 1 2 0 2 16 22 2 0 0 8 1 0 16 0 16 0 0 0 0 5 0 11 8 1 20 0 16 0 8 1 0 2 0 3 8 2 0 16 0 0 8 1 0 0 16 0 4 0 16 4 0 8 0 2 2 0 2 24 20 0 16 16 0 0 2 16 4 8 8 6 0 4 16 0 1 0 0 8 0 0 0 0 5 4 4 1 0 0 19 0 8 6 0 2 0 0 0 20 9 5 0 1 8 2 8 2 0 16 8 0 4 8 0 20 0 0 16 2 16 16 2 0 0 0 1 0 8 16 8 4 12 0 8 1 2 0 0 0 8 4 0 0 0 12 4 0 24 0 0 24 0 0 2 0 2 5 0 1 0 2 0 0 6 0 0 0 0 18 2 0 16 6 0 16 2 12 0 4 0 8 16 1 0 14 0 1 6 4 8 0 24 0 0 0 5 2 2 0 1 4 0 0 0 1 10 8 8 0 4 0 0 24 4 0 8 0 1 2 0 0 4 0 0 24 8 4 0 2 0 0 0 0 0 4 18 0 1 2 0 2 0 16 0 4 16 0 8 17 0 8 16 0 16 20 2 0 0 0 0 4 0 24 0 0 8 16 0 0 8 4 0 13 2 0 12 0 1 8 2 0 0 4 0 16 16 16 16 20 0 0 0 24 0 0 0 10 9 0 16 0 4 0],[45 46];\r\n    [3 0 8 0 2 0 1 16 4 0 2 1 0 1 16 0 4 0 8 0 4 2 0 9 4 1 17 0 12 0 4 4 4 20 0 0 2 0 19 2 1 8 0 1 2 0 2 2 0 0 8 2 24 10 6 0 0 19 1 2 0 16 0 0 0 16 10 2 0 16 8 0 0 3 0 0 0 8 0 20 0 5 16 0 8 7 2 1 20 0 2 1 17 1 0 0 0 1 20 4 1 24 0 6 1 16 0 8 8 1 2 0 4 0 16 8 2 0 1 4 2 1 16 17 0 9 16 2 8 5 16 16 0 8 16 0 0 16 0 4 4 0 1 4 0 0 8 0 2 0 0 0 0 20 7 8 4 8 0 6 4 1 0 2 8 4 0 26 20 16 8 0 2 1 4 0 0 0 0 3 2 0 2 4 0 0 0 0 20 4 0 0 8 0 3 17 18 0 1 3 2 3 0 12 16 0 8 11 3 0 8 6 16 0 0 0 0 0 4 6 16 0 2 0 0 8 0 1 0 8 12 0 0 8 0 7 8 8 0 18 20 0 10 0 0 0 1 8 4 10],[26 27];\r\n    [0 0 4 0 18 4 0 0 10 17 16 0 2 0 16 4 25 0 0 2 0 16 0 0 2 16 0 0 8 8 1 22 16 1 16 16 0 0 3 16 2 0 0 1 8 4 0 18 0 16 16 0 24 0 8 2 0 0 2 2 0 8 4 4 3 0 0 0 2 4 16 24 0 16 0 21 0 0 2 16 8 0 0 1 7 0 8 2 2 20 0 0 2 8 16 0 0 2 16 0 0 0 20 8 17 0 1 0 0 0 0 4 1 16 0 0 4 6 0 10 8 0 9 0 10 0 0 0 1 12 4 0 18 9 0 1 0 0 0 0 0 20 0 2 1 1 1 16 0 2 3 0 24 14 0 0 9 16 0 2 0 0 1 4 0 4 8 5 0 4 16 2 1 16 0 4 0 0 0 0 0 0 2 0 16 8 16 16 0 0 2 0 4 0 8 0 0 2 0 1 0 0 4 0 4 22 0 8 4 10 4 8 0 0 0 0 0 0 12 0 16 4 0 1 2 4 0 1 0 2 8 5 0 0 0 0 0 0 0 16 10 0 4 0 0 0 4 0 0 7 0 0 2 0 4 3 0 1 4 0 0 18 0 0 2 0 8 0 0 0 4 0 0 16 16 0 0 0 0 17 0 0 0 0 0 0 4 16 0 1 18 0 10 0 4 0 10 25 10 0 0 0 0 1 0 0 0 0 0 17 0 2 4 0 2 0 8 8 1 0 0 0 4 24 0 4 0 0 4 0 0 1 6 0 0 0 0 24 10 0 2 2 2 10 0 0 2 1 4 2 0 2 1 10 0 2 0 0 0 4 0 4 8 16 0 1 0 0 16 0],[35 36];\r\n    [0 0 0 17 0 4 8 30 0 2 0 0 1 0 0 4 4 0 1 0 4 0 16 0 2 12 16 0 0 0 12 0 1 0 4 0 0 1 1 1 2 9 0 0 4 0 1 0 0 2 8 0 0 0 0 0 8 2 9 0 2 16 0 0 2 0 8 1 10 0 2 0 16 20 1 2 0 4 0 0 17 1 8 1 0 3 3 2 0 1 24 8 1 7 6 16 4 0 0 8 0 22 3 0 12 8 0 2 0 1 3 0 0 0 8 4 2 0 4 0 2 4 16 4 16 0 2 0 17 0 2 6 8 0 1 0 4 8 16 0 6 2 10 16 0 2 0 4 0 0 2 0 0 5 0 22 1 2 0 4 16 0 18 0 0 4 8 8 2 4 0 0 0 21 0 0 2 16 2 0 12 0 4 4 2 2 16 8 0 0],[17 18];\r\n    [0 0 0 0 9 0 2 4 1 0 6 8 0 1 0 18 16 21 4 6 16 8 0 0 1 14 0 0 8 8 0 28 2 0 10 0 0 0 20 0 5 16 0 16 8 8 8 3 8 9 0 9 3 4 4 0 2 4 0 0 0 0 0 5 15 3 0 0 0 11 0 0 1 0 0 1 0 8 0 0 1 4 0 5 16 4 18 8 0 0 1 4 4 1 0 4 0 8 4 0 0 8 2 2 20 4 0 0 0 0 20 4 8 0 0 0 1 0 0 16 0 0 19 2 0 4 3 0 10 0 18 4 12 0 0 7 0 8 0 2 16 4 4 16 16 0 1 0 0 8 16 0 0 0 9 17 0 8 4 2 0 1 4 0 26 0 0 0 0 2 0 4 16 1 2 2 0 0 2 0 0 0 0 8 0 1 0 0 0 0 0 20 1 16 0 4 0 0 3 0 0 0 0 6 9 8 8 0 8 1 0 0 16 0 0 0 0 16 8 0 17 24 16 4 2 1 8 0 0 0 1 5 0 8 12 0 2 2 0 0 0 0 0 4 2 0 0 2 0 8 2 0 1 2 4 0 4 0 4 0 0 0 8 5 17 0 10 8 8 0 0 8 0 20 1 0 24 8 0 4 16 1 8 0 4 16 0 1 0 2 11 0 16 0 0 12 0 0 10 1 18 16 0 1 12 0 0 0 1 0 0 0 0 4 11 0 0 16 1 0 0 1 8 0 16 4 8 4 16 0 0 0 0 1 3 16 0 2 0 0 0 0 0 1 16 0 2 0 2 0 3 16 2 0 0 0 2 8 4 0 0 0 4 2 5 0 16 8 26 8],[34 35];\r\n    [0 11 2 12 0 20 0 0 16 0 16 8 1 2 0 4 8 8 9 16 0 20 0 5 8 8 24 2 0 0 8 8 1 0 0 4 20 8 0 0 16 0 0 4 0 4 16 28 0 0 2 0 0 20 0 0 0 16 0 0 0 0 0 20 0 2 0 2 24 4 26 0 0 0 16 8 0 2 4 12 0 0 1 1 4 8 0 0 8 12 0 2 2 16 0 0 18 0 16 8 18 0 2 8 17 4 4 2 18 8 16 0 0 8 12 0 12 0 9 0 4 16 0 0 16 8 0 1 0 8 0 0 0 0 10 4 0 26 6 0 4 2 2 8 8 1 0 20 0 2 1 16 0 8 0 4 0 16 0 4 1 0 3 12 0 4 1 2 0 0 4 0 0 0 0 0 18 4 16 1 4 28 8 0 0 4 2 0 20 2 0 5 0 2 0 8 8 0 0 0],[18 19]};\r\nfor n=randperm(size(X,1))\r\n  x=dec2bin(X{n,1})'-'0';\r\n  if rand\u003c.5, x=fliplr(x); end\r\n  if rand\u003c.5, x=flipud(x); end\r\n  x=x(:,ceil(rand:.5+.5*rand:end));\r\n  i=2+find(all(~x(:,3:end-3)));i=i(randi(numel(i))); \r\n  m=fivelanes(x(:,1:i-1))+fivelanes(x(:,i+1:end)); \r\n  if ~isscalar(m)|m~=X{n,2},error('please do not use look-up table solutions');[a,b]=0; end\r\nend\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":5,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":73,"test_suite_updated_at":"2017-12-23T05:22:30.000Z","rescore_all_solutions":false,"group_id":35,"created_at":"2017-10-12T15:29:04.000Z","updated_at":"2026-02-03T07:48:41.000Z","published_at":"2017-10-16T01:51:02.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/media/image2.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind the minimum number of lane changes necessary to cross the entire track without running into any obstacles\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA track is represented by a 5xN board (with 5 lanes and N squares in each lane). Some of the squares are blocked and the runner cannot pass through them (red blocks in the image above). The runner may\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eonly move forward or laterally\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (i.e. advancing or switching lanes), and cannot run into or jump over any obstacles. Diagonal or backward moves through the board are also not allowed. The runner may start and finish in any arbitrary lane of his choosing. Your job is to determine, given the track, the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eminimum number of lane changes\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e necessary to finish the race.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe input matrix will be a 5xN matrix with 1's representing blocked squares and 0's representing available/free squares. The output of your function should be a number indicating the minimum number of lane changes necessary to finish the race. For example, the track shown in the picture above would be represented as:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ x = [0 1 0 0 0 0 1 0\\n      0 0 0 0 1 0 0 0\\n      0 0 1 0 0 1 0 0\\n      0 0 0 1 0 0 0 0\\n      0 1 0 0 0 1 0 0];]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eand your function\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ n = fivelanes(x);]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eshould return n=2, since there are multiple paths available (e.g. yellow line in the picture above) that would allow the runner to reach the end of the track with only 2 lane changes, but none that would allow the runner to complete the track with only one or less lane changes.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eSmall print\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e: You may assume that there will always be a direct path between the start and finish requiring only forward- and lateral- movements. The testsuite does not include cases where there are no possible paths of this form. Lane changes are counted identically irrespective of whether they involve adjacent or non-adjacent lanes (i.e. switching from lane 1 to lane 4 counts as one lane-change, just the same as switching from lane 1 to lane 2). When switching lanes the runner may\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003enot\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e run over obstacles (i.e. switching from lane 1 to lane 3 is not possible if there is an obstacle in lane 2 at that point in the track). Below a few examples of tracks and possible minimal-lane-changes paths (note: optimal paths are not unique; in all of these examples the optimal number of lane-changes is, coincidentally, 5)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" 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maze","description":"*Description*\r\n\r\nThe traditional maze is 2-dimensional: the navigator can move in the positive or negative directions along two axes _x_ and _y_. Now imagine, if you will, a 5-dimensional maze. As in the 2-dimensional case, the navigator may only move along one of these directions at any time, and some of the directions are blocked by walls. Your task is to find and give the shortest path through the given maze.\r\n\r\nThis problem is a generalization of \u003chttps://www.mathworks.com/matlabcentral/cody/problems/283 Problem 283\u003e. If you haven't solved that yet, I would recommend solving it first.\r\n\r\n*Encoding*\r\n\r\n* The maze will be represented by an [ _M_ x _N_ x _O_ x _P_ x _Q_ ] matrix. \r\n* Each element of the matrix represents a valid location in the maze and the value of each element is a binary-coded representation of the walls, positive directions in which you can not move. If a value reads 0, it means the navigator is permitted to move along any of the five dimensions in the positive direction.\r\n* Walls are bi-directional: if a wall exists between two locations, you cannot traverse it in either direction. A skilled navigator must check the destination location's walls if she wishes to move in the negative direction along any dimension.\r\n* The start position is at the origin: subscript |(1,1,1,1,1)|.\r\n* The end position is at the furthest extent: subscript |(M,N,O,P,Q)|.\r\n* The output should be a matrix of the same size as the input matrix that lists the steps you need to go through to traverse the maze with the remaining squares being 0. Refer to \u003chttps://www.mathworks.com/matlabcentral/cody/problems/283 Problem 283\u003e for a 2-D example.\r\n* You are *NOT* guaranteed that there will be only one shortest path for the test cases. If there exist multiple shortest paths, you must represent them all. It can easily be shown that the superposition of two shortest paths will never lead to a multi-valued element in the output matrix.","description_html":"\u003cp\u003e\u003cb\u003eDescription\u003c/b\u003e\u003c/p\u003e\u003cp\u003eThe traditional maze is 2-dimensional: the navigator can move in the positive or negative directions along two axes \u003ci\u003ex\u003c/i\u003e and \u003ci\u003ey\u003c/i\u003e. Now imagine, if you will, a 5-dimensional maze. As in the 2-dimensional case, the navigator may only move along one of these directions at any time, and some of the directions are blocked by walls. Your task is to find and give the shortest path through the given maze.\u003c/p\u003e\u003cp\u003eThis problem is a generalization of \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/283\"\u003eProblem 283\u003c/a\u003e. If you haven't solved that yet, I would recommend solving it first.\u003c/p\u003e\u003cp\u003e\u003cb\u003eEncoding\u003c/b\u003e\u003c/p\u003e\u003cul\u003e\u003cli\u003eThe maze will be represented by an [ \u003ci\u003eM\u003c/i\u003e x \u003ci\u003eN\u003c/i\u003e x \u003ci\u003eO\u003c/i\u003e x \u003ci\u003eP\u003c/i\u003e x \u003ci\u003eQ\u003c/i\u003e ] matrix.\u003c/li\u003e\u003cli\u003eEach element of the matrix represents a valid location in the maze and the value of each element is a binary-coded representation of the walls, positive directions in which you can not move. If a value reads 0, it means the navigator is permitted to move along any of the five dimensions in the positive direction.\u003c/li\u003e\u003cli\u003eWalls are bi-directional: if a wall exists between two locations, you cannot traverse it in either direction. A skilled navigator must check the destination location's walls if she wishes to move in the negative direction along any dimension.\u003c/li\u003e\u003cli\u003eThe start position is at the origin: subscript \u003ctt\u003e(1,1,1,1,1)\u003c/tt\u003e.\u003c/li\u003e\u003cli\u003eThe end position is at the furthest extent: subscript \u003ctt\u003e(M,N,O,P,Q)\u003c/tt\u003e.\u003c/li\u003e\u003cli\u003eThe output should be a matrix of the same size as the input matrix that lists the steps you need to go through to traverse the maze with the remaining squares being 0. Refer to \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/283\"\u003eProblem 283\u003c/a\u003e for a 2-D example.\u003c/li\u003e\u003cli\u003eYou are \u003cb\u003eNOT\u003c/b\u003e guaranteed that there will be only one shortest path for the test cases. If there exist multiple shortest paths, you must represent them all. It can easily be shown that the superposition of two shortest paths will never lead to a multi-valued element in the output matrix.\u003c/li\u003e\u003c/ul\u003e","function_template":"function path = solve_maze5(maze)\r\n    path = zeros(size(maze));\r\n    path(1) = 1;\r\nend","test_suite":"%%\r\nmaze = reshape([15 15 15 15 15 15 15 15 15 31], [1 1 1 1 10]);\r\ntruth = reshape([1 2 3 4 5 6 7 8 9 10], [1 1 1 1 10]);\r\nassert(isequal(solve_maze5(maze), truth));\r\n\r\n%%\r\nmaze = reshape([28 28 30 28 30 30 29 30 28 29 29 30 31 29 28 29 30 30 31 29 29 28 30 29 29 29 28 30 31 29 29 30 29 31 29 29 30 30 28 31 30 29 28 30 31 30 30 29 30 29 28 31 30 29 28 30 29 29 28 31 29 28 30 31 30 29 30 31 29 29 29 29 28 30 30 31 28 30 31 29 29 31 29 28 29 28 31 30 30 29 30 30 31 31 30 30 30 30 30 31], [10 10 1 1 1]);\r\ntruth = reshape([1 2 3 4 5 6 7 0 11 12 0 0 0 0 0 0 8 9 10 13 0 0 0 0 0 0 0 0 0 14 0 0 0 0 0 0 0 0 16 15 0 0 0 0 0 0 0 0 17 18 0 0 0 0 0 0 0 0 20 19 0 0 0 0 0 0 0 0 21 0 0 0 0 0 0 0 24 23 22 0 0 0 0 0 0 26 25 0 0 0 0 0 0 0 0 27 28 29 30 31], [10 10 1 1 1]);\r\nassert(isequal(solve_maze5(maze), truth));\r\n\r\n%%\r\nmaze = reshape([20 29 22 23 23 23 22 30 29 21 28 29 23 29 29 29 30 29 29 29 23 22 31 30 31 23 23 29 23 21 29 29 23 22 31 23 23 22 22 31 28 23 21 28 29 31 23 30 31 23 30 22 31 23 23 28 30 31 29 21 31 29 31 21 29 22 31 29 29 29 23 23 23 31 23 22 31 22 31 31 28 23 28 23 23 23 22 31 30 23 28 23 23 28 23 31 30 31 23 23 28 31 29 28 29 31 29 29 31 31 29 31 30 29 31 29 30 31 30 31 30 30 30 31 31], [5 5 1 5 1]);\r\ntruth = reshape([1 2 0 0 0 0 3 0 0 0 13 14 0 0 0 12 15 16 0 0 11 18 17 0 0 0 0 0 0 0 0 4 0 0 0 0 5 0 0 0 9 8 25 28 29 10 19 26 27 30 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 7 24 0 0 0 20 23 0 31 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21 22 0 32 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 33], [5 5 1 5 1]);\r\nassert(isequal(solve_maze5(maze), truth));\r\n\r\n%%\r\nmaze = reshape([18 23 19 28 27 22 23 22 31 19 25 22 29 25 21 27 25 29 27 29 30 30 31 22 31 29 23 29 29 29 29 21 29 21 31 31 30 31 31 29 29 29 21 29 29 23 23 23 30 31 23 23 29 27 19 27 27 31 22 31 30 23 28 23 27 22 29 29 19 25 19 30 31 27 23 30 22 30 28 31 29 31 21 23 23 30 29 29 21 29 22 31 31 31 31 31 30 31 30 23 27 23 22 23 29 17 19 29 23 29 25 23 19 27 29 31 22 30 31 29 18 31 19 27 31 23 31 21 28 29 31 23 31 31 29 30 29 29 31 29 23 29 30 28 31 23 30 31 31 23 19 27 29 23 27 31 30 31 27 25 19 27 30 30 31 22 31 21 26 27 31 19 31 22 23 31 30 31 22 29 28 31 28 31 31 31 29 23 21 21 23 30 23 31 31 23 23 22 30 31 29 26 31 30 29 27 26 30 29 29 30 30 30 31 27 29 26 31 25 25 30 31 27 31 31 30 30 28 31 29 30 31 30 30 31 28 29 30 31 31 31 31 30 31 29 30 31 30 30 31], [5 5 2 5 1]);\r\ntruth = reshape([1 2 0 0 0 0 0 0 0 0 0 24 23 0 0 0 19 22 0 0 0 20 21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 18 13 0 0 0 17 14 0 0 0 3 0 0 0 0 0 0 0 0 0 25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 11 0 0 0 0 12 0 0 0 16 15 0 0 0 4 0 0 0 0 0 0 0 0 0 26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 27 0 0 0 0 0 0 0 0 0 0 0 35 36 0 6 7 0 0 0 0 0 0 0 0 28 0 0 0 0 29 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 33 38 0 0 0 34 37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 31 32 39 0 0 0 0 40], [5 5 2 5 1]);\r\nassert(isequal(solve_maze5(maze), truth));\r\n\r\n%%\r\nmaze = reshape([21 5 22 29 19 23 31 7 30 15 21 26 23 7 19 23 22 29 11 11 14 15 30 30 23 11 7 11 25 15 13 13 15 15 27 23 31 28 29 27 13 14 31 31 15 23 14 23 30 19 30 30 31 29 25 7 14 29 23 31 25 27 30 29 23 30 29 12 31 19 7 23 31 19 11 28 30 15 26 27 15 13 25 26 23 27 23 23 28 15 19 20 23 27 15 7 31 19 23 27 28 23 22 31 15 30 23 29 30 15 15 28 31 23 21 23 30 23 29 23 22 15 15 23 23 26 15 23 7 29 23 28 31 25 15 23 27 27 31 23 29 23 14 29 25 23 7 15 23 31 27 30 15 25 21 28 23 19 31 15 31 27 23 19 23 22 30 30 27 15 30 15 27 7 23 30 27 26 31 25 23 19 30 31 23 29 29 14 31 27 23 30 23 15 23 23 23 30 31 19 7 23 23 25 27 26 27 23 13 23 21 31 23 27 15 31 15 29 26 23 15 19 31 23 15 29 23 30 31 15 31 31 7 28 31 14 23 13 23 15 29 21 31 30 31 31 31 23 30 31 26 27 25 31 21 15 21 31 28 31 15 23 21 29 29 26 31 29 27 29 30 31 27 15 15 27 23 23 13 27 25 23 23 29 19 30 27 27 31 19 31 28 27 15 29 15 23 23 23 15 15 26 31 5 15 31 30 15 29 31 26 31 30 31 29 15 13 31 17 31 27 31 27 15 15 27 31 30 30 27 11 13 23 19 29 31 27 29 14 31 28 29 27 27 15 31 31 27 30 23 30 31 15 13 15 15 15 29 31 13 13 31 15 31 29 29 29 23 23 23 15 23 30 23 7 22 27 7 19 29 25 30 30 30 31 23 29 23 30 25 11 29 7 22 31 26 31 26 30 27 29 31 27 28 27 15 15 27 27 27 28 30 27 19 31 31 14 15 27 21 30 31 31 23 31 19 28 31 27 15 21 21 23 31 29 27 31 29 23 15 22 29 29 31 25 27 23 15 7 15 29 25 13 30 29 15 27 21 27 23 30 15 29 26 23 28 29 15 22 31 27 23 3 14 31 13 15 14 30 29 29 15 23 23 29 31 14 30 31 23 22 23 15 15 29 23 15 23 15 31 15 30 28 30 29 28 27 31 11 27 31 13 30 15 11 13 28 31 15 11 15 27 14 30 15 28 27 28 15 11 30 31 15 29 13 28 30 27 31 31 30 30 30 27 31 30 31 26 31 15 15 29 28 15 27 25 31 31 13 13 31 26 31 31 29 29 27 26 31 29 27 30 31 30 31 25 28 27 30 31 31 27 27 28 31 26 31 26 31 15 26 29 30 31 27 15 31 31 14 27 29 15 15 14 15 30 31 31 29 15 30 15 30 31 15 31 29 30 30 15 15 15 15 14 31 25 30 30 18 31 15 21 23 14 31 7 30 29 15 13 14 27 27 23 31 23 27 7 26 27 31 27 23 31 29 29 15 15 15 29 30 15 19 21 15 29 31 29 29 27 15 31 23 31 23 21 29 13 22 15 31 31 27 25 11 14 29 29 22 31 28 31 31 11 27 31 14 30 30 31 7 22 31 25 13 23 25 27 23 31 25 23 25 22 31 29 28 31 27 31 31 27 30 26 15 21 23 21 29 15 15 23 31 15 23 31 13 30 30 23 28 31 21 15 13 23 31 31 22 31 19 31 7 30 23 26 31 30 29 15 30 15 22 31 15 19 28 31 30 23 23 31 26 31 7 15 7 27 14 29 29 26 30 27 31 23 26 31 23 25 30 30 14 31 31 26 31 27 30 31 23 11 31 15 21 7 23 28 31 23 26 31 31 31 27 26 30 30 31 25 30 23 31 14 31 31 31 21 26 15 30 30 31 31 7 15 23 28 31 31 15 29 27 13 15 15 30 30 31 27 29 23 29 29 15 23 23 31 30 31 30 23 30 29 31 28 31 31 15 15 15 14 15 31 15 30 23 27 7 17 30 15 19 13 31 27 7 23 30 23 31 22 27 29 27 30 23 22 31 31 22 31 23 15 15 22 29 15 19 11 31 23 19 30 29 22 23 27 23 31 19 19 22 15 31 31 11 19 31 31 31 29 30 31 31 19 29 29 14 29 29 31 31 25 29 31 31 19 31 31 27 29 31 11 19 29 31 28 30 31 31 29 23 30 15 14 29 13 23 29 7 27 31 14 31 22 30 31 31 31 31 15 7 13 15 15 29 30 31 23 7 23 15 14 15 15 31 14 15 23 21 23 31 27 27 30 23 27 28 27 27 27 15 29 27 27 29 21 30 27 27 31 31 14 27 15 11 23 27 23 31 23 27 23 15 15 31 30 15 23 31 31 15 23 27 15 27 30 30 31 25 27 30 31 23 30 29 30 27 27 15 30 27 14 31 14 23 27 13 27 7 27 31 31 23 15 27 23 19 15 29 22 30 31 25 27 23 31 25 27 21 7 23 31 23 31 15 27 15 15 21 31 15 29 15 15 29 29 15 7 15 31 29 23 29 30 31 31 23 7 14 31 30 15 15 31 30 30 30 29 25 15 11 15 15 27 29 29 29 31 30 31 31 31 15 15 14 31 11 27 28 27 27 29 29 31 27 31 31 31 29 28 30 29 15 27 30 29 31 9 14 27 27 15 31 15 15 30 31 27 11 29 13 15 29 13 30 31 25 15 31 30 30 31 29 15 30 31 11 31 13 14 31 30 31 31 15 28 30 29 26 31 27 27 15 30 31 30 15 29 15 30 11 31 27 29 14 31 29 15 31 14 29 15 31 30 31 31 31 15 28 30 30 31 15 31 15 31 30 31 7 28 30 15 13 15 30 23 15 15 15 21 21 30 31 29 23 27 7 27 23 23 23 22 15 24 30 29 19 21 21 15 31 27 23 31 30 29 28 31 22 15 31 29 29 30 23 30 23 23 31 11 27 15 23 25 28 15 29 29 31 30 23 29 29 23 11 19 31 27 19 27 19 26 27 23 23 29 7 23 23 7 30 29 9 30 11 15 23 15 25 27 30 15 15 31 27 15 27 31 14 30 29 14 31 29 13 29 29 31 23 31 15 23 7 30 31 21 23 15 23 15 30 31 15 30 27 30 15 19 22 27 30 28 31 13 31 29 30 31 29 27 30 31 13 31 30 27 23 31 27 31 21 31 31 27 15 27 14 31 22 15 11 25 19 30 31 27 30 23 19 23 30 31 15 23 29 26 31 29 15 27 30 29 15 28 27 31 31 27 23 21 14 30 29 31 23 23 23 15 29 30 31 27 31 31 31 19 26 31 15 15 28 31 23 30 29 23 29 23 30 31 26 31 23 22 29 29 29 29 28 31 29 31 15 31 22 31 30 29 14 30 31 31 31 31 23 31 14 31 11 15 11 23 29 30 31 22 31 23 29 29 19 24 27 26 31 22 31 13 26 15 14 31 31 30 29 31 23 11 13 30 31 14 31 31 7 23 31 31 14 31 11 25 27 31 15 23 31 19 27 15 7 13 19 28 15 25 15 7 30 27 27 27 15 30 31 15 23 15 14 31 27 30 31 27 19 29 29 31 21 7 31 30 23 30 31 27 27 31 30 29 31 13 15 27 15 27 31 7 31 15 7 22 29 7 29 15 15 31 23 31 29 15 13 15 30 15 23 31 31 23 31 30 23 29 11 7 30 27 11 27 27 25 15 28 23 31 15 19 15 28 31 11 13 11 30 23 30 31 27 31 27 30 31 11 7 29 29 23 29 15 31 31 29 29 22 31 23 15 15 14 11 19 23 30 23 30 27 23 31 19 22 15 29 23 21 21 15 29 30 15 15 31 29 27 30 31 30 31 23 30 29 15 15 29 31 29 21 15 30 23 15 27 11 21 27 22 30 25 31 23 7 23 31 14 23 31 15 29 15 14 23 23 15 31 23 14 31 23 7 23 7 15 31 15 15 30 15 31 13 11 27 13 13 30 31 29 31 31 14 31 15 11 27 28 30 28 31 15 31 15 31 30 27 25 29 30 29 27 15 31 14 31 15 28 30 30 31 31 27 29 27 15 31 15 30 27 31 31 31 31 26 29 29 30 31 31 31 15 31 31 27 26 31 27 25 30 27 11 30 31 15 30 15 31 31 30 30 15 30 30 15 30 27 14 31 30 31 31 31 29 14 31 15 15 31 31 27 27 13 31 28 15 15 30 31 31 31 15 14 31 13 13 31 29 15 31 15 29 30 31 14 31 31 30 27 21 30 31 30 29 27 30 31 23 29 28 15 21 21 15 30 31 29 15 22 15 11 31 25 27 11 30 25 27 27 15 13 15 11 26 31 27 7 22 31 25 26 29 22 30 31 27 15 23 31 27 27 21 29 23 27 30 27 31 27 14 31 7 28 31 15 26 31 15 7 23 30 15 28 31 29 31 25 25 23 31 13 31 27 14 31 15 31 26 15 7 31 27 19 19 23 11 7 30 15 13 15 29 30 7 30 23 15 23 14 31 21 15 15 22 30 31 31 15 31 7 30 15 30 7 29 30 27 26 27 30 29 13 31 22 29 23 31 30 31 27 19 27 22 31 26 15 15 14 30 30 23 15 23 31 26 31 25 22 31 27 11 31 29 25 30 31 27 31 15 23 22 27 30 30 15 19 31 25 29 23 7 31 29 27 23 27 27 29 29 29 28 31 15 31 31 23 31 21 13 21 29 19 31 31 29 23 21 29 31 23 15 31 27 28 31 26 15 27 31 15 26 31 21 7 14 30 31 29 20 30 31 15 31 31 13 30 29 31 29 30 31 29 30 31 23 31 15 27 11 15 22 23 14 27 15 7 15 25 30 29 29 11 23 28 31 31 27 27 31 30 30 15 23 31 22 31 31 31 23 21 30 29 31 29 30 23 31 27 30 31 22 15 15 30 31 15 19 14 31 29 31 13 22 31 31 31 31 25 27 23 25 19 31 11 30 31 27 27 27 22 31 23 26 31 27 19 27 15 30 23 15 27 30 15 29 15 31 7 27 30 31 31 27 15 30 22 27 31 31 31 15 15 14 31 30 31 15 14 29 13 30 31 15 31 31 7 29 30 15 30 23 23 22 31 27 15 27 15 21 28 31 7 15 15 15 23 13 31 13 25 23 31 23 31 22 30 23 30 27 31 11 15 15 31 30 15 25 14 31 22 31 27 26 29 23 31 27 15 31 23 11 23 22 31 21 15 19 29 14 31 23 23 23 7 15 29 15 23 29 30 31 27 14 31 15 23 23 28 30 23 29 31 29 19 27 29 15 23 25 29 31 15 29 15 27 14 31 30 30 31 31 7 30 30 30 31 7 29 31 29 13 29 23 29 31 23 23 15 29 31 31 7 23 31 7 31 15 31 15 26 31 15 13 29 13 30 31 31 29 31 31 13 29 30 30 31 31 15 27 30 27 31 11 28 31 28 15 27 29 27 29 15 13 15 27 15 13 29 25 15 30 31 31 31 15 15 15 31 25 30 15 15 29 30 31 29 31 31 29 27 27 25 25 31 28 27 31 14 31 31 27 31 28 31 15 13 29 27 15 30 31 15 31 15 30 31 15 15 13 11 27 15 30 31 14 31 15 29 28 29 29 31 31 15 31 15 15 31 14 31 31 31 28 31 31 31 29 31 15 31 14 31 30 18 22 30 31 26 23 22 30 25 22 29 26 31 31 19 31 28 30 23 26 31 31 27 23 25 29 23 22 27 31 31 23 27 31 30 30 31 27 29 23 21 22 27 27 22 30 23 30 31 27 26 29 26 31 29 25 23 30 27 29 29 29 27 23 27 23 31 23 23 30 31 26 30 31 29 23 28 31 19 27 23 29 23 23 26 23 27 30 23 28 27 30 27 27 23 23 30 27 23 22 31 31 30 31 23 31 22 29 29 29 23 29 29 29 31 31 23 31 23 30 30 31 31 23 21 31 29 28 23 29 27 31 27 27 31 25 25 22 27 29 23 30 29 23 30 23 19 31 27 29 25 23 21 27 27 31 23 31 23 21 29 23 23 23 31 31 23 30 23 27 27 31 22 23 25 29 27 26 31 31 27 30 31 23 21 22 23 26 31 23 27 22 31 23 31 30 27 26 27 27 31 30 31 23 23 31 28 31 27 19 31 21 31 29 25 27 31 21 31 30 31 31 31 31 31 30 31 22 23 29 21 30 29 31 31 31 23 29 23 31 29 29 29 23 22 31 30 31 31 27 29 30 29 21 23 29 29 31 23 28 31 29 23 23 29 23 29 19 23 23 23 30 31 23 29 22 31 27 19 29 25 29 28 31 31 29 31 31 21 21 23 30 31 31 31 26 23 31 27 23 19 30 31 31 28 31 22 27 19 31 29 29 21 25 29 31 31 31 31 30 31 27 26 31 23 30 30 23 29 18 31 25 31 31 30 31 31 23 23 29 29 22 31 21 27 30 30 31 19 22 23 23 31 31 31 29 23 29 23 30 31 31 30 21 30 30 30 31 31 31 23 30 22 31 26 30 29 27 31 31 28 31 29 31 21 31 29 27 31 29 23 30 31 23 31 23 26 23 23 27 27 19 31 31 23 26 30 31 25 23 25 19 27 31 27 31 26 23 25 23 19 31 30 31 31 31 23 29 29 21 31 23 27 31 27 31 31 21 29 27 29 29 23 31 27 27 31 30 19 29 26 29 30 23 31 25 30 31 27 29 27 19 23 31 31 29 30 31 31 23 31 22 23 31 23 31 30 30 23 28 31 29 29 31 23 23 31 29 29 23 23 28 31 31 22 31 31 30 31 30 27 30 27 27 30 29 29 26 29 29 27 30 29 31 29 27 28 31 29 31 27 30 31 31 29 30 30 31 31 31 26 30 31 29 31 31 30 31 31 28 31 27 30 29 31 31 27 27 31 28 30 31 27 27 31 30 31 29 25 25 26 30 31 27 30 27 30 31 29 30 27 30 31 31 26 30 31 31 31 28 31 27 25 31 31 31 27 31 31 31 31 31 25 27 27 27 31 31 27 31 28 28 30 31 30 31 29 31 29 29 31 31 29 29 31 29 28 31 31 31 30 31 30 31], [5 5 5 5 5]);\r\ntruth = reshape([1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 93 92 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 95 94 91 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 98 0 0 0 0 99 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 96 97 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 6 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 38 37 0 0 40 39 122 123], [5 5 5 5 5]);\r\nassert(isequal(solve_maze5(maze), truth));","published":true,"deleted":false,"likes_count":5,"comments_count":19,"created_by":134,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":48,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":35,"created_at":"2017-10-12T15:00:57.000Z","updated_at":"2026-03-19T20:06:56.000Z","published_at":"2017-10-16T01:51:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eDescription\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe traditional maze is 2-dimensional: the navigator can move in the positive or negative directions along two axes\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Now imagine, if you will, a 5-dimensional maze. As in the 2-dimensional case, the navigator may only move along one of these directions at any time, and some of the directions are blocked by walls. Your task is to find and give the shortest path through the given maze.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is a generalization of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/283\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 283\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. If you haven't solved that yet, I would recommend solving it first.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eEncoding\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe maze will be represented by an [\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eM\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eN\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eO\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eP\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e x\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eQ\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e ] matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach element of the matrix represents a valid location in the maze and the value of each element is a binary-coded representation of the walls, positive directions in which you can not move. If a value reads 0, it means the navigator is permitted to move along any of the five dimensions in the positive direction.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWalls are bi-directional: if a wall exists between two locations, you cannot traverse it in either direction. A skilled navigator must check the destination location's walls if she wishes to move in the negative direction along any dimension.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe start position is at the origin: subscript\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(1,1,1,1,1)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe end position is at the furthest extent: subscript\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:rFonts w:cs=\\\"monospace\\\"/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e(M,N,O,P,Q)\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe output should be a matrix of the same size as the input matrix that lists the steps you need to go through to traverse the maze with the remaining squares being 0. Refer to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/283\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 283\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e for a 2-D example.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou are\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOT\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e guaranteed that there will be only one shortest path for the test cases. If there exist multiple shortest paths, you must represent them all. It can easily be shown that the superposition of two shortest paths will never lead to a multi-valued element in the output matrix.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44377,"title":"Five steps to enlightenment","description":"This problem asks you to identify valid variations of the famous \u003chttps://en.wikipedia.org/wiki/Sum_and_Product_Puzzle sum and product puzzle\u003e.\r\n\r\n\u003c\u003chttp://www.alfnie.com/software/printnumbers.jpg\u003e\u003e\r\n\r\nThe original _sum and product_ puzzle goes somewhat like this:\r\n\r\nScott and Priscilla are asked to guess two numbers X and Y, *ranging between 2 and 100* and with X\u003cY. Scott is told their sum S (=X+Y) and Priscilla is told their product P (=X*Y). After this, they have the following conversation:\r\n\r\n  Scott:      I don't know X and Y                                                (Step 1)\r\n  Priscilla:  Neither do I                                                        (Step 2)\r\n  Scott:      Before our conversation I already knew that you didn't know         (Step 3)\r\n  Priscilla:  But now I do know X and Y                                           (Step 4)\r\n  Scott:      And so do I!                                                        (Step 5)\r\n\r\nThe original puzzle asks you to deduce the value of X and Y from the above information\r\n\r\nTo solve this puzzle you may assume that: a) Scott and Priscilla are perfect mathematicians/logicians and always speak the truth; b) they are aware of each other circumstances (Scott knows that Priscilla has been told the product of X and Y, and Priscilla knows that Scott has been told the sum of X and Y before the beginning of their conversation); and c) the third sentence refers to Scott and Priscilla state before the beginning of the conversation (i.e. Scott already knew -at the outset of this conversation- that Priscilla did not know the solution -at the time-)\r\n\r\nBriefly, the deduction for this seemingly impossible puzzle starts with all possible pairs of values of X and Y, and uses  the information in the sentences above to sequentially reduce the range of possible (X,Y) pairs to those that would be consistent with each sentence (see figure below; blue dots represent (X,Y) pairs still possible after each of the sentences/steps above; plot uses matrix convention with origin at the upper-left corner, X in vertical axis, and Y in horizontal axis; upper triangular segment represents all possible X\u003cY pairs before the start of S\u0026P conversation). \r\n\r\n\u003c\u003chttp://www.alfnie.com/software/printnumbers_b.jpg\u003e\u003e\r\n\r\nFor example, in *Step 1* after S says _\"I don't know X and Y\"_ we learn that the pair (X,Y) = (2,3) (and a few others) are no longer possible, since otherwise S would have known the solution as soon as he was told their sum (X+Y=5), which takes a unique value among all possible (X,Y) pairs. Similarly, in *Step 2*, after P says _\"Neither do I\"_, the pair (X,Y) = (5,7) (and many others) are no longer possible, since otherwise P would have known the solution as soon as she was told their product X*Y=35, which turns out to be unique among all remaining X,Y pairs. In *Step 3*, S asserting _\"I knew that you didn't know\"_ tells us that, knowing only X+Y, he was able to determine beforehand that it would be _impossible_ for P to know both X and Y from their product X*Y alone, which, again, rules out a considerable number of (X,Y) pairs (e.g. all solutions with X+Y=12 can be ruled out, because if S was told that X+Y=12 he could not have possibly dismissed beforehand the possibility that perhaps X=5 and Y=7 which would have allowed P to know both X and Y as soon as she was told their product X*Y=35). In *Step 4*, P suddenly become aware of the solution after S revelation informs us that, unlike in Step 2, she is now (after step-3 crop in possible X,Y pairs) able to uniquely determine the solution (X,Y) from their product (X*Y). This allows us to rule out many (X,Y) pairs among the remaining possible values, such as (X,Y)=(2,15) or (5,6), because P would not have been able to uniquely identify the solution at this point if she was told that the product X*Y was 30. Last, in *Step 5*, S suddenly becoming aware of the solution after P revelation, again allows us to rule out any remaining (X,Y) pair where knowing the sum S would still not suffice to uniquely identify the solution.\r\n\r\nThis puzzle is very neat because, somewhat surprisingly, after sequentially reducing the range of possible (X,Y) pairs from the five sentences/steps above, only one possible pair remains. The solution X=4 and Y=13, which Priscilla learns after the third sentence, Scott learns after the fourth sentence, and you, the reader, learn after the fifth sentence. \r\n\r\nKey to the existence of a unique solution to this puzzle is the initial range of possible (X,Y) pairs that we are told to consider. If, for example, instead of considering all X,Y values between 2 and 100, we were told to consider all X,Y values between 1 and 100, the puzzle would not be solvable, as in this case there will be multiple possible solutions that would all be consistent with the five sentences above (see figure below; at Step 5 there still exist 6 different possible solutions to this puzzle). \r\n\r\n\u003c\u003chttp://www.alfnie.com/software/printnumbers_c.jpg\u003e\u003e\r\n\r\nSimilarly, if we were told to consider all X,Y values between 2 and 50, the puzzle would again not be solvable, as in this case there would be _no solution_ consistent with all five sentences (perhaps surprisingly, since the X=4 Y=13 solution above is in fact within the stated range). \r\n\r\n\u003c\u003chttp://www.alfnie.com/software/printnumbers_d.jpg\u003e\u003e\r\n\r\nOn the other hand, if we were told to consider X and Y values ranging between 1 and 24, for example, the puzzle would again become solvable, now with a new unique solution X=1 and Y=6. \r\n\r\n\u003c\u003chttp://www.alfnie.com/software/printnumbers_e.jpg\u003e\u003e\r\n\r\nIn this problem you are tasked to create a function that would determine whether a particular variation of this puzzle would work or not. Specifically, given an initial set of possible (X,Y) pairs (entered as a Nx2 matrix and representing the full set of possible X,Y pairs that Scott and Priscilla are told to consider), you should determine whether it is possible to solve this puzzle (i.e. whether one, and only one, (X,Y) pair is consistent with the five sequential sentences above). Your function should simply return 1 (or true) if the puzzle is solvable, and 0 (or false) otherwise. \r\n\r\nGood luck!","description_html":"\u003cp\u003eThis problem asks you to identify valid variations of the famous \u003ca href = \"https://en.wikipedia.org/wiki/Sum_and_Product_Puzzle\"\u003esum and product puzzle\u003c/a\u003e.\u003c/p\u003e\u003cimg src = \"http://www.alfnie.com/software/printnumbers.jpg\"\u003e\u003cp\u003eThe original \u003ci\u003esum and product\u003c/i\u003e puzzle goes somewhat like this:\u003c/p\u003e\u003cp\u003eScott and Priscilla are asked to guess two numbers X and Y, \u003cb\u003eranging between 2 and 100\u003c/b\u003e and with X\u0026lt;Y. Scott is told their sum S (=X+Y) and Priscilla is told their product P (=X*Y). After this, they have the following conversation:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eScott:      I don't know X and Y                                                (Step 1)\r\nPriscilla:  Neither do I                                                        (Step 2)\r\nScott:      Before our conversation I already knew that you didn't know         (Step 3)\r\nPriscilla:  But now I do know X and Y                                           (Step 4)\r\nScott:      And so do I!                                                        (Step 5)\r\n\u003c/pre\u003e\u003cp\u003eThe original puzzle asks you to deduce the value of X and Y from the above information\u003c/p\u003e\u003cp\u003eTo solve this puzzle you may assume that: a) Scott and Priscilla are perfect mathematicians/logicians and always speak the truth; b) they are aware of each other circumstances (Scott knows that Priscilla has been told the product of X and Y, and Priscilla knows that Scott has been told the sum of X and Y before the beginning of their conversation); and c) the third sentence refers to Scott and Priscilla state before the beginning of the conversation (i.e. Scott already knew -at the outset of this conversation- that Priscilla did not know the solution -at the time-)\u003c/p\u003e\u003cp\u003eBriefly, the deduction for this seemingly impossible puzzle starts with all possible pairs of values of X and Y, and uses  the information in the sentences above to sequentially reduce the range of possible (X,Y) pairs to those that would be consistent with each sentence (see figure below; blue dots represent (X,Y) pairs still possible after each of the sentences/steps above; plot uses matrix convention with origin at the upper-left corner, X in vertical axis, and Y in horizontal axis; upper triangular segment represents all possible X\u0026lt;Y pairs before the start of S\u0026P conversation).\u003c/p\u003e\u003cimg src = \"http://www.alfnie.com/software/printnumbers_b.jpg\"\u003e\u003cp\u003eFor example, in \u003cb\u003eStep 1\u003c/b\u003e after S says \u003ci\u003e\"I don't know X and Y\"\u003c/i\u003e we learn that the pair (X,Y) = (2,3) (and a few others) are no longer possible, since otherwise S would have known the solution as soon as he was told their sum (X+Y=5), which takes a unique value among all possible (X,Y) pairs. Similarly, in \u003cb\u003eStep 2\u003c/b\u003e, after P says \u003ci\u003e\"Neither do I\"\u003c/i\u003e, the pair (X,Y) = (5,7) (and many others) are no longer possible, since otherwise P would have known the solution as soon as she was told their product X*Y=35, which turns out to be unique among all remaining X,Y pairs. In \u003cb\u003eStep 3\u003c/b\u003e, S asserting \u003ci\u003e\"I knew that you didn't know\"\u003c/i\u003e tells us that, knowing only X+Y, he was able to determine beforehand that it would be \u003ci\u003eimpossible\u003c/i\u003e for P to know both X and Y from their product X*Y alone, which, again, rules out a considerable number of (X,Y) pairs (e.g. all solutions with X+Y=12 can be ruled out, because if S was told that X+Y=12 he could not have possibly dismissed beforehand the possibility that perhaps X=5 and Y=7 which would have allowed P to know both X and Y as soon as she was told their product X*Y=35). In \u003cb\u003eStep 4\u003c/b\u003e, P suddenly become aware of the solution after S revelation informs us that, unlike in Step 2, she is now (after step-3 crop in possible X,Y pairs) able to uniquely determine the solution (X,Y) from their product (X*Y). This allows us to rule out many (X,Y) pairs among the remaining possible values, such as (X,Y)=(2,15) or (5,6), because P would not have been able to uniquely identify the solution at this point if she was told that the product X*Y was 30. Last, in \u003cb\u003eStep 5\u003c/b\u003e, S suddenly becoming aware of the solution after P revelation, again allows us to rule out any remaining (X,Y) pair where knowing the sum S would still not suffice to uniquely identify the solution.\u003c/p\u003e\u003cp\u003eThis puzzle is very neat because, somewhat surprisingly, after sequentially reducing the range of possible (X,Y) pairs from the five sentences/steps above, only one possible pair remains. The solution X=4 and Y=13, which Priscilla learns after the third sentence, Scott learns after the fourth sentence, and you, the reader, learn after the fifth sentence.\u003c/p\u003e\u003cp\u003eKey to the existence of a unique solution to this puzzle is the initial range of possible (X,Y) pairs that we are told to consider. If, for example, instead of considering all X,Y values between 2 and 100, we were told to consider all X,Y values between 1 and 100, the puzzle would not be solvable, as in this case there will be multiple possible solutions that would all be consistent with the five sentences above (see figure below; at Step 5 there still exist 6 different possible solutions to this puzzle).\u003c/p\u003e\u003cimg src = \"http://www.alfnie.com/software/printnumbers_c.jpg\"\u003e\u003cp\u003eSimilarly, if we were told to consider all X,Y values between 2 and 50, the puzzle would again not be solvable, as in this case there would be \u003ci\u003eno solution\u003c/i\u003e consistent with all five sentences (perhaps surprisingly, since the X=4 Y=13 solution above is in fact within the stated range).\u003c/p\u003e\u003cimg src = \"http://www.alfnie.com/software/printnumbers_d.jpg\"\u003e\u003cp\u003eOn the other hand, if we were told to consider X and Y values ranging between 1 and 24, for example, the puzzle would again become solvable, now with a new unique solution X=1 and Y=6.\u003c/p\u003e\u003cimg src = \"http://www.alfnie.com/software/printnumbers_e.jpg\"\u003e\u003cp\u003eIn this problem you are tasked to create a function that would determine whether a particular variation of this puzzle would work or not. Specifically, given an initial set of possible (X,Y) pairs (entered as a Nx2 matrix and representing the full set of possible X,Y pairs that Scott and Priscilla are told to consider), you should determine whether it is possible to solve this puzzle (i.e. whether one, and only one, (X,Y) pair is consistent with the five sequential sentences above). Your function should simply return 1 (or true) if the puzzle is solvable, and 0 (or false) otherwise.\u003c/p\u003e\u003cp\u003eGood luck!\u003c/p\u003e","function_template":"function valid = fivesteps(XY)\r\n  % XY is a Nx2 matrix, where each row represents a possible X,Y combination\r\n  % valid is 1 if the puzzle is solvable or 0 otherwise\r\n  valid = true;\r\nend","test_suite":"%%\r\nassessFunctionAbsence({'regexp','regexpi','regexprep','str2num'},'FileName','fivesteps.m')\r\nassert(isempty(regexp(fileread('fivesteps.m'),'assert')));\r\n[~,~]=system('rm freepass*');\r\n%%\r\n%lines=textread('fivesteps.m','%s'); \r\n%id=str2num(regexp(lines{end},'\\d+','match','once'));\r\n%assert(~ismember(id,[3430216]),'Please submit a valid non-cheating solution and ask the problem author to manually evaluate it'); % [3931805,3397427,3430216]\r\n%%\r\n% X,Y X\u003cY between 2 and 100\r\n[x,y]=find(triu(ones(100),1));\r\nz=[x y];\r\nvalid=all(z\u003e1,2);\r\nassert(fivesteps(z(valid,:))==true);\r\n%%\r\n% X,Y X\u003cY between 2 and 60\r\n[x,y]=find(triu(ones(60),1));\r\nz=[x y];\r\nvalid=all(z\u003e1,2);\r\nassert(fivesteps(z(valid,:))==false);\r\n%%\r\n% X,Y X\u003cY between 2 and 200\r\n[x,y]=find(triu(ones(200),1));\r\nz=[x y];\r\nvalid=all(z\u003e1,2);\r\nassert(fivesteps(z(valid,:))==true);\r\n%%\r\n% X,Y X\u003cY between 2 and 1680\r\n[x,y]=find(triu(ones(1680),1));\r\nz=[x y];\r\nvalid=all(z\u003e1,2);\r\nassert(fivesteps(z(valid,:))==true);\r\n%%\r\n% X,Y X\u003cY between 2 and 1700\r\n[x,y]=find(triu(ones(1700),1));\r\nz=[x y];\r\nvalid=all(z\u003e1,2);\r\nassert(fivesteps(z(valid,:))==false);\r\n%%\r\n% X,Y X\u003cY between 1 and 20\r\n[x,y]=find(triu(ones(20),1));\r\nz=[x y];\r\nvalid=all(z\u003e=1,2);\r\nassert(fivesteps(z(valid,:))==false);\r\n%%\r\n% X,Y X\u003cY between 1 and 30\r\n[x,y]=find(triu(ones(30),1));\r\nz=[x y];\r\nvalid=all(z\u003e=1,2);\r\nassert(fivesteps(z(valid,:))==true);\r\n%%\r\n% X,Y X\u003cY between 1 and 40\r\n[x,y]=find(triu(ones(40),1));\r\nz=[x y];\r\nvalid=all(z\u003e=1,2);\r\nassert(fivesteps(z(valid,:))==false);\r\n%%\r\n% X,Y X\u003cY between 3 and 5000\r\n[x,y]=find(triu(ones(3000),1));\r\nz=[x y];\r\nvalid=all(z\u003e=3,2);\r\nassert(fivesteps(z(valid,:))==true);\r\n%%\r\n% X,Y X\u003cY between 3 and 100\r\n[x,y]=find(triu(ones(100),1));\r\nz=[x y];\r\nvalid=all(z\u003e=3,2);\r\nassert(fivesteps(z(valid,:))==false);\r\n%%\r\n% X,Y X\u003cY even between 2 and 40\r\n[x,y]=meshgrid(2:2:40);\r\nz=[x(:) y(:)];\r\nvalid=y\u003ex;\r\nassert(fivesteps(z(valid,:))==false);\r\n%%\r\n% X,Y X\u003cY odd between 1 and 1000\r\n[x,y]=meshgrid(1:2:1000);\r\nz=[x(:) y(:)];\r\nvalid=y\u003ex;\r\nassert(fivesteps(z(valid,:))==true);\r\n%%\r\n% X,Y X\u003cY non-primes between 1 and 50\r\n[x,y]=meshgrid(setdiff(1:50,primes(50)));\r\nz=[x(:) y(:)];\r\nvalid=y\u003ex;\r\nassert(fivesteps(z(valid,:))==true);\r\n%%\r\n% X,Y X\u003cY primes between 1 and 50\r\n[x,y]=meshgrid(primes(50));\r\nz=[x(:) y(:)];\r\nvalid=y\u003ex;\r\nassert(fivesteps(z(valid,:))==false);\r\n%%\r\n% X,Y X\u003cY between 3 and 100\r\n[x,y]=find(triu(ones(randi([10,100])),1));\r\nz=[x y];\r\nvalid=all(z\u003e2,2);\r\nassert(fivesteps(z(valid,:))==false);\r\n%%\r\n% X,Y X\u003cY between 1 and 100\r\n[x,y]=find(triu(ones(randi([40,100])),1));\r\nz=[x y];\r\nvalid=all(z\u003e=1,2);\r\nassert(fivesteps(z(valid,:))==false);\r\n%%\r\n% X,Y X\u003cY between 2 and 100\r\n[x,y]=find(triu(ones(randi([62,100])),1));\r\nz=[x y];\r\nvalid=all(z\u003e1,2);\r\nassert(fivesteps(z(valid,:))==true);\r\n%%\r\n% X,Y X\u003cY between 2 and 100\r\n[x,y]=find(triu(ones(randi([10,61])),1));\r\nz=[x y];\r\nvalid=all(z\u003e1,2);\r\nassert(fivesteps(z(valid,:))==false); \r\n%%\r\n% X,Y X\u003cY in 3 5 12 18 20 28 30\r\n% Possible solutions after step 1: [3,20] [3,30] [5,18] [5,28] [18,30] [20,28] \r\n% Possible solutions after step 2: [3,30] [5,18] \r\n% Possible solutions after step 3: [5,18] \r\n% Possible solutions after step 4: [5,18] \r\n% Possible solutions after step 5: [5,18] \r\n[x,y]=meshgrid([3 5 12 18 20 28 30]);\r\nz=[x(:) y(:)];\r\nvalid=y\u003ex;\r\nassert(fivesteps(z(valid,:))==true);\r\n%%\r\n% X,Y X\u003cY in 3 5 12 15 28 30\r\n% Possible solutions after step 1: [3,30] [5,28] \r\n% Possible solutions after step 2: \r\n[x,y]=meshgrid([3 5 12 15 28 30]);\r\nz=[x(:) y(:)];\r\nvalid=y\u003ex;\r\nassert(fivesteps(z(valid,:))==false);\r\n%%\r\n% X,Y X\u003cY in 2 4 6 8 12 16 18\r\n% Possible solutions after step 1: [2,8] [2,12] [2,16] [2,18] [4,6] [4,16] [4,18] [6,8] [6,12] [6,16] [6,18] [8,12] [8,16] \r\n% Possible solutions after step 2: [2,12] [4,6] [4,18] [6,12] [6,16] [8,12] \r\n% Possible solutions after step 3: [2,12] [4,18] [6,12] [6,16] \r\n% Possible solutions after step 4: [2,12] [6,16] \r\n% Possible solutions after step 5: [2,12] [6,16] \r\n[x,y]=meshgrid([2 4 6 8 12 16 18]);\r\nz=[x(:) y(:)];\r\nvalid=y\u003ex;\r\nassert(fivesteps(z(valid,:))==false);\r\n%%\r\n% X,Y X\u003cY in 4 6 8 12 16 18\r\n% Possible solutions after step 1: [4,16] [4,18] [6,16] [6,18] [8,12] [8,16] \r\n% Possible solutions after step 2: [6,16] [8,12] \r\n% Possible solutions after step 3: [6,16] \r\n% Possible solutions after step 4: [6,16] \r\n% Possible solutions after step 5: [6,16] \r\n[x,y]=meshgrid([4 6 8 12 16 18]);\r\nz=[x(:) y(:)];\r\nvalid=y\u003ex;\r\nassert(fivesteps(z(valid,:))==true);\r\n%%\r\n% X,Y X\u003cY in 2 3 10 14 15 20 21\r\n% Possible solutions after step 1: [2,15] [2,21] [3,14] [3,20] [3,21] [10,14] [14,21] [15,20] \r\n% Possible solutions after step 2: [2,21] [3,14] \r\n% Possible solutions after step 3: [3,14] \r\n% Possible solutions after step 4: [3,14] \r\n% Possible solutions after step 5: [3,14] \r\n[x,y]=meshgrid([2 3 10 14 15 20 21]);\r\nz=[x(:) y(:)];\r\nvalid=y\u003ex;\r\nassert(fivesteps(z(valid,:))==true);\r\n%%\r\n% X,Y X\u003cY in 2 3 5 8 10 14 15 20 21\r\n% Possible solutions after step 1: [2,15] [2,20] [2,21] [3,10] [3,14] [3,15] [3,20] [3,21] [5,8] [5,20] [8,10] [8,14] [8,15] [8,21] [10,14] [10,15] [14,15] [14,21] [15,20] \r\n% Possible solutions after step 2: [2,15] [2,20] [2,21] [3,10] [3,14] [5,8] \r\n% Possible solutions after step 3: [2,15] [3,10] [3,14] [5,8] \r\n% Possible solutions after step 4: [3,14] [5,8] \r\n% Possible solutions after step 5: [3,14] [5,8] \r\n[x,y]=meshgrid([2 3 5 8 10 14 15 20 21]);\r\nz=[x(:) y(:)];\r\nvalid=y\u003ex;\r\nassert(fivesteps(z(valid,:))==false);\r\n%%\r\n% a few random cases to discourage look-up table solutions\r\n    data={[2 5 6 7 9 10 12 16 23 25 26 27 28 29 31],[49 94 97 109 112 113 154 157 158 161 184 187 188 191 193 199 202 203 206 208 209 214 217 218 221 223 224 225];...\r\n        [2 4 6 9 10 11 12 13 14 20 22 23 25 26 28],[49 64 79 81 109 111 113 124 125 126 128 129 154 156 158 159 161 169 171 173 174 176 177 184 186 188 189 191 192 193 199 201 203 204 206 207 208 209 214 216 218 219 221 222 223 224 225];...\r\n        [2 3 4 6 7 9 10 11 12 14 19 20 21 24 25 28 31],[19 35 87 89 108 109 121 124 126 127 142 144 145 155 156 171 174 175 177 180 206 215 223 230 240 241 245 247 253 257 262 263 264 270 271 274 278 279 280 281 285 288 289];...\r\n        [2 4 5 6 8 9 10 11 15 16 18 19 20 21 23 24 25 26 27 28 29],[45 66 67 87 109 111 150 152 153 171 174 177 214 219 221 234 235 237 240 242 243 256 258 261 263 264 265 276 277 279 282 284 285 286 287 297 298 300 303 305 306 307 308 309 319 321 324 326 327 328 329 330 331 339 340 342 345 347 348 349 350 351 352 353 360 361 363 366 368 369 370 371 372 373 374 375 381 382 384 387 389 390 391 392 393 394 395 396 397 402 403 405 408 410 411 412 413 414 415 416 417 418 419 423 424 426 429 431 432 433 434 435 436 437 438 439 440 441];...\r\n        [2 4 5 6 8 10 11 12 14 16 17 25 27 28 29 30 31],[1 54 89 109 125 137 140 144 145 154 156 171 177 179 181 188 194 196 198 199 205 208 211 213 216 217 222 225 228 229 230 232 233 234 235 239 245 247 248 250 251 252 253 256 262 264 266 267 268 269 270 271 273 279 281 283 284 285 286 287 288 289];...\r\n        [2 5 6 7 10 14 15 16 17 20 21 23 24 25 29 30],[120 152 154 168 170 171 184 185 186 187 188 200 202 203 204 205 216 218 219 220 221 222 232 234 235 236 237 238 239 248 250 251 252 253 254 255 256];...\r\n        [4 5 7 8 9 11 12 15 16 17 20 21 24 27 28 30],[18 68 82 85 86 98 100 102 103 116 118 119 120 129 130 136 146 150 151 152 153 162 166 168 169 171 194 196 198 199 202 203 205 212 226 230 231 232 233 235 237 239 244 249 250];...\r\n        [2 3 4 6 8 9 11 12 13 15 17 19 20 21 22 23 25 28 29 31],[22 43 102 122 123 127 147 148 162 163 168 169 182 187 188 190 202 203 207 208 209 210 211 222 223 227 228 229 230 231 232 242 243 247 248 249 250 251 252 253 262 263 267 268 269 270 271 272 273 274 282 283 287 288 289 290 291 292 293 294 295 302 303 307 308 309 310 311 312 313 314 315 316 322 323 327 328 329 330 331 332 333 334 335 336 337 342 343 347 348 349 350 351 352 353 354 355 356 357 358 362 363 367 368 369 370 371 372 373 374 375 376 377 378 379 382 383 387 388 389 390 391 392 393 394 395 396 397 398 399 400];...\r\n        [3 4 5 6 8 9 10 11 13 14 18 19 21 22 23 25 26 28 29 30 31],[111 150 153 154 155 174 176 177 195 197 198 199 216 218 219 220 221 237 239 240 242 243 258 260 261 262 263 264 265 279 281 282 283 284 285 286 287 300 302 303 304 305 306 307 308 309 321 323 324 325 326 327 328 329 330 331 342 344 345 346 347 348 349 350 351 352 353 363 365 366 367 368 369 370 371 372 373 374 375 384 386 387 388 389 390 391 392 393 394 395 396 397 405 407 408 409 410 411 412 413 414 415 416 417 418 419 426 428 429 430 431 432 433 434 435 436 437 438 439 440 441];...\r\n        [2 4 5 6 8 10 11 13 14 15 16 17 20 22 28 31],[51 52 83 100 103 132 135 136 137 148 151 153 154 168 183 185 187 188 196 199 200 201 202 204 205 212 215 217 218 220 221 222 228 231 232 233 234 236 237 238 239 244 247 249 250 252 253 254 255 256];...\r\n        [2 4 5 8 10 11 12 15 20 21 22 26 28 29 30 31],[1 65 82 103 119 120 129 145 151 152 154 177 183 184 186 188 193 199 200 204 205 209 215 216 218 220 221 222 225 231 232 234 236 237 238 239 241 247 248 250 252 253 254 255 256];...\r\n        [2 4 5 7 8 12 13 17 18 19 22 26 28 29 30],[49 64 65 109 110 113 124 125 128 129 139 140 143 144 145 154 155 158 159 160 161 184 185 188 189 191 193 199 200 203 204 205 206 208 209];...\r\n        [2 3 6 8 9 12 15 17 18 19 21 22 23 24 25 27 28 29 30],[81 96 119 121 137 138 140 141 157 159 160 161 176 180 195 197 198 199 201 214 216 217 218 220 221 233 235 237 239 240 241 254 255 256 258 259 260 261 271 273 274 275 277 278 279 280 281 290 292 293 294 296 297 298 299 300 301 309 311 312 313 315 316 317 318 319 320 321 328 330 331 332 334 335 336 337 338 339 340 341 347 349 350 351 352 353 354 355 356 357 358 359 360 361];...\r\n        [6 7 9 11 17 18 21 22 23 27 28 29],[53 101 105 125 129 131 137 141 143 144];...\r\n        [2 3 4 6 8 9 11 12 15 16 18 19 20 22 24 25 27 28 29 30],[22 81 83 102 103 121 122 127 147 148 161 164 166 167 168 188 189 190 202 203 208 210 211 222 231 232 242 247 248 250 251 252 253 262 263 267 268 269 270 271 272 273 274 285 287 288 290 291 292 293 294 295 310 314 315 316 322 323 327 328 330 331 332 333 334 335 336 337 347 348 350 351 352 353 354 355 356 357 358 362 367 368 370 371 372 373 374 375 376 377 378 379 382 387 388 390 391 392 393 394 395 396 397 398 399 400];...\r\n        [3 4 5 6 10 11 13 17 20 21 25 26 30],[57 70 71 96 97 99 161 162 164 169];...\r\n        [2 3 4 10 12 15 16 18 19 20 21 22 25 26 28 30 31],[1 52 55 120 123 127 140 144 145 157 161 162 163 171 174 178 179 180 181 188 191 195 196 197 198 199 205 208 212 213 214 215 216 217 222 225 229 230 231 232 233 234 235 239 242 246 247 248 249 250 251 252 253 256 259 263 264 266 267 268 269 270 271 273 276 280 281 282 283 284 285 286 287 288 289];...\r\n        [2 4 5 7 10 15 16 18 20 24 25 27 28 29 30 31],[17 18 82 86 98 102 103 114 118 119 120 146 150 151 152 154 178 182 183 186 187 188 209 210 214 215 216 218 220 222 226 230 231 232 234 236 238 239 242 246 247 248 250 252 254 255 256];...\r\n        [4 6 7 10 11 12 18 20 21 22 24 28],[26 27 40 51 52 88 97 99 101 103 105 112 113 117 123 124 131 133 134 136 139 141 143];...\r\n        [2 3 4 6 8 10 12 14 15 17 18 19 20 21 22 24 26 28 30],[20 41 79 80 117 118 119 121 137 138 141 156 157 160 174 178 181 193 197 198 200 201 212 213 214 220 221 229 231 232 233 235 238 239 240 241 251 252 255 269 272 274 276 277 279 281 288 292 293 295 296 297 298 300 301 307 311 312 314 315 316 317 319 320 321 326 330 331 333 334 335 336 338 339 340 341 345 349 350 352 353 354 355 357 358 359 360 361];...\r\n        [2 3 4 6 8 10 12 13 15 16 18 19 20 22 25 26 29],[18 35 37 70 72 88 91 105 106 107 121 124 139 140 141 144 145 160 161 163 173 176 179 180 181 190 195 197 207 208 209 211 214 215 216 217 224 227 230 231 232 234 235 241 247 248 249 251 252 253 258 259 260 275 278 281 282 283 285 286 287 289];...\r\n        [3 4 5 8 9 12 14 21 23 24 28 30],[1 49 53 97 101 105 121 125 129 131];...\r\n        [2 3 6 7 8 9 12 13 15 16 18 19 22 23 24 26 28],[52 55 89 103 120 124 140 145 157 159 174 179 181 191 196 198 199 208 213 215 216 217 230 232 235 242 245 247 249 250 251 252 253 259 261 276 278];...\r\n        [2 4 6 8 9 10 11 12 21 22 24 25 26 27 28 29 31],[1 19 37 55 73 86 87 89 90 104 121 123 124 125 127 137 139 140 141 144 145 155 159 172 174 178 179 181 188 189 190 192 194 195 198 199 205 206 207 208 212 215 216 217 222 224 226 227 239 241 242 243 246 247 249 250 251 253 256 257 258 259 260 263 264 266 267 268 270 271 273 274 275 276 277 280 281 283 284 285 287 288 289]};\r\n    for ndata=randi(size(data,1),1,20)\r\n        a=data{ndata,1};\r\n        N=numel(a);\r\n        A=zeros(N);\r\n        A(data{ndata,2})=1;A=A|A';\r\n        if rand\u003c.5, idx=find(A); else idx=find(~A); end\r\n        [b,c]=ind2sub(size(A),idx(randi(numel(idx))));\r\n        d=a;d([b c])=[];\r\n        [x,y]=meshgrid(d);\r\n        z=[x(:) y(:)];\r\n        valid=y\u003ex;\r\n        assert(fivesteps(z(valid,:))==A(b,c),'failed on d = %s (correct output = %s)',mat2str(d),mat2str(A(b,c)));\r\n    end\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":36,"created_by":43,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":42,"test_suite_updated_at":"2018-01-02T21:35:48.000Z","rescore_all_solutions":true,"group_id":35,"created_at":"2017-10-11T19:04:33.000Z","updated_at":"2026-01-17T20:25:15.000Z","published_at":"2017-10-16T01:51:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/media/image1.JPEG\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/media/image2.JPEG\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId3\",\"target\":\"/media/image3.JPEG\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId4\",\"target\":\"/media/image4.JPEG\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/image\",\"targetMode\":\"\",\"relationshipId\":\"rId5\",\"target\":\"/media/image5.JPEG\"}],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem asks you to identify valid variations of the famous\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Sum_and_Product_Puzzle\\\"\u003e\u003cw:r\u003e\u003cw:t\u003esum and product puzzle\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe original\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003esum and product\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e puzzle goes somewhat like this:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eScott and Priscilla are asked to guess two numbers X and Y,\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eranging between 2 and 100\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e and with X\u0026lt;Y. Scott is told their sum S (=X+Y) and Priscilla is told their product P (=X*Y). After this, they have the following conversation:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[Scott:      I don't know X and Y                                                (Step 1)\\nPriscilla:  Neither do I                                                        (Step 2)\\nScott:      Before our conversation I already knew that you didn't know         (Step 3)\\nPriscilla:  But now I do know X and Y                                           (Step 4)\\nScott:      And so do I!                                                        (Step 5)]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe original puzzle asks you to deduce the value of X and Y from the above information\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTo solve this puzzle you may assume that: a) Scott and Priscilla are perfect mathematicians/logicians and always speak the truth; b) they are aware of each other circumstances (Scott knows that Priscilla has been told the product of X and Y, and Priscilla knows that Scott has been told the sum of X and Y before the beginning of their conversation); and c) the third sentence refers to Scott and Priscilla state before the beginning of the conversation (i.e. Scott already knew -at the outset of this conversation- that Priscilla did not know the solution -at the time-)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eBriefly, the deduction for this seemingly impossible puzzle starts with all possible pairs of values of X and Y, and uses the information in the sentences above to sequentially reduce the range of possible (X,Y) pairs to those that would be consistent with each sentence (see figure below; blue dots represent (X,Y) pairs still possible after each of the sentences/steps above; plot uses matrix convention with origin at the upper-left corner, X in vertical axis, and Y in horizontal axis; upper triangular segment represents all possible X\u0026lt;Y pairs before the start of S\u0026amp;P conversation).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId2\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eStep 1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e after S says\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\\\"I don't know X and Y\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e we learn that the pair (X,Y) = (2,3) (and a few others) are no longer possible, since otherwise S would have known the solution as soon as he was told their sum (X+Y=5), which takes a unique value among all possible (X,Y) pairs. Similarly, in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eStep 2\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, after P says\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\\\"Neither do I\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, the pair (X,Y) = (5,7) (and many others) are no longer possible, since otherwise P would have known the solution as soon as she was told their product X*Y=35, which turns out to be unique among all remaining X,Y pairs. In\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eStep 3\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, S asserting\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e\\\"I knew that you didn't know\\\"\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e tells us that, knowing only X+Y, he was able to determine beforehand that it would be\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eimpossible\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e for P to know both X and Y from their product X*Y alone, which, again, rules out a considerable number of (X,Y) pairs (e.g. all solutions with X+Y=12 can be ruled out, because if S was told that X+Y=12 he could not have possibly dismissed beforehand the possibility that perhaps X=5 and Y=7 which would have allowed P to know both X and Y as soon as she was told their product X*Y=35). In\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eStep 4\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, P suddenly become aware of the solution after S revelation informs us that, unlike in Step 2, she is now (after step-3 crop in possible X,Y pairs) able to uniquely determine the solution (X,Y) from their product (X*Y). This allows us to rule out many (X,Y) pairs among the remaining possible values, such as (X,Y)=(2,15) or (5,6), because P would not have been able to uniquely identify the solution at this point if she was told that the product X*Y was 30. Last, in\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eStep 5\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, S suddenly becoming aware of the solution after P revelation, again allows us to rule out any remaining (X,Y) pair where knowing the sum S would still not suffice to uniquely identify the solution.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis puzzle is very neat because, somewhat surprisingly, after sequentially reducing the range of possible (X,Y) pairs from the five sentences/steps above, only one possible pair remains. The solution X=4 and Y=13, which Priscilla learns after the third sentence, Scott learns after the fourth sentence, and you, the reader, learn after the fifth sentence.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eKey to the existence of a unique solution to this puzzle is the initial range of possible (X,Y) pairs that we are told to consider. If, for example, instead of considering all X,Y values between 2 and 100, we were told to consider all X,Y values between 1 and 100, the puzzle would not be solvable, as in this case there will be multiple possible solutions that would all be consistent with the five sentences above (see figure below; at Step 5 there still exist 6 different possible solutions to this puzzle).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId3\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSimilarly, if we were told to consider all X,Y values between 2 and 50, the puzzle would again not be solvable, as in this case there would be\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eno solution\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e consistent with all five sentences (perhaps surprisingly, since the X=4 Y=13 solution above is in fact within the stated range).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId4\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOn the other hand, if we were told to consider X and Y values ranging between 1 and 24, for example, the puzzle would again become solvable, now with a new unique solution X=1 and Y=6.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"-1\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId5\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this problem you are tasked to create a function that would determine whether a particular variation of this puzzle would work or not. Specifically, given an initial set of possible (X,Y) pairs (entered as a Nx2 matrix and representing the full set of possible X,Y pairs that Scott and Priscilla are told to consider), you should determine whether it is possible to solve this puzzle (i.e. whether one, and only one, (X,Y) pair is consistent with the five sequential sentences above). Your function should simply return 1 (or true) if the puzzle is solvable, and 0 (or false) otherwise.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGood luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray 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sliding puzzle: 3D","description":"This is an extension of problem 42842. In this case, the puzzle is three-dimensional and is of size 3x3x3. Of the 27 positions in the puzzle, 26 are occupied by cubes numbered 1 thru 26, while the remaining position is empty. You can slide an adjacent cube into the empty position, similarly to sliding an adjacent tile into the empty position in the 15 puzzle.\r\nIn this case, for simplicity, the puzzle is represented by a vectorized form of the puzzle, such that the 3D form of the puzzle can be obtained by reshape(p,[3 3 3]). Therefore, a solved cube shall look like this:\r\n p = [1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21;22;23;24;25;26;0]\r\nGiven the initial state vector, p, return a vector, m, comprising a sequence of integers, representing the linear indices of the cubes you wish to slide, in turn, into the empty position, in order to solve the puzzle.\r\nAs before, the solution does not have to be efficient. It must simply result in a correctly solved puzzle. Illegal moves, such as trying to slide a tile that is not adjacent to the open slot, will be ignored.\r\nExample:\r\n p = [0;2;3;1;5;6;4;7;9;10;11;12;13;17;14;16;8;18;19;20;21;22;23;15;25;26;24]\r\n\r\n m = [4 7 8 17 14 15 24 27]","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 348.75px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 174.375px; transform-origin: 407px 174.375px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eThis is an extension of\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/42842\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eproblem 42842\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. In this case, the puzzle is three-dimensional and is of size 3x3x3. Of the 27 positions in the puzzle, 26 are occupied by cubes numbered 1 thru 26, while the remaining position is empty. You can slide an adjacent cube into the empty position, similarly to sliding an adjacent tile into the empty position in the 15 puzzle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eIn this case, for simplicity, the puzzle is represented by a vectorized form of the puzzle, such that the 3D form of the puzzle can be obtained by\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"font-style: italic; \"\u003ereshape(p,[3 3 3])\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e. Therefore, a solved cube shall look like this:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4375px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e p = [1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21;22;23;24;25;26;0]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eGiven the initial state vector, p, return a vector, m, comprising a sequence of integers, representing the linear indices of the cubes you wish to slide, in turn, into the empty position, in order to solve the puzzle.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eAs before, the solution does not have to be efficient. It must simply result in a correctly solved puzzle. Illegal moves, such as trying to slide a tile that is not adjacent to the open slot, will be ignored.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eExample:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 61.3125px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.6562px; transform-origin: 404px 30.6562px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e p = [0;2;3;1;5;6;4;7;9;10;11;12;13;17;14;16;8;18;19;20;21;22;23;15;25;26;24]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); block-size: 20.4375px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2188px; transform-origin: 404px 10.2188px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 0px 0px; tab-size: 4; transform-origin: 0px 0px; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003e m = [4 7 8 17 14 15 24 27]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function m = sliding3d(p)\r\n  m = -1;\r\nend","test_suite":"%%\r\nfiletext = fileread('sliding3d.m');\r\nassert(isempty(strfind(filetext,'eval')))\r\nassert(isempty(strfind(filetext,'assign')))\r\nassert(isempty(strfind(filetext,'echo')))\r\nassert(isempty(strfind(filetext,'freepass')))\r\n\r\n%%\r\np = [0;2;3;1;5;6;4;7;9;10;11;12;13;17;14;16;8;18;19;20;21;22;23;15;25;26;24];\r\nm = sliding3d(p);\r\nfor i = 1:numel(m)\r\n  if round(m(i)) == m(i) \u0026\u0026 m(i) \u003c= numel(p) \u0026\u0026 m(i) \u003e 0\r\n    zero=find(p == 0);\r\n    [a0 b0 c0] = ind2sub([3 3 3],zero);\r\n    [a1 b1 c1] = ind2sub([3 3 3],m(i));\r\n    if abs(a1 - a0) + abs(b1 - b0) + abs(c1 - c0) == 1\r\n      p([m(i) zero]) = p([zero m(i)]);\r\n    end\r\n  end\r\nend\r\nassert(isequal(p,[1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21;22;23;24;25;26;0]))\r\n\r\n%%\r\np = [1;0;2;4;8;5;7;9;18;10;21;12;11;14;15;16;17;6;13;3;19;20;22;24;25;23;26];\r\nm = sliding3d(p);\r\nfor i = 1:numel(m)\r\n  if round(m(i)) == m(i) \u0026\u0026 m(i) \u003c= numel(p) \u0026\u0026 m(i) \u003e 0\r\n    zero=find(p == 0);\r\n    [a0 b0 c0] = ind2sub([3 3 3],zero);\r\n    [a1 b1 c1] = ind2sub([3 3 3],m(i));\r\n    if abs(a1 - a0) + abs(b1 - b0) + abs(c1 - c0) == 1\r\n      p([m(i) zero]) = p([zero m(i)]);\r\n    end\r\n  end\r\nend\r\nassert(isequal(p,[1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21;22;23;24;25;26;0]))\r\n\r\n%%\r\np = [1;4;3;19;10;6;7;2;9;20;11;0;16;14;12;5;13;18;22;23;21;17;15;24;25;8;26];\r\nm = sliding3d(p);\r\nfor i = 1:numel(m)\r\n  if round(m(i)) == m(i) \u0026\u0026 m(i) \u003c= numel(p) \u0026\u0026 m(i) \u003e 0\r\n    zero=find(p == 0);\r\n    [a0 b0 c0] = ind2sub([3 3 3],zero);\r\n    [a1 b1 c1] = ind2sub([3 3 3],m(i));\r\n    if abs(a1 - a0) + abs(b1 - b0) + abs(c1 - c0) == 1\r\n      p([m(i) zero]) = p([zero m(i)]);\r\n    end\r\n  end\r\nend\r\nassert(isequal(p,[1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21;22;23;24;25;26;0]))\r\n\r\n%%\r\np = [1;5;3;10;7;0;13;9;24;22;2;15;16;11;17;12;8;6;19;20;21;26;14;23;4;25;18];\r\nm = sliding3d(p);\r\nfor i = 1:numel(m)\r\n  if round(m(i)) == m(i) \u0026\u0026 m(i) \u003c= numel(p) \u0026\u0026 m(i) \u003e 0\r\n    zero=find(p == 0);\r\n    [a0 b0 c0] = ind2sub([3 3 3],zero);\r\n    [a1 b1 c1] = ind2sub([3 3 3],m(i));\r\n    if abs(a1 - a0) + abs(b1 - b0) + abs(c1 - c0) == 1\r\n      p([m(i) zero]) = p([zero m(i)]);\r\n    end\r\n  end\r\nend\r\nassert(isequal(p,[1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21;22;23;24;25;26;0]))\r\n","published":true,"deleted":false,"likes_count":14,"comments_count":9,"created_by":15521,"edited_by":15521,"edited_at":"2022-11-18T05:31:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":53,"test_suite_updated_at":"2022-11-18T05:31:46.000Z","rescore_all_solutions":false,"group_id":35,"created_at":"2017-10-11T12:38:57.000Z","updated_at":"2026-02-03T07:53:47.000Z","published_at":"2017-10-16T01:51:01.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis is an extension of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/42842\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eproblem 42842\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e. In this case, the puzzle is three-dimensional and is of size 3x3x3. Of the 27 positions in the puzzle, 26 are occupied by cubes numbered 1 thru 26, while the remaining position is empty. You can slide an adjacent cube into the empty position, similarly to sliding an adjacent tile into the empty position in the 15 puzzle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIn this case, for simplicity, the puzzle is represented by a vectorized form of the puzzle, such that the 3D form of the puzzle can be obtained by\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ereshape(p,[3 3 3])\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, a solved cube shall look like this:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ p = [1;2;3;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21;22;23;24;25;26;0]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the initial state vector, p, return a vector, m, comprising a sequence of integers, representing the linear indices of the cubes you wish to slide, in turn, into the empty position, in order to solve the puzzle.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs before, the solution does not have to be efficient. It must simply result in a correctly solved puzzle. Illegal moves, such as trying to slide a tile that is not adjacent to the open slot, will be ignored.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ p = [0;2;3;1;5;6;4;7;9;10;11;12;13;17;14;16;8;18;19;20;21;22;23;15;25;26;24]\\n\\n m = [4 7 8 17 14 15 24 27]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44374,"title":"Tautology","description":"Check if the given expression is always true. For example, the sentence\r\n\r\n  '~(A \u0026 B) == (~A | ~B)'\r\n\r\nis always true.\r\n\r\nCharacters in the input sequences may include *~ \u0026 | == ( )*, whitespace, 0 for false, 1 for true and letters for variables.","description_html":"\u003cp\u003eCheck if the given expression is always true. For example, the sentence\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e'~(A \u0026 B) == (~A | ~B)'\r\n\u003c/pre\u003e\u003cp\u003eis always true.\u003c/p\u003e\u003cp\u003eCharacters in the input sequences may include \u003cb\u003e~ \u0026 | == ( )\u003c/b\u003e, whitespace, 0 for false, 1 for true and letters for variables.\u003c/p\u003e","function_template":"function y = tautology(x)\r\n  y = true;\r\nend","test_suite":"%%\r\nx = '0';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '1';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|1';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '1\u0026A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A\u0026B';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|A';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|~A';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '0==0';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~0';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~(A \u0026 B) == (~A | ~B)';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = '~(Z \u0026 Y) == (~Y | ~Z)';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|X|V|W|Y|Z';\r\ny_correct = false;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nx = 'A|B|C|D|E|F|G|H|I|J|K|L|M|~A|O|P|Q|R|S|T|U|X|V|W|Y|Z';\r\ny_correct = true;\r\nassert(isequal(tautology(x),y_correct))\r\n%%\r\nassert(isequal(tautology('(A|B)|C'),false));\r\n%%\r\nassert(isequal(tautology('(A|B)|(C == C)'),true));\r\n%%\r\nassert(isequal(tautology('(A == B)|(B == C)|(C == A)'),true));\r\n%%\r\nassert(isequal(tautology('~(~(~(~(~(~(0))))))'),false)); \r\n%%\r\nassert(isequal(tautology('~(~(~(~(~(~(~0))))))'),true));\r\n% provided by Alfonso:\r\nassert(isequal(tautology('((0\u00261)|~B)\u0026~B'),false)); \r\n%%\r\nassert(isequal(tautology('((0\u0026~B)\u0026~B)'),false)); \r\n%%\r\nassert(isequal(tautology('((0|A)\u0026~A)'),false)); \r\n%%\r\nassert(isequal(tautology('((0|A)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((0|~B)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((1\u00260)|B)'),false)); \r\n%%\r\nassert(isequal(tautology('((1\u00261)\u0026A)'),false)); \r\n%%\r\nassert(isequal(tautology('((1|0)|A)'),true)); \r\n%%\r\nassert(isequal(tautology('((1|A)|0)'),true)); \r\n%%\r\nassert(isequal(tautology('((1|~A)\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('((A\u00261)|~A)|A'),true)); \r\n%%\r\nassert(isequal(tautology('((A\u0026~A)\u0026~B)|~A'),false)); \r\n%%\r\nassert(isequal(tautology('((A\u0026~B)\u00261)|B'),false)); \r\n%%\r\nassert(isequal(tautology('((A|0)\u00261)\u0026~B'),false)); \r\n%%\r\nassert(isequal(tautology('((A|A)\u0026A)|~A'),true)); \r\n%%\r\nassert(isequal(tautology('((B|0)\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('((B|1)\u0026B)\u0026A'),false)); \r\n%%\r\nassert(isequal(tautology('((B|A)|~A)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)\u00260)\u0026B'),false)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)|0)'),false)); \r\n%%\r\nassert(isequal(tautology('((~A\u0026~A)|~A)|1'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|A)|~B)\u00261'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|B)|A)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|~A)|1)'),true)); \r\n%%\r\nassert(isequal(tautology('((~A|~B)\u00260)'),false)); \r\n%%\r\nassert(isequal(tautology('((~B\u00260)\u0026A)'),false)); \r\n%%\r\nassert(isequal(tautology('(0\u00261)|1\u00261'),true)); \r\n%%\r\nassert(isequal(tautology('(0|~A\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('(1|A\u00260)'),true)); \r\n%%\r\nassert(isequal(tautology('(A\u0026A\u0026~B)'),false)); \r\n%%\r\nassert(isequal(tautology('(A\u0026~A|1)'),true)); \r\n%%\r\nassert(isequal(tautology('(A|1)|B'),true)); \r\n%%\r\nassert(isequal(tautology('(A|A)|A|1'),true)); \r\n%%\r\nassert(isequal(tautology('(B\u00261)|~B'),true)); \r\n%%\r\nassert(isequal(tautology('(B\u0026~B)\u0026~B\u00260'),false)); \r\n%%\r\nassert(isequal(tautology('(B|~B)|B'),true)); \r\n%%\r\nassert(isequal(tautology('(~A\u0026B\u00260)'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|0)|~B\u0026~A'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|1)|1'),true)); \r\n%%\r\nassert(isequal(tautology('(~A|B\u0026B)'),false)); \r\n%%\r\nassert(isequal(tautology('(~A|B)|~B'),true)); \r\n%%\r\nassert(isequal(tautology('(~A|~A)|0'),false)); \r\n%%\r\nassert(isequal(tautology('(~B\u00260)\u00261|1'),true)); \r\n%%\r\nassert(isequal(tautology('1\u0026B|~B|0'),true)); \r\n%%\r\nassert(isequal(tautology('B\u00261\u0026A\u00261'),false)); \r\n%%\r\nassert(isequal(tautology('~A\u00260\u00261|1'),true)); \r\n%%\r\nassert(isequal(tautology('~B\u00260\u0026~A|B'),false)); \r\n%%\r\nassert(isequal(tautology('~B|1|1|~B'),true)); \r\n%%\r\nassert(isequal(tautology('~B|~B\u00261|1'),true));\r\n%%\r\nassert(isequal(tautology('A==~A'),false));\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n","published":true,"deleted":false,"likes_count":3,"comments_count":30,"created_by":14358,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":44,"test_suite_updated_at":"2017-10-31T07:45:16.000Z","rescore_all_solutions":true,"group_id":35,"created_at":"2017-10-10T23:20:08.000Z","updated_at":"2026-02-03T08:59:32.000Z","published_at":"2017-10-16T01:51:01.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCheck if the given expression is always true. For example, the sentence\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA['~(A \u0026 B) == (~A | ~B)']]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eis always true.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCharacters in the input sequences may include\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e~ \u0026amp; | == ( )\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, whitespace, 0 for false, 1 for true and letters for variables.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44367,"title":"Inscribed Pentagon? 2","description":"Your function will be provided with the five vertices of a pentagon (p) as well as the center point (cp) and radius (r) of a circle. The pentagon may or may not be centered on the circle. The function should return one of the following values:\r\n\r\n -1: the pentagon is not centered on the circle (within 5% of r)^\r\n  0: the pentagon is completely enclosed within the circle but is not inscribed\r\n  1: the pentagon is inscribed in the circle (within ±0.02)\r\n  2: the vertices of the pentagon extend beyond the circle\r\n\r\nPoints will be rounded to the nearest hundredth. See the test cases for examples. (There will not be a case where some vertices are within the circle and others without.)\r\n\r\n^ Due to the asymmetric nature of the pentagon, its centroid does not coincide with center of its inscribing circle, hence the ±5% tolerance window. ","description_html":"\u003cp\u003eYour function will be provided with the five vertices of a pentagon (p) as well as the center point (cp) and radius (r) of a circle. The pentagon may or may not be centered on the circle. The function should return one of the following values:\u003c/p\u003e\u003cpre\u003e -1: the pentagon is not centered on the circle (within 5% of r)^\r\n  0: the pentagon is completely enclosed within the circle but is not inscribed\r\n  1: the pentagon is inscribed in the circle (within ±0.02)\r\n  2: the vertices of the pentagon extend beyond the circle\u003c/pre\u003e\u003cp\u003ePoints will be rounded to the nearest hundredth. See the test cases for examples. (There will not be a case where some vertices are within the circle and others without.)\u003c/p\u003e\u003cp\u003e^ Due to the asymmetric nature of the pentagon, its centroid does not coincide with center of its inscribing circle, hence the ±5% tolerance window.\u003c/p\u003e","function_template":"function y = inscribed_pentagon2(p,cp,r)\r\n y = -1;\r\nend","test_suite":"%%\r\np = [0,5; 4.76,1.55; 2.94,-4.05; -2.94,-4.05; -4.76,1.55];\r\ncp = [0,0];\r\nr = 5;\r\ny_correct = 1;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\np = [0,6.58; 6.42,1.92; 3.97,-5.63; -3.97,-5.63; -6.42,1.92];\r\ncp = [0,0];\r\nr = 5;\r\ny_correct = 2;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\np = [0,4.55; 4.28,1.44; 2.65,-3.59; -2.65,-3.59; -4.28,1.44];\r\ncp = [0,0];\r\nr = 5;\r\ny_correct = 0;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\np = [0,5; 4.76,1.55; 2.94,-4.05; -2.94,-4.05; -4.76,1.55];\r\ncp = [0,0.5];\r\nr = 8.75;\r\ny_correct = -1;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\np = [0,5; 4.76,1.55; 2.94,-4.05; -2.94,-4.05; -4.76,1.55];\r\ncp = [1.98,-0.47];\r\nr = 8.75;\r\ny_correct = -1;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\ncp = [20,8];\r\np = [0,5; 4.76,1.55; 2.94,-4.05; -2.94,-4.05; -4.76,1.55] + repmat(cp,[5,1]);\r\nr = 5;\r\ny_correct = 1;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\ncp = [20,8];\r\np = [0,6.58; 6.42,1.92; 3.97,-5.63; -3.97,-5.63; -6.42,1.92] + repmat(cp,[5,1]);\r\nr = 5;\r\ny_correct = 2;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\ncp = [20,8];\r\np = [0,4.55; 4.28,1.44; 2.65,-3.59; -2.65,-3.59; -4.28,1.44] + repmat(cp,[5,1]);\r\nr = 5;\r\ny_correct = 0;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\ncp_temp = [20,8];\r\np = [0,5; 4.76,1.55; 2.94,-4.05; -2.94,-4.05; -4.76,1.55] + repmat(cp_temp,[5,1]);\r\ncp = [19.5,9.08];\r\nr = 2.5;\r\ny_correct = -1;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\ncp_temp = [20,8];\r\np = [0,5; 4.76,1.55; 2.94,-4.05; -2.94,-4.05; -4.76,1.55] + repmat(cp_temp,[5,1]);\r\ncp = [19.86,7.19];\r\nr = 7.5;\r\ny_correct = -1;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\np = [23.66,11.42; 24.37,5.58; 19.05,3.10; 15.04,7.40; 17.89,12.54];\r\ncp = [20,8];\r\nr = 5;\r\ny_correct = 1;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\np = [25.01,12.47; 25.98,4.58; 18.78,1.23; 13.37,7.03; 17.22,13.97];\r\ncp = [20,8];\r\nr = 5;\r\ny_correct = 2;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\np = [23.27,11.12; 23.92,5.87; 19.12,3.63; 15.52,7.50; 18.08,12.13];\r\ncp = [20,8];\r\nr = 5;\r\ny_correct = 0;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\np = [30.94,36.26; 35.61,27.09; 28.34,19.82; 19.17,24.49; 20.78,34.65];\r\ncp = [26.97,28.45];\r\nr = 8.75;\r\ny_correct = 1;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\np = [32.54,38.78; 38.84,26.41; 29.02,16.59; 16.65,22.89; 18.83,36.61];\r\ncp = [26.97,28.45];\r\nr = 8.75;\r\ny_correct = 2;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\np = [30.49,35.54; 34.69,27.29; 28.14,20.74; 19.89,24.95; 21.34,34.09];\r\ncp = [26.97,28.45];\r\nr = 8.75;\r\ny_correct = 0;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\np = [30.94,36.26; 35.61,27.09; 28.34,19.82; 19.17,24.49; 20.78,34.65];\r\ncp = [26.41,29.04];\r\nr = 6.13;\r\ny_correct = -1;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))\r\n\r\n%%\r\np = [30.94,36.26; 35.61,27.09; 28.34,19.82; 19.17,24.49; 20.78,34.65];\r\ncp = [27.07,27.66];\r\nr = 9.63;\r\ny_correct = -1;\r\nassert(isequal(inscribed_pentagon2(p,cp,r),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":88,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":35,"created_at":"2017-10-10T15:28:54.000Z","updated_at":"2026-04-02T01:39:53.000Z","published_at":"2017-10-16T01:51:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function will be provided with the five vertices of a pentagon (p) as well as the center point (cp) and radius (r) of a circle. The pentagon may or may not be centered on the circle. The function should return one of the following values:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ -1: the pentagon is not centered on the circle (within 5% of r)^\\n  0: the pentagon is completely enclosed within the circle but is not inscribed\\n  1: the pentagon is inscribed in the circle (within ±0.02)\\n  2: the vertices of the pentagon extend beyond the circle]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePoints will be rounded to the nearest hundredth. See the test cases for examples. (There will not be a case where some vertices are within the circle and others without.)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e^ Due to the asymmetric nature of the pentagon, its centroid does not coincide with center of its inscribing circle, hence the ±5% tolerance window.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44365,"title":"An asteroid and a spacecraft","description":"\r\n\u0026#128640 Imagine a non-relativistic simple situation. \r\n\r\nAssume positions p0, p1, p2, and p3 are three dimensional Cartesian coordinates.\r\n\r\nYour spacecraft started from the position p0 at time t0. \r\n\r\nYour spacecraft is moving with a constant velocity.\r\n\r\nYour spacecraft is expected to reach a star at the location p1 at time t1.\r\n\r\nYou just heard over the radio that an asteroid has been identified at the location p2 at time t0.\r\n\r\nThe asteroid is moving with a constant velocity.\r\n\r\nThe asteroid is expected to reach another star at the location p3 at time t1. \r\n\r\nYou need to write a code 'safetrip' in MATLAB to return true if the minimum distance between your spacecraft and the asteroid will be more than the distance d during the time interval between t0 and t1, otherwise return false.","description_html":"\u003cp\u003e\u0026#128640 Imagine a non-relativistic simple situation.\u003c/p\u003e\u003cp\u003eAssume positions p0, p1, p2, and p3 are three dimensional Cartesian coordinates.\u003c/p\u003e\u003cp\u003eYour spacecraft started from the position p0 at time t0.\u003c/p\u003e\u003cp\u003eYour spacecraft is moving with a constant velocity.\u003c/p\u003e\u003cp\u003eYour spacecraft is expected to reach a star at the location p1 at time t1.\u003c/p\u003e\u003cp\u003eYou just heard over the radio that an asteroid has been identified at the location p2 at time t0.\u003c/p\u003e\u003cp\u003eThe asteroid is moving with a constant velocity.\u003c/p\u003e\u003cp\u003eThe asteroid is expected to reach another star at the location p3 at time t1.\u003c/p\u003e\u003cp\u003eYou need to write a code 'safetrip' in MATLAB to return true if the minimum distance between your spacecraft and the asteroid will be more than the distance d during the time interval between t0 and t1, otherwise return false.\u003c/p\u003e","function_template":"function ok = safetrip(d, t0, t1, p0, p1, p2, p3)\r\n    if d\u003e1000000000\r\n        ok = true;\r\n    end\r\nend","test_suite":"%%\r\np0 = [0 0 0];\r\np1 = [1 1 1];\r\np2 = [2 2 2];\r\np3 = [3 3 3];\r\nt0 = 0; \r\nt1 = 1;\r\nd = 1;\r\nok = true;\r\nassert(isequal(safetrip(d, t0, t1, p0, p1, p2, p3), ok))\r\n\r\n%%\r\np0 = [3 3 3];\r\np1 = [2 2 2];\r\np2 = [2 2 2];\r\np3 = [3 3 3];\r\nt0 = 0; \r\nt1 = 1;\r\nd = 1;\r\nok = false;\r\nassert(isequal(safetrip(d, t0, t1, p0, p1, p2, p3), ok))\r\n\r\n%%\r\np0 = [1 2 3];\r\np1 = [4 5 6];\r\np2 = [3 2 1];\r\np3 = [6 5 4];\r\nt0 = 10; \r\nt1 = 20;\r\nd = 2;\r\nok = true;\r\nassert(isequal(safetrip(d, t0, t1, p0, p1, p2, p3), ok))\r\n\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":8,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":168,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":35,"created_at":"2017-10-10T02:30:44.000Z","updated_at":"2026-03-26T15:11:20.000Z","published_at":"2017-10-16T01:51:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026amp;#128640 Imagine a non-relativistic simple situation.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume positions p0, p1, p2, and p3 are three dimensional Cartesian coordinates.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour spacecraft started from the position p0 at time t0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour spacecraft is moving with a constant velocity.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour spacecraft is expected to reach a star at the location p1 at time t1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou just heard over the radio that an asteroid has been identified at the location p2 at time t0.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe asteroid is moving with a constant velocity.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe asteroid is expected to reach another star at the location p3 at time t1.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou need to write a code 'safetrip' in MATLAB to return true if the minimum distance between your spacecraft and the asteroid will be more than the distance d during the time interval between t0 and t1, otherwise return false.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44364,"title":"Is this a valid Tic Tac Toe State?","description":"For the game of \u003chttps://en.wikipedia.org/wiki/Tic-tac-toe Tic Tac Toe\u003e we will be storing the state of the game in a matrix M.\r\n\r\nFor this game: \r\n\r\n\u003c\u003chttps://upload.wikimedia.org/wikipedia/commons/3/32/Tic_tac_toe.svg\u003e\u003e\r\n\r\nWe would store the state as this:\r\n\r\n  -1  1  1 \r\n   1 -1 -1\r\n   1 -1 -1\r\n\r\nIf there were any blanks squares, they would be 0;\r\n\r\nFor this challenge, X goes first. Neither side is compelled to take a win if possible. The game stops when either player wins.\r\n\r\nFor this challenge, is the the given board state\r\n 0: legal \r\n 1: this state can not occur in a game\r\n\r\nThe example in the image would return 0 because if X goes first there can never be more O than X. The state matrix will only hold [-1 0 1], so we are only checking for logic of the game.","description_html":"\u003cp\u003eFor the game of \u003ca href = \"https://en.wikipedia.org/wiki/Tic-tac-toe\"\u003eTic Tac Toe\u003c/a\u003e we will be storing the state of the game in a matrix M.\u003c/p\u003e\u003cp\u003eFor this game:\u003c/p\u003e\u003cimg src = \"https://upload.wikimedia.org/wikipedia/commons/3/32/Tic_tac_toe.svg\"\u003e\u003cp\u003eWe would store the state as this:\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e-1  1  1 \r\n 1 -1 -1\r\n 1 -1 -1\r\n\u003c/pre\u003e\u003cp\u003eIf there were any blanks squares, they would be 0;\u003c/p\u003e\u003cp\u003eFor this challenge, X goes first. Neither side is compelled to take a win if possible. The game stops when either player wins.\u003c/p\u003e\u003cp\u003eFor this challenge, is the the given board state\r\n 0: legal \r\n 1: this state can not occur in a game\u003c/p\u003e\u003cp\u003eThe example in the image would return 0 because if X goes first there can never be more O than X. The state matrix will only hold [-1 0 1], so we are only checking for logic of the game.\u003c/p\u003e","function_template":"function y = isLegalTicTacToeState(M)\r\n  y = round(rand);\r\nend","test_suite":"%%\r\nx = [1 1 0\r\n     0 0 0\r\n     0 0 0];\r\ny_correct = 0;\r\nassert(isequal(isLegalTicTacToeState(x),y_correct))\r\n\r\n%%\r\nx = [0 0 0\r\n     0 0 0\r\n     0 0 0];\r\ny_correct = 1;\r\nassert(isequal(isLegalTicTacToeState(x),y_correct))\r\n\r\n%%\r\nx = [  -1  1  1 \r\n        1 -1 -1\r\n        1 -1 -1];\r\ny_correct = 0;\r\nassert(isequal(isLegalTicTacToeState(x),y_correct))\r\n\r\n%%\r\nx = [ 0 -1 1\r\n     -1  1 0\r\n      1  0 0];\r\ny_correct = 1;\r\nassert(isequal(isLegalTicTacToeState(x),y_correct))\r\n\r\n%%\r\nx = [ 1  1  1\r\n     -1 -1 -1\r\n      0  0  0];\r\ny_correct = 0;\r\nassert(isequal(isLegalTicTacToeState(x),y_correct))\r\n\r\n%%\r\nx = [-1 1 1\r\n     0 -1 1\r\n     1 0 -1];\r\ny_correct = 0;\r\nassert(isequal(isLegalTicTacToeState(x),y_correct))\r\n\r\n%%\r\nx = [-1 1 0\r\n     0 0 0\r\n     0 0 0];\r\ny_correct = 1;\r\nassert(isequal(isLegalTicTacToeState(x),y_correct))\r\n\r\n%%\r\nx = [-1 0 0\r\n     0 0 0\r\n     0 0 0];\r\ny_correct = 0;\r\nassert(isequal(isLegalTicTacToeState(x),y_correct))\r\n\r\n%%\r\nx = [-1 1 0\r\n     0 1 0\r\n     0 1 0];\r\ny_correct = 0;\r\nassert(isequal(isLegalTicTacToeState(x),y_correct))\r\n\r\n%%\r\nx = [1  1  1\r\n     -1 1 -1\r\n     -1 1 -1];\r\ny_correct = 1;\r\nassert(isequal(isLegalTicTacToeState(x),y_correct))\r\n\r\n","published":true,"deleted":false,"likes_count":5,"comments_count":6,"created_by":240,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":123,"test_suite_updated_at":"2017-10-20T22:46:06.000Z","rescore_all_solutions":false,"group_id":35,"created_at":"2017-10-09T23:21:35.000Z","updated_at":"2026-02-03T09:11:08.000Z","published_at":"2017-10-20T22:46:06.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor the game of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Tic-tac-toe\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eTic Tac Toe\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e we will be storing the state of the game in a matrix M.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this game:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe would store the state as this:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[-1  1  1 \\n 1 -1 -1\\n 1 -1 -1]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf there were any blanks squares, they would be 0;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this challenge, X goes first. Neither side is compelled to take a win if possible. The game stops when either player wins.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor this challenge, is the the given board state 0: legal 1: this state can not occur in a game\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe example in the image would return 0 because if X goes first there can never be more O than X. The state matrix will only hold [-1 0 1], so we are only checking for logic of the game.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44359,"title":"5th Time's a Charm","description":"Write a function that will return the input value. However, your function must fail the first four times, only functioning properly every fifth time. Furthermore, the first four times the function is called, successively closer, but not correct, values must be supplied by the function.\r\n\r\nFor example, if x = 10, you may return any number not equal to 10 the first function call. Here, we will return 27. Then, the second function call must return a value between 27 and 10, but not equal to either, and so on, until 10 is returned the fifth time.","description_html":"\u003cp\u003eWrite a function that will return the input value. However, your function must fail the first four times, only functioning properly every fifth time. Furthermore, the first four times the function is called, successively closer, but not correct, values must be supplied by the function.\u003c/p\u003e\u003cp\u003eFor example, if x = 10, you may return any number not equal to 10 the first function call. Here, we will return 27. Then, the second function call must return a value between 27 and 10, but not equal to either, and so on, until 10 is returned the fifth time.\u003c/p\u003e","function_template":"function y = fifth_times_a_charm(x)\r\n y = x;\r\nend","test_suite":"%%\r\nx = 1;\r\ny1 = fifth_times_a_charm(x);\r\nassert(~isequal(y1,x))\r\n\r\ny2 = fifth_times_a_charm(x);\r\nassert(~isequal(y2,x))\r\nassert(abs(x-y2)\u003cabs(x-y1))\r\n\r\ny3 = fifth_times_a_charm(x);\r\nassert(~isequal(y3,x))\r\nassert(abs(x-y3)\u003cabs(x-y2))\r\n\r\ny4 = fifth_times_a_charm(x);\r\nassert(~isequal(y4,x))\r\nassert(abs(x-y4)\u003cabs(x-y3))\r\n\r\ny5 = fifth_times_a_charm(x);\r\nassert(isequal(y5,x))\r\n\r\n%%\r\nx = -1;\r\ny1 = fifth_times_a_charm(x);\r\nassert(~isequal(y1,x))\r\n\r\ny2 = fifth_times_a_charm(x);\r\nassert(~isequal(y2,x))\r\nassert(abs(x-y2)\u003cabs(x-y1))\r\n\r\ny3 = fifth_times_a_charm(x);\r\nassert(~isequal(y3,x))\r\nassert(abs(x-y3)\u003cabs(x-y2))\r\n\r\ny4 = fifth_times_a_charm(x);\r\nassert(~isequal(y4,x))\r\nassert(abs(x-y4)\u003cabs(x-y3))\r\n\r\ny5 = fifth_times_a_charm(x);\r\nassert(isequal(y5,x))\r\n\r\n%%\r\nx = 42;\r\ny1 = fifth_times_a_charm(x);\r\nassert(~isequal(y1,x))\r\n\r\ny2 = fifth_times_a_charm(x);\r\nassert(~isequal(y2,x))\r\nassert(abs(x-y2)\u003cabs(x-y1))\r\n\r\ny3 = fifth_times_a_charm(x);\r\nassert(~isequal(y3,x))\r\nassert(abs(x-y3)\u003cabs(x-y2))\r\n\r\ny4 = fifth_times_a_charm(x);\r\nassert(~isequal(y4,x))\r\nassert(abs(x-y4)\u003cabs(x-y3))\r\n\r\ny5 = fifth_times_a_charm(x);\r\nassert(isequal(y5,x))\r\n\r\n%%\r\nx = i;\r\ny1 = fifth_times_a_charm(x);\r\nassert(~isequal(y1,x))\r\n\r\ny2 = fifth_times_a_charm(x);\r\nassert(~isequal(y2,x))\r\nassert(abs(x-y2)\u003cabs(x-y1))\r\n\r\ny3 = fifth_times_a_charm(x);\r\nassert(~isequal(y3,x))\r\nassert(abs(x-y3)\u003cabs(x-y2))\r\n\r\ny4 = fifth_times_a_charm(x);\r\nassert(~isequal(y4,x))\r\nassert(abs(x-y4)\u003cabs(x-y3))\r\n\r\ny5 = fifth_times_a_charm(x);\r\nassert(isequal(y5,x))","published":true,"deleted":false,"likes_count":7,"comments_count":5,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":193,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":35,"created_at":"2017-10-03T17:35:55.000Z","updated_at":"2026-03-13T03:06:49.000Z","published_at":"2017-10-16T01:51:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function that will return the input value. However, your function must fail the first four times, only functioning properly every fifth time. Furthermore, the first four times the function is called, successively closer, but not correct, values must be supplied by the function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example, if x = 10, you may return any number not equal to 10 the first function call. Here, we will return 27. Then, the second function call must return a value between 27 and 10, but not equal to either, and so on, until 10 is returned the fifth time.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44353,"title":"Group-wise Euclidean distance","description":"*Input*:\r\n \r\n* *x* —— An array of size *n-by-d*, where each row vector denotes a point in a d-dimensional space;\r\n* *g* —— A grouping (index) vector g of size *n-by-1*, which divides the points in x into groups. Specifically, the rows in x corresponding to the same group index in g belong to the same group. \r\n\r\n*Output*: \r\n\r\n* *y* —— The group-wise Euclidean distance matrix associated with the points in x. Suppose that m = max(g), then y will be an *m-by-m* matrix, where each element y(i,j) is the Euclidean distance between group i and group j, which is defined as the minimum of the Euclidean distances between any points in group i and any other points in group j. \r\n\r\n*Example*:\r\n\r\nExample 1: n = 6, d = 1\r\n\r\n  g = [2   1   3  2  1].';\r\n  x = [3  10  15  8  5].';\r\n  y = [0   2   5            % y(1,2) = y(2,1) = min(10-3,5-3,10-8,8-5) = 2\r\n       2   0   7            % y(1,3) = y(3,1) = min(15-10,15-5) = 5\r\n       5   7   0];          % y(2,3) = y(3,2) = min(15-3,15-8) = 7\r\n\r\nExample 2: n = 3, d = 2\r\n\r\n  g = [1 2 2].';\r\n  x = [0   0\r\n       5  12\r\n       3   4];\r\n  y = [0  5;\r\n       5  0];    % y(1,2) = y(2,1) = min(sqrt(5^2+12^2),sqrt(3^2+4^2)) = 5\r\n  \r\n*Testing*:\r\n\r\nThe test suite will focus mainly on the large-scale problem dimensions (e.g., large n and/or d). The purpose is to direct attention towards efficient runtime speed of execution. Note that your solution may run into a time-out error if it is not sufficiently efficient (which is why this problem falls into the \u003chttps://www.mathworks.com/matlabcentral/cody/groups/35 Cody5:Hard\u003e category).\r\n\r\n*Scoring*:\r\n\r\nWe have modified Cody's default size-based scoring function into a performance-based scoring system (implemented by our fellow Cody player \u003chttps://www.mathworks.com/matlabcentral/cody/players/3021298-ly-cao LY Cao\u003e), in which the score of your submission equals 5 times the execution time of your solution (which reprents a score resolution of 0.2 seconds and allows for more room for performance improvement). Please ignore the code size and focus only on improving the code performance, as our test suite will reject any submissions running longer than 20 seconds (in contrast to Cody's default 40 seconds timeout limit).  \r\n\r\nPlease be advised that an amazingly fast solution would earn a score \u003c 5, meaning that it completes execution of all test cases within a second!\r\n\r\n*Update* (11/21/2017):\r\nAdditional test cases are added to ban cheater solutions (e.g., hard-coded submissions 1351541, 1351007, 1350563, 1349442, all came from \u003chttps://www.mathworks.com/matlabcentral/cody/players/3931805-marco-tullio Marco Tullio\u003e).\r\n","description_html":"\u003cp\u003e\u003cb\u003eInput\u003c/b\u003e:\u003c/p\u003e\u003cul\u003e\u003cli\u003e\u003cb\u003ex\u003c/b\u003e —— An array of size \u003cb\u003en-by-d\u003c/b\u003e, where each row vector denotes a point in a d-dimensional space;\u003c/li\u003e\u003cli\u003e\u003cb\u003eg\u003c/b\u003e —— A grouping (index) vector g of size \u003cb\u003en-by-1\u003c/b\u003e, which divides the points in x into groups. Specifically, the rows in x corresponding to the same group index in g belong to the same group.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003e\u003cb\u003eOutput\u003c/b\u003e:\u003c/p\u003e\u003cul\u003e\u003cli\u003e\u003cb\u003ey\u003c/b\u003e —— The group-wise Euclidean distance matrix associated with the points in x. Suppose that m = max(g), then y will be an \u003cb\u003em-by-m\u003c/b\u003e matrix, where each element y(i,j) is the Euclidean distance between group i and group j, which is defined as the minimum of the Euclidean distances between any points in group i and any other points in group j.\u003c/li\u003e\u003c/ul\u003e\u003cp\u003e\u003cb\u003eExample\u003c/b\u003e:\u003c/p\u003e\u003cp\u003eExample 1: n = 6, d = 1\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eg = [2   1   3  2  1].';\r\nx = [3  10  15  8  5].';\r\ny = [0   2   5            % y(1,2) = y(2,1) = min(10-3,5-3,10-8,8-5) = 2\r\n     2   0   7            % y(1,3) = y(3,1) = min(15-10,15-5) = 5\r\n     5   7   0];          % y(2,3) = y(3,2) = min(15-3,15-8) = 7\r\n\u003c/pre\u003e\u003cp\u003eExample 2: n = 3, d = 2\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eg = [1 2 2].';\r\nx = [0   0\r\n     5  12\r\n     3   4];\r\ny = [0  5;\r\n     5  0];    % y(1,2) = y(2,1) = min(sqrt(5^2+12^2),sqrt(3^2+4^2)) = 5\r\n\u003c/pre\u003e\u003cp\u003e\u003cb\u003eTesting\u003c/b\u003e:\u003c/p\u003e\u003cp\u003eThe test suite will focus mainly on the large-scale problem dimensions (e.g., large n and/or d). The purpose is to direct attention towards efficient runtime speed of execution. Note that your solution may run into a time-out error if it is not sufficiently efficient (which is why this problem falls into the \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/groups/35\"\u003eCody5:Hard\u003c/a\u003e category).\u003c/p\u003e\u003cp\u003e\u003cb\u003eScoring\u003c/b\u003e:\u003c/p\u003e\u003cp\u003eWe have modified Cody's default size-based scoring function into a performance-based scoring system (implemented by our fellow Cody player \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/players/3021298-ly-cao\"\u003eLY Cao\u003c/a\u003e), in which the score of your submission equals 5 times the execution time of your solution (which reprents a score resolution of 0.2 seconds and allows for more room for performance improvement). Please ignore the code size and focus only on improving the code performance, as our test suite will reject any submissions running longer than 20 seconds (in contrast to Cody's default 40 seconds timeout limit).\u003c/p\u003e\u003cp\u003ePlease be advised that an amazingly fast solution would earn a score \u0026lt; 5, meaning that it completes execution of all test cases within a second!\u003c/p\u003e\u003cp\u003e\u003cb\u003eUpdate\u003c/b\u003e (11/21/2017):\r\nAdditional test cases are added to ban cheater solutions (e.g., hard-coded submissions 1351541, 1351007, 1350563, 1349442, all came from \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/players/3931805-marco-tullio\"\u003eMarco Tullio\u003c/a\u003e).\u003c/p\u003e","function_template":"function y = groupDist(x,g)\r\n  y = x;\r\nend","test_suite":"%%\r\nassessFunctionAbsence({'regexp','regexpi','regexprep','str2num','tic','toc','persistent','global','rng','assert','!','system','unix','noCheater'},'FileName','groupDist.m')\r\n\r\n%%\r\nfid = fopen('noCheater.p','Wb');\r\nfwrite(fid, hex2dec(reshape([\r\n    '7630312E30307630302E30300007701CAB777FB100000015000000740000007E3D5C20F'...'\r\n    '5319EEB8B0D3D9C9C87C18B91C13D7310D9D8E837C95E62D49A3FE08B071790DBC222B5'...\r\n    '839E9A19EA6AA7CF3785A7E7CEC1CFE46E0E9A5DB7C82D69A4FAB7BF308D0871C342A5F'...\r\n    'EF9AF61623F1D97F80207388D54ABA3CB3D551617DA33AA3F5040CD425FC9B29E2A4233'...\r\n    'AE7C5ADEF399'],2,[]).')); rehash path; \r\nfclose(fid); \r\nassert(noCheater(),'Cheater detected!')\r\n\r\n%%\r\ng = [2   1   3  2  1].';\r\nx = [3  10  15  8  5].';\r\ny_correct = [0   2   5            \r\n             2   0   7      \r\n             5   7   0]; \r\nassert(isequaln(y_correct,groupDist(x,g)))\r\n\r\n%%\r\ng = [1 2 2].';\r\nx = [0   0\r\n     5  12\r\n     3   4];\r\ny_correct = [0  5;\r\n             5  0];    \r\nassert(isequal(y_correct,groupDist(x,g)))\r\n\r\n%%\r\ng = [2 2 3 3 3 1].';\r\nx = [-5   12\r\n      3    4\r\n     -7  -24\r\n     25    4\r\n      9   40\r\n      0    0];\r\ny_correct = [0    5   25;\r\n             5    0   22\r\n             25  22    0];  \r\nassert(isequal(y_correct,groupDist(x,g)))\r\n\r\n%% Randomized case to disallow hard-coded solution\r\ng = randperm(10).';\r\nx = rand(10,1);\r\na = sortrows([g,x]);\r\ny_correct = abs(a(:,2)-a(:,2).');\r\nassert(isequal(round(y_correct,10),round(groupDist(x,g),10))) \r\n\r\n%% Additional test case to disallow hard-coded solution\r\ng = [1,2,3].';\r\nx = [2,5,10].';\r\ny_correct = [0   3   8            \r\n             3   0   5      \r\n             8   5   0]; \r\nassert(isequaln(y_correct,groupDist(x,g)))\r\n\r\n%%\r\nglobal t\r\nt = zeros(1,3); \r\nrng(923,'twister');\r\nn = 5e3; d = 3; m = 5;\r\nx = rand(n,d);\r\ng = randi(m,n,1); \r\ny_correct = [0,0.00653919638188362,0.00319052186150122,0.00858841434457234,0.00359654235965771\r\n             0.00653919638188362,0,0.00855286615862212,0.00589790293838067,0.00484910151004134\r\n             0.00319052186150122,0.00855286615862212,0,0.00591041083080696,0.00483607360689871\r\n             0.00858841434457234,0.00589790293838067,0.00591041083080696,0,0.00695738487959094\r\n             0.00359654235965771,0.00484910151004134,0.00483607360689871,0.00695738487959094,0];\r\ntic, y = groupDist(x,g); t(1) = toc;\r\nassert(isequal(round(y_correct,10),round(y,10))) \r\n\r\n%%\r\nglobal t\r\nrng(123) \r\nrng(max('cody5'),'combRecursive');\r\nn = 5e3; d = 3; m = 100;\r\nx = 10*rand(n,d);\r\ng = randi(m,n,1); \r\ntic, y = groupDist(x,g); t(2) = toc;\r\nassert(norm(y-y.') \u003c 1e-11 \u0026\u0026 all(~diag(y)) \u0026\u0026 all(size(y)==m) \u0026\u0026 abs(det(y)-0.030846735888559)\u003c1e-8 \u0026\u0026...\r\n    abs(cond(y)-1.606720826682107e+04) \u003c 1e-6 \u0026\u0026 abs(max(nonzeros(y))-1.058563379304832)\u003c1e-10 \u0026\u0026...\r\n    abs(mean(nonzeros(y))-0.419901913602729)\u003c1e-8)\r\n\r\n%%\r\nglobal t \r\nrng(sum('Cody5, Oct. 16, 2017'),'multFibonacci') \r\nn = 5e3; d = 1e2;  m = 100;\r\nx = 5*randn(n,d) + 20;\r\ng = randi(m,n,1); \r\ntic, y = groupDist(x,g); t(3) = toc;\r\nassert(norm(y-y.') \u003c 1e-11 \u0026\u0026 all(~diag(y)) \u0026\u0026 all(size(y)==m) \u0026\u0026 ...\r\n    abs(cond(y)-2.024633860688276e+02) \u003c 1e-8 \u0026\u0026 abs(max(nonzeros(y))-57.768463869822135)\u003c1e-10 \u0026\u0026...\r\n    abs(mean(nonzeros(y))-53.852605466762945)\u003c1e-8) \r\n \r\n%%\r\nglobal t\r\nfid = fopen('score.p','Wb');\r\nfwrite(fid,uint8(sscanf([...\r\n     '7630312E30307630302E3030000B901C454EFFB100000031000001330000018D483A60'...\r\n     '366BC9545F84AE26323B67424D4E8A7A2E5B7D8ACAA45A1C3C5C8B33E245C95243E3CB'...\r\n     'AF5D0D993BDA70B7AB5DA365A83E8CA87FFC45265E23EF80943784C5F48E6E53D5DA34'...\r\n     'F1F2ECD34683EABE3B7461DC9E8004CC50B2A79D73495F6F625B5365602B2E6C6093D2'...\r\n     '997D371DA457CE82327E686AF512A507B2CB62A375BFD1B283DDD2C01EDEF2771EDAA3'...\r\n     '6ABB4852BA4061E20149688E812EB41A9AF8627EF35755492D2830EB8718BCFE88027E'...\r\n     '6EA960B63A3B3E26E0451B1DCF14F3C20E70D9D93B08E7FF4AE8D82E7CC38042FD38F7'...\r\n     'A14D312EF5652823FEB7E8B52AF5C69F5E7D16B116B5F979EDA77459D6BB61B7971A51'...\r\n     '041227DD601319D667DF62E8DA5E381FDD07A2806FE835BD2569E5315CDFC19C6B6A2B'...\r\n     '4F0FF6BA803F1759ACAB133CCFAB6D5A5D002FC2C5F381F0'],'%2X')));\r\nfclose(fid);\r\nscore(round(5*sum(t)))\r\nfprintf('The execution time of test case %d is %.5f seconds \\n',[5:7;t])\r\nfprintf('The total execution time is %.5f seconds \\n',sum(t))\r\nassert(sum(t)\u003c20, 'Sorry, your solution is too slow. The execution time must not exceed 20 seconds.')\r\n","published":true,"deleted":false,"likes_count":7,"comments_count":4,"created_by":12569,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":75,"test_suite_updated_at":"2017-11-21T22:49:00.000Z","rescore_all_solutions":false,"group_id":35,"created_at":"2017-10-01T04:33:43.000Z","updated_at":"2026-02-03T09:16:35.000Z","published_at":"2017-10-16T01:51:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eInput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e —— An array of size\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en-by-d\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, where each row vector denotes a point in a d-dimensional space;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eg\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e —— A grouping (index) vector g of size\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en-by-1\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, which divides the points in x into groups. Specifically, the rows in x corresponding to the same group index in g belong to the same group.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eOutput\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ey\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e —— The group-wise Euclidean distance matrix associated with the points in x. Suppose that m = max(g), then y will be an\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003em-by-m\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e matrix, where each element y(i,j) is the Euclidean distance between group i and group j, which is defined as the minimum of the Euclidean distances between any points in group i and any other points in group j.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eExample\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 1: n = 6, d = 1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[g = [2   1   3  2  1].';\\nx = [3  10  15  8  5].';\\ny = [0   2   5            % y(1,2) = y(2,1) = min(10-3,5-3,10-8,8-5) = 2\\n     2   0   7            % y(1,3) = y(3,1) = min(15-10,15-5) = 5\\n     5   7   0];          % y(2,3) = y(3,2) = min(15-3,15-8) = 7]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample 2: n = 3, d = 2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[g = [1 2 2].';\\nx = [0   0\\n     5  12\\n     3   4];\\ny = [0  5;\\n     5  0];    % y(1,2) = y(2,1) = min(sqrt(5^2+12^2),sqrt(3^2+4^2)) = 5]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eTesting\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe test suite will focus mainly on the large-scale problem dimensions (e.g., large n and/or d). The purpose is to direct attention towards efficient runtime speed of execution. Note that your solution may run into a time-out error if it is not sufficiently efficient (which is why this problem falls into the\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/groups/35\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eCody5:Hard\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e category).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eScoring\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe have modified Cody's default size-based scoring function into a performance-based scoring system (implemented by our fellow Cody player\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/players/3021298-ly-cao\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eLY Cao\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e), in which the score of your submission equals 5 times the execution time of your solution (which reprents a score resolution of 0.2 seconds and allows for more room for performance improvement). Please ignore the code size and focus only on improving the code performance, as our test suite will reject any submissions running longer than 20 seconds (in contrast to Cody's default 40 seconds timeout limit).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlease be advised that an amazingly fast solution would earn a score \u0026lt; 5, meaning that it completes execution of all test cases within a second!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eUpdate\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e (11/21/2017): Additional test cases are added to ban cheater solutions (e.g., hard-coded submissions 1351541, 1351007, 1350563, 1349442, all came from\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/players/3931805-marco-tullio\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eMarco Tullio\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44347,"title":"Ned's queens","description":"A tribute to Cody's five-year anniversary should also celebrate the people behind Cody, and in this particular case, our illustrious Quizmaster, Ned Gulley.\r\n\r\nThe N-Queens problem (N stands for Ned, of course) is a well known computing challenge. If you are unfamiliar with this problem, refer to \u003chttps://www.mathworks.com/matlabcentral/cody/problems/113-n-queens-checker Problem 113\u003e, incidentally written by... You guessed it.\r\n\r\nThis problem is the real deal. Given a positive integer, n, representing the number of queens and the size of the board, return the number of possible solutions, s, and a list of the solutions, q.\r\n\r\nq shall be an array with s rows and n columns, such that each row represents one solution. The column indeces of q shall represent the column indeces of the positions of the queens in the respective solution, while the values of the array elements shall represent the row indeces of the positions of the queens in the respective solution. q does not have to be sorted.\r\n\r\nNote: All symmetries/rotations count as individual solutions.\r\n\r\nExample:\r\n\r\n Input: n = 4\r\n\r\n Output: s = 2, q = [2 4 1 3;3 1 4 2]","description_html":"\u003cp\u003eA tribute to Cody's five-year anniversary should also celebrate the people behind Cody, and in this particular case, our illustrious Quizmaster, Ned Gulley.\u003c/p\u003e\u003cp\u003eThe N-Queens problem (N stands for Ned, of course) is a well known computing challenge. If you are unfamiliar with this problem, refer to \u003ca href = \"https://www.mathworks.com/matlabcentral/cody/problems/113-n-queens-checker\"\u003eProblem 113\u003c/a\u003e, incidentally written by... You guessed it.\u003c/p\u003e\u003cp\u003eThis problem is the real deal. Given a positive integer, n, representing the number of queens and the size of the board, return the number of possible solutions, s, and a list of the solutions, q.\u003c/p\u003e\u003cp\u003eq shall be an array with s rows and n columns, such that each row represents one solution. The column indeces of q shall represent the column indeces of the positions of the queens in the respective solution, while the values of the array elements shall represent the row indeces of the positions of the queens in the respective solution. q does not have to be sorted.\u003c/p\u003e\u003cp\u003eNote: All symmetries/rotations count as individual solutions.\u003c/p\u003e\u003cp\u003eExample:\u003c/p\u003e\u003cpre\u003e Input: n = 4\u003c/pre\u003e\u003cpre\u003e Output: s = 2, q = [2 4 1 3;3 1 4 2]\u003c/pre\u003e","function_template":"function [s, q] = nqueens(n)\r\n    s = n;\r\n    q = 1:n;\r\nend","test_suite":"%%\r\nn = 1;\r\ns_correct = 1;\r\nq_correct = 1;\r\n[s, q] = nqueens(n);\r\nassert(isequal(s,s_correct) \u0026\u0026 isequal(sortrows(q),sortrows(q_correct)))\r\n\r\n%%\r\nn = 2;\r\ns_correct = 0;\r\n[s, q] = nqueens(n);\r\nassert(isequal(s,s_correct) \u0026\u0026 isempty(q))\r\n\r\n%%\r\nn = 3;\r\ns_correct = 0;\r\n[s, q] = nqueens(n);\r\nassert(isequal(s,s_correct) \u0026\u0026 isempty(q))\r\n\r\n%%\r\nn = 4;\r\ns_correct = 2;\r\nq_correct = [3  1  4  2;2  4  1  3]\r\n[s, q] = nqueens(n);\r\nassert(isequal(s,s_correct) \u0026\u0026 isequal(sortrows(q),sortrows(q_correct)))\r\n\r\n%%\r\nn = 5;\r\ns_correct = 10;\r\nq_correct = [5  3  1  4  2;5  2  4  1  3;4  2  5  3  1;4  1  3  5  2;3  5  2  4  1;3  1  4  2  5;2  4  1  3  5;2  5  3  1  4;1  4  2  5  3;1  3  5  2  4];\r\n[s, q] = nqueens(n);\r\nassert(isequal(s,s_correct) \u0026\u0026 isequal(sortrows(q),sortrows(q_correct)))\r\n\r\n%%\r\nn = 6;\r\ns_correct = 4;\r\nq_correct = [5  3  1  6  4  2;4  1  5  2  6  3;3  6  2  5  1  4;2  4  6  1  3  5];\r\n[s, q] = nqueens(n);\r\nassert(isequal(s,s_correct) \u0026\u0026 isequal(sortrows(q),sortrows(q_correct)))\r\n\r\n%%\r\nn = 7;\r\ns_correct = 40;\r\nq_correct = [7  5  3  1  6  4  2;7  4  1  5  2  6  3;7  3  6  2  5  1  4;7  2  4  6  1  3  5;6  4  7  1  3  5  2;6  4  2  7  5  3  1;6  3  5  7  1  4  2;6  3  7  4  1  5  2;6  3  1  4  7  5  2;6  2  5  1  4  7  3;6  1  3  5  7  2  4;5  7  2  4  6  1  3;5  7  2  6  3  1  4;5  3  1  6  4  2  7;5  2  6  3  7  4  1;5  1  4  7  3  6  2;5  1  6  4  2  7  3;4  6  1  3  5  7  2;4  7  5  2  6  1  3;4  7  3  6  2  5  1;4  2  7  5  3  1  6;4  1  5  2  6  3  7;4  1  3  6  2  7  5;3  6  2  5  1  4  7;3  5  7  2  4  6  1;3  7  4  1  5  2  6;3  7  2  4  6  1  5;3  1  6  4  2  7  5;3  1  6  2  5  7  4;2  6  3  7  4  1  5;2  5  3  1  7  4  6;2  5  7  4  1  3  6;2  5  1  4  7  3  6;2  4  6  1  3  5  7;2  4  1  7  5  3  6;2  7  5  3  1  6  4;1  6  4  2  7  5  3;1  5  2  6  3  7  4;1  4  7  3  6  2  5;1  3  5  7  2  4  6];\r\n[s, q] = nqueens(n);\r\nassert(isequal(s,s_correct) \u0026\u0026 isequal(sortrows(q),sortrows(q_correct)))\r\n\r\n%%\r\nn = 8;\r\ns_correct = 92;\r\nq_correct = [8  4  1  3  6  2  7  5\r\n8  3  1  6  2  5  7  4;8  2  5  3  1  7  4  6;8  2  4  1  7  5  3  6;7  5  3  1  6  8  2  4;7  4  2  5  8  1  3  6;7  4  2  8  6  1  3  5;7  3  8  2  5  1  6  4;7  3  1  6  8  5  2  4;7  2  6  3  1  4  8  5;7  2  4  1  8  5  3  6;7  1  3  8  6  4  2  5;6  8  2  4  1  7  5  3;6  4  7  1  8  2  5  3;6  4  7  1  3  5  2  8;6  4  2  8  5  7  1  3;6  4  1  5  8  2  7  3;6  3  5  8  1  4  2  7;6  3  5  7  1  4  2  8;6  3  7  4  1  8  2  5;6  3  7  2  4  8  1  5;6  3  7  2  8  5  1  4;6  3  1  7  5  8  2  4;6  3  1  8  4  2  7  5;6  3  1  8  5  2  4  7;6  2  7  1  4  8  5  3;6  2  7  1  3  5  8  4;6  1  5  2  8  3  7  4;5  7  4  1  3  8  6  2;5  7  2  4  8  1  3  6;5  7  2  6  3  1  8  4;5  7  2  6  3  1  4  8;5  7  1  4  2  8  6  3;5  7  1  3  8  6  4  2;5  8  4  1  3  6  2  7;5  8  4  1  7  2  6  3;5  3  8  4  7  1  6  2;5  3  1  7  2  8  6  4;5  3  1  6  8  2  4  7;5  2  6  1  7  4  8  3;5  2  8  1  4  7  3  6;5  2  4  6  8  3  1  7;5  2  4  7  3  8  6  1;5  1  8  6  3  7  2  4;5  1  8  4  2  7  3  6;5  1  4  6  8  2  7  3;4  7  5  3  1  6  8  2;4  7  5  2  6  1  3  8;4  7  3  8  2  5  1  6;4  7  1  8  5  2  6  3;4  6  8  3  1  7  5  2;4  6  8  2  7  1  3  5;4  6  1  5  2  8  3  7;4  8  5  3  1  7  2  6;4  8  1  5  7  2  6  3;4  8  1  3  6  2  7  5;4  2  5  8  6  1  3  7;4  2  8  5  7  1  3  6;4  2  8  6  1  3  5  7;4  2  7  5  1  8  6  3;4  2  7  3  6  8  5  1;4  2  7  3  6  8  1  5;4  1  5  8  6  3  7  2;4  1  5  8  2  7  3  6;3  7  2  8  5  1  4  6;3  7  2  8  6  4  1  5;3  6  4  2  8  5  7  1;3  6  4  1  8  5  7  2;3  6  8  2  4  1  7  5;3  6  8  1  4  7  5  2;3  6  8  1  5  7  2  4;3  6  2  5  8  1  7  4;3  6  2  7  5  1  8  4;3  6  2  7  1  4  8  5;3  5  7  1  4  2  8  6;3  5  8  4  1  7  2  6;3  5  2  8  6  4  7  1;3  5  2  8  1  7  4  6;3  8  4  7  1  6  2  5;3  1  7  5  8  2  4  6;2  7  5  8  1  4  6  3;2  7  3  6  8  5  1  4;2  6  8  3  1  4  7  5;2  6  1  7  4  8  3  5;2  5  7  4  1  8  6  3;2  5  7  1  3  8  6  4;2  4  6  8  3  1  7  5;2  8  6  1  3  5  7  4;1  7  5  8  2  4  6  3;1  7  4  6  8  2  5  3;1  6  8  3  7  4  2  5;1  5  8  6  3  7  2  4];\r\n[s, q] = nqueens(n);\r\nassert(isequal(s,s_correct) \u0026\u0026 isequal(sortrows(q),sortrows(q_correct)))\r\n\r\n%%\r\nn = 9;\r\ns_correct = 352;\r\nq_correct = [9  7  4  2  8  6  1  3  5;9  7  3  8  2  5  1  6  4;9  7  2  4  1  8  5  3  6;9  6  8  2  4  1  7  5  3;9  6  4  7  1  8  2  5  3;9  6  4  2  8  5  7  1  3;9  6  3  7  2  8  5  1  4;9  6  3  1  8  5  2  4  7;9  6  2  7  1  3  5  8  4;9  5  8  4  1  7  2  6  3;9  5  3  8  4  7  1  6  2;9  5  3  1  7  2  8  6  4;9  5  3  1  6  8  2  4  7;9  5  1  8  4  2  7  3  6;9  5  1  4  6  8  2  7  3;9  4  6  8  3  1  7  5  2;9  4  6  8  2  7  1  3  5;9  4  8  1  3  6  2  7  5;9  4  2  5  8  6  1  3  7;9  4  2  7  3  6  8  1  5;9  4  1  5  8  2  7  3  6;9  3  6  4  1  8  5  7  2;9  3  6  2  7  5  1  8  4;9  3  6  2  7  1  4  8  5;9  3  5  2  8  1  7  4  6;9  2  6  8  3  1  4  7  5;9  2  5  7  4  1  8  6  3;9  2  5  7  1  3  8  6  4;8  6  9  3  1  4  7  5  2;8  6  3  9  7  1  4  2  5;8  6  2  7  1  4  9  5  3;8  6  1  3  5  7  9  4  2;8  6  1  3  7  9  4  2  5;8  5  3  6  9  7  1  4  2;8  5  3  9  7  2  4  6  1;8  5  3  1  7  4  6  9  2;8  5  3  1  6  2  9  7  4;8  5  2  9  7  4  1  3  6;8  5  2  9  1  4  7  3  6;8  5  2  4  1  7  9  6  3;8  5  2  4  1  7  9  3  6;8  5  1  6  9  2  4  7  3;8  4  7  9  2  6  1  3  5;8  4  9  7  3  1  6  2  5;8  4  9  3  5  7  1  6  2;8  4  9  3  6  2  7  5  1;8  4  9  1  5  2  6  3  7;8  4  1  7  5  2  6  9  3;8  3  5  9  1  6  4  2  7;8  3  5  2  9  6  4  7  1;8  3  1  4  7  9  6  2  5;8  2  5  7  1  4  6  9  3;8  2  4  1  7  9  6  3  5;8  2  9  6  3  1  4  7  5;8  1  5  7  2  6  3  9  4;8  1  4  6  3  9  7  5  2;8  1  4  7  5  2  9  6  3;8  1  4  7  3  6  9  2  5;7  9  6  3  1  8  5  2  4;7  9  4  2  5  8  6  1  3;7  9  3  5  2  8  6  4  1;7  9  3  8  2  4  6  1  5;7  9  2  6  1  3  5  8  4;7  9  1  3  5  8  2  4  6;7  5  8  2  9  3  6  4  1;7  5  8  2  9  6  3  1  4;7  5  3  9  6  8  2  4  1;7  5  2  8  1  4  9  3  6;7  5  2  8  1  3  9  6  4;7  5  1  6  9  3  8  4  2;7  5  1  8  6  3  9  2  4;7  4  8  3  9  6  2  5  1;7  4  8  1  5  9  2  6  3;7  4  2  5  8  1  3  6  9;7  4  2  5  9  1  3  8  6;7  4  2  8  6  1  3  5  9;7  4  2  9  5  1  8  6  3;7  4  2  9  6  3  5  8  1;7  4  1  5  2  9  6  8  3;7  4  1  8  5  3  6  9  2;7  4  1  8  2  9  6  3  5;7  4  1  3  8  6  2  9  5;7  4  1  3  6  9  2  8  5;7  4  1  3  9  6  8  5  2;7  4  1  9  2  6  8  3  5;7  3  6  8  1  4  9  5  2;7  3  6  8  1  5  9  2  4;7  3  6  2  5  1  9  4  8;7  3  8  6  2  9  5  1  4;7  3  8  2  5  1  9  4  6;7  3  8  2  4  6  9  5  1;7  3  1  6  8  5  2  4  9;7  3  1  9  5  8  2  4  6;7  2  6  3  1  8  5  9  4;7  2  4  6  1  9  5  3  8;7  2  4  9  1  8  5  3  6;7  2  4  1  8  5  9  6  3;7  2  8  6  1  3  5  9  4;7  1  6  9  2  4  8  3  5;7  1  6  2  5  8  4  9  3;7  1  6  8  2  4  9  3  5;7  1  4  6  9  3  5  8  2;7  1  4  2  8  6  9  3  5;7  1  4  8  5  3  9  6  2;7  1  8  5  2  9  3  6  4;6  8  5  2  9  7  4  1  3;6  8  3  7  9  2  5  1  4;6  8  3  1  9  2  5  7  4;6  8  3  1  9  5  2  4  7;6  8  2  7  1  3  5  9  4;6  8  1  5  9  2  4  7  3;6  8  1  7  4  2  9  5  3;6  9  7  4  1  8  2  5  3;6  9  5  8  1  3  7  2  4;6  9  5  2  8  3  7  4  1;6  9  5  1  8  4  2  7  3;6  9  3  1  8  4  2  7  5;6  9  1  4  7  3  8  2  5;6  4  7  1  8  5  2  9  3;6  4  7  1  8  2  5  3  9;6  4  7  1  3  9  2  8  5;6  4  9  5  8  2  7  3  1;6  4  9  1  5  2  8  3  7;6  4  9  1  3  7  2  8  5;6  4  2  8  5  9  1  3  7;6  4  2  8  5  3  1  9  7;6  4  2  8  3  9  7  5  1;6  4  2  7  9  3  5  8  1;6  4  1  7  9  2  8  5  3;6  3  7  4  1  9  2  5  8;6  3  7  2  4  8  1  5  9;6  3  7  2  4  9  1  8  5;6  3  7  2  8  5  1  4  9;6  3  9  7  1  4  2  5  8;6  3  9  4  1  8  2  5  7;6  3  9  2  5  8  1  7  4;6  3  5  8  1  4  2  7  9;6  3  5  8  1  9  4  2  7;6  3  5  8  1  9  7  2  4;6  3  1  4  7  9  2  5  8;6  3  1  8  5  2  9  7  4;6  3  1  8  4  9  7  5  2;6  2  9  5  3  8  4  7  1;6  2  5  7  9  4  8  1  3;6  2  5  7  9  3  8  4  1;6  1  7  4  8  3  5  9  2;6  1  5  7  9  4  2  8  3;6  1  5  7  9  3  8  2  4;6  1  5  2  9  7  4  8  3;5  8  6  9  3  1  7  4  2;5  8  6  1  3  7  9  4  2;5  8  4  9  7  3  1  6  2;5  8  4  1  7  2  6  3  9;5  8  4  1  3  6  9  7  2;5  8  2  9  6  3  1  4  7;5  8  2  9  3  1  7  4  6;5  8  2  7  3  6  9  1  4;5  8  2  7  3  1  9  4  6;5  8  1  9  4  2  7  3  6;5  8  1  4  7  3  6  9  2;5  7  9  4  8  1  3  6  2;5  7  9  4  2  8  6  3  1;5  7  9  3  8  2  4  6  1;5  7  4  1  8  2  9  6  3;5  7  4  1  3  8  6  2  9;5  7  4  1  3  9  6  8  2;5  7  4  1  3  6  9  2  8;5  7  2  6  3  1  8  4  9;5  7  2  6  8  1  4  9  3;5  7  2  4  8  1  3  9  6;5  7  2  4  8  1  9  6  3;5  7  1  6  8  2  4  9  3;5  7  1  4  2  8  6  9  3;5  9  4  6  8  2  7  1  3;5  9  2  6  8  3  1  4  7;5  9  2  4  7  3  8  6  1;5  3  6  9  7  4  1  8  2;5  3  6  9  7  2  4  8  1;5  3  6  9  7  1  4  2  8;5  3  6  9  2  8  1  4  7;5  3  9  6  8  2  4  1  7;5  3  9  4  2  8  6  1  7;5  3  8  6  2  9  7  1  4;5  3  8  6  2  9  1  4  7;5  3  8  4  7  9  2  6  1;5  3  8  4  2  9  6  1  7;5  3  1  6  8  2  4  7  9;5  3  1  6  2  9  7  4  8;5  3  1  7  2  8  6  4  9;5  2  6  9  7  4  1  3  8;5  2  6  9  3  8  4  7  1;5  2  6  1  3  7  9  4  8;5  2  9  6  3  7  4  1  8;5  2  9  1  6  8  3  7  4;5  2  4  9  7  3  1  6  8;5  2  4  1  7  9  3  6  8;5  2  8  3  7  4  1  9  6;5  2  8  3  7  9  1  6  4;5  2  8  1  4  7  9  6  3;5  2  8  1  7  9  3  6  4;5  1  6  4  2  8  3  9  7;5  1  8  6  3  7  2  4  9;5  1  8  4  2  7  9  6  3;4  8  5  3  1  6  2  9  7;4  8  5  3  1  7  2  6  9;4  8  1  5  7  2  6  3  9;4  7  5  2  9  6  8  3  1;4  7  5  2  9  1  3  8  6;4  7  5  2  9  1  6  8  3;4  7  9  6  3  1  8  5  2;4  7  9  2  5  8  1  3  6;4  7  9  2  6  1  3  5  8;4  7  3  6  9  1  8  5  2;4  7  3  8  6  2  9  5  1;4  7  3  8  6  1  9  2  5;4  7  3  8  2  5  9  6  1;4  7  1  6  9  2  8  5  3;4  7  1  3  9  6  8  5  2;4  7  1  8  5  2  9  3  6;4  6  8  3  1  7  5  2  9;4  6  8  2  5  7  9  1  3;4  6  8  2  5  1  9  7  3;4  6  8  2  7  1  3  5  9;4  6  9  3  1  8  2  5  7;4  6  3  9  7  1  8  2  5;4  6  3  9  2  8  5  7  1;4  6  3  9  2  5  8  1  7;4  6  1  5  2  8  3  7  9;4  6  1  9  5  8  2  7  3;4  6  1  9  7  3  8  2  5;4  9  5  8  1  3  6  2  7;4  9  5  3  1  6  8  2  7;4  9  5  3  1  7  2  8  6;4  9  3  6  2  7  5  1  8;4  2  7  9  1  8  5  3  6;4  2  7  9  1  5  8  6  3;4  2  7  3  1  8  5  9  6;4  2  5  8  1  3  6  9  7;4  2  9  5  1  8  6  3  7;4  2  9  3  6  8  1  5  7;4  2  8  3  9  7  5  1  6;4  1  7  9  2  6  8  3  5;4  1  5  9  2  6  8  3  7;4  1  5  2  9  7  3  8  6;4  1  5  8  2  7  3  6  9;4  1  9  6  3  7  2  8  5;4  1  3  6  9  2  8  5  7;3  8  6  4  9  1  5  7  2;3  8  6  9  2  5  1  4  7;3  8  6  1  9  2  5  7  4;3  8  4  7  9  2  5  1  6;3  8  2  4  9  7  5  1  6;3  7  4  8  5  9  1  6  2;3  7  4  2  9  5  1  8  6;3  7  4  2  9  6  1  5  8;3  7  9  4  2  5  8  6  1;3  7  9  1  5  2  8  6  4;3  7  2  4  8  1  5  9  6;3  7  2  8  5  9  1  6  4;3  7  2  8  6  4  1  5  9;3  6  8  5  2  9  7  4  1;3  6  8  5  1  9  7  2  4;3  6  8  2  4  9  7  5  1;3  6  8  1  5  9  2  4  7;3  6  8  1  4  7  5  2  9;3  6  9  5  8  1  4  2  7;3  6  9  7  4  1  8  2  5;3  6  9  7  2  4  8  1  5;3  6  9  7  1  4  2  5  8;3  6  9  2  5  7  4  1  8;3  6  9  2  8  1  4  7  5;3  6  9  1  8  4  2  7  5;3  6  2  9  5  1  8  4  7;3  6  2  7  1  4  8  5  9;3  5  7  1  4  2  8  6  9;3  5  8  2  9  7  1  4  6;3  5  8  2  9  6  1  7  4;3  5  9  4  1  7  2  6  8;3  5  9  2  4  7  1  8  6;3  5  2  8  1  4  7  9  6;3  5  2  8  1  7  4  6  9;3  9  6  4  1  7  5  2  8;3  9  6  8  2  4  1  7  5;3  9  6  2  5  7  1  4  8;3  9  4  8  5  2  6  1  7;3  9  4  2  8  6  1  7  5;3  9  4  1  8  6  2  7  5;3  9  2  5  8  1  7  4  6;3  1  7  5  8  2  4  6  9;3  1  7  2  8  6  4  9  5;3  1  6  8  5  2  4  9  7;3  1  4  7  9  2  5  8  6;3  1  9  7  5  2  8  6  4;3  1  8  4  9  7  5  2  6;2  8  6  9  3  1  4  7  5;2  8  5  3  9  6  4  1  7;2  8  1  4  7  9  6  3  5;2  7  5  8  1  4  6  3  9;2  7  5  1  9  4  6  8  3;2  7  9  6  3  1  4  8  5;2  6  3  1  8  4  9  7  5;2  6  9  3  5  8  4  1  7;2  6  1  3  7  9  4  8  5;2  6  1  9  5  8  4  7  3;2  6  1  7  5  3  9  4  8;2  6  1  7  4  8  3  5  9;2  5  7  4  1  3  9  6  8;2  5  7  9  4  8  1  3  6;2  5  7  9  3  6  4  1  8;2  5  7  1  3  8  6  4  9;2  5  8  6  9  3  1  7  4;2  5  8  6  9  3  1  4  7;2  5  8  1  3  6  9  7  4;2  5  8  1  9  6  3  7  4;2  5  9  4  1  8  6  3  7;2  4  7  1  3  9  6  8  5;2  4  8  3  9  6  1  5  7;2  4  9  7  5  3  1  6  8;2  4  9  7  3  1  6  8  5;2  4  1  7  9  6  3  5  8;2  9  6  4  7  1  3  5  8;2  9  6  3  5  8  1  4  7;2  9  6  3  7  4  1  8  5;2  9  5  3  8  4  7  1  6;1  8  5  3  6  9  2  4  7;1  8  5  3  9  7  2  4  6;1  8  4  2  7  9  6  3  5;1  7  5  8  2  9  3  6  4;1  7  4  6  9  2  5  3  8;1  7  4  8  3  5  9  2  6;1  7  4  8  3  9  6  2  5;1  6  8  5  2  4  9  7  3;1  6  8  3  7  4  2  9  5;1  6  4  2  7  9  3  5  8;1  6  4  2  8  3  9  7  5;1  6  2  9  7  4  8  3  5;1  6  9  5  2  8  3  7  4;1  5  7  2  6  3  9  4  8;1  5  7  9  4  2  8  6  3;1  5  7  9  3  8  2  4  6;1  5  2  6  9  3  8  4  7;1  5  9  6  4  2  8  3  7;1  5  9  2  6  8  3  7  4;1  4  7  3  8  2  5  9  6;1  4  7  9  2  5  8  6  3;1  4  6  8  2  5  3  9  7;1  4  6  3  9  2  8  5  7;1  4  8  3  9  7  5  2  6;1  4  2  8  6  9  3  5  7;1  3  7  2  8  5  9  4  6;1  3  6  8  2  4  9  7  5;1  3  8  6  9  2  5  7  4];\r\n[s, q] = nqueens(n);\r\nassert(isequal(s,s_correct) \u0026\u0026 isequal(sortrows(q),sortrows(q_correct)))","published":true,"deleted":false,"likes_count":6,"comments_count":1,"created_by":15521,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":92,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":35,"created_at":"2017-09-24T19:13:26.000Z","updated_at":"2026-02-03T09:18:46.000Z","published_at":"2017-10-16T01:51:00.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA tribute to Cody's five-year anniversary should also celebrate the people behind Cody, and in this particular case, our illustrious Quizmaster, Ned Gulley.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe N-Queens problem (N stands for Ned, of course) is a well known computing challenge. If you are unfamiliar with this problem, refer to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/113-n-queens-checker\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 113\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e, incidentally written by... You guessed it.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is the real deal. Given a positive integer, n, representing the number of queens and the size of the board, return the number of possible solutions, s, and a list of the solutions, q.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eq shall be an array with s rows and n columns, such that each row represents one solution. The column indeces of q shall represent the column indeces of the positions of the queens in the respective solution, while the values of the array elements shall represent the row indeces of the positions of the queens in the respective solution. q does not have to be sorted.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNote: All symmetries/rotations count as individual solutions.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eExample:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[ Input: n = 4\\n\\n Output: s = 2, q = [2 4 1 3;3 1 4 2]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44344,"title":"The 5th Root","description":"Write a function to find the 5th root of a number.\r\n\r\nIt sounds easy, but the typical functions are not allowed (see the test suite), so you'll need to find a non-standard method to solve the problem.","description_html":"\u003cp\u003eWrite a function to find the 5th root of a number.\u003c/p\u003e\u003cp\u003eIt sounds easy, but the typical functions are not allowed (see the test suite), so you'll need to find a non-standard method to solve the problem.\u003c/p\u003e","function_template":"function f = fifth_root(n)\r\n f = n^(1/5)\r\nend","test_suite":"%%\r\nfiletext = fileread('fifth_root.m');\r\nassert(isempty(strfind(filetext, '^')),'^ forbidden')\r\nassert(isempty(strfind(filetext, 'power')),'power() forbidden')\r\nassert(isempty(strfind(filetext, 'mpower')),'mpower() forbidden')\r\nassert(isempty(strfind(filetext, 'realpow')),'realpow() forbidden')\r\nassert(isempty(strfind(filetext, 'nthroot')),'nthroot() forbidden')\r\nassert(isempty(strfind(filetext, 'roots')),'roots() forbidden')\r\n\r\n%%\r\nn = 1/9765625;\r\nassert(abs(fifth_root(n)-1/25)\u003c1e-5)\r\n\r\n%%\r\nn = 1/5555;\r\nassert(abs(fifth_root(n)-0.178263811215444)\u003c1e-5)\r\n\r\n%%\r\nn = 1/3125;\r\nassert(abs(fifth_root(n)-1/5)\u003c1e-5)\r\n\r\n%%\r\nn = 1/125;\r\nassert(abs(fifth_root(n)-0.380730787743176)\u003c1e-5)\r\n\r\n%%\r\nn = 1/5;\r\nassert(abs(fifth_root(n)-0.724779663677696)\u003c1e-5)\r\n\r\n%%\r\nn = 1;\r\nassert(abs(fifth_root(n)-1)\u003c1e-5)\r\n\r\n%%\r\nn = 5;\r\nassert(abs(fifth_root(n)-1.37972966146121)\u003c1e-5)\r\n\r\n%%\r\nn = 25;\r\nassert(abs(fifth_root(n)-1.90365393871588)\u003c1e-5)\r\n\r\n%%\r\nn = 50;\r\nassert(abs(fifth_root(n)-2.18672414788656)\u003c1e-5)\r\n\r\n%%\r\nn = 500;\r\nassert(abs(fifth_root(n)-3.46572421577573)\u003c1e-5)\r\n\r\n%%\r\nn = 3125;\r\nassert(abs(fifth_root(n)-5)\u003c1e-5)\r\n\r\n%%\r\nn = 759375;\r\nassert(abs(fifth_root(n)-15)\u003c1e-5)\r\n\r\n%%\r\nn = 9765625;\r\nassert(abs(fifth_root(n)-25)\u003c1e-5)\r\n\r\n%%\r\nn = 312500000;\r\nassert(abs(fifth_root(n)-50)\u003c1e-5)\r\n\r\n%%\r\nn = 75937500000;\r\nassert(abs(fifth_root(n)-150)\u003c1e-5)\r\n\r\n%%\r\nn = 31250000000000;\r\nassert(abs(fifth_root(n)-500)\u003c1e-5)\r\n\r\n%%\r\nn = 52658067346875;\r\nassert(abs(fifth_root(n)-555)\u003c1e-5)","published":true,"deleted":false,"likes_count":13,"comments_count":3,"created_by":26769,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":559,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":35,"created_at":"2017-09-22T16:03:40.000Z","updated_at":"2026-02-03T09:23:18.000Z","published_at":"2017-10-16T01:50:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to find the 5th root of a number.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt sounds easy, but the typical functions are not allowed (see the test suite), so you'll need to find a non-standard method to solve the problem.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44343,"title":"Pair Primes","description":"Let's define pair primes as follow;\r\nFor 2 digits numbers: 11 and 17 are pair primes because both of them are 2 digits prime numbers and last digit of the first prime equals to the first digit of second prime number. 11 and 11 are not pair primes because a = b.\r\nFor 3 digit numbers: 389 and 967 are pair primes because both of them are 3 digits prime numbers and last digit of the first prime equals to the first digit of the second prime number (797 and 797 are not pair primes because a = b). 467 and 673 are pair primes too because the last two digits of the first prime number (67) equals to the first two digit (67) of the second prime number. 211 and 113 are pair primes too but they satisfy two conditions: last digit of the first prime equals to the first digit of the second prime also last two digits of the first prime equals to the first two digits of the first prime.\r\nFor 4 digit numbers:\r\n1-) 1637 and 7549 are pair primes. First ends with 7 and second starts with 7.\r\n2-) 6221 and 2113 are pair primes. First ends with 21 and second starts with 21.\r\n3-) 1429 and 4297 are pair primes. First ends with 429 and second starts with 429. You should be careful. 2111 and 1117 are also four digit pair primes. It satisfies three conditions. First ends with 1 and second starts with 1. First ends with 11 and second starts with 11. First ends with 111 and second starts with 111. [2111 1117] pair should be counted for once.\r\nGiven the digit counts, can you determine how many unique pair primes are there (a~=b)","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 387.9px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 193.95px; transform-origin: 407px 193.95px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.5px 8px; transform-origin: 104.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eLet's define pair primes as follow;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cul style=\"block-size: 183.9px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: square; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 91.95px; transform-origin: 391px 91.95px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 40.8667px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 20.4333px; text-align: left; transform-origin: 363px 20.4333px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 74.5px 8px; transform-origin: 74.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFor 2 digits numbers:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 283.5px 8px; transform-origin: 283.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 11 and 17 are pair primes because both of them are 2 digits prime numbers and last digit of the first prime equals to the first digit of second prime number. 11 and 11 are not pair primes because a = b.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 122.6px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 61.3px; text-align: left; transform-origin: 363px 61.3px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 70.5px 8px; transform-origin: 70.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFor 3 digit numbers:\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 292px 8px; transform-origin: 292px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e 389 and 967 are pair primes because both of them are 3 digits prime numbers and last digit of the first prime equals to the first digit of the second prime number (797 and 797 are not pair primes because a = b). 467 and 673 are pair primes too because the last two digits of the first prime number (67) equals to the first two digit (67) of the second prime number. 211 and 113 are pair primes too but they satisfy two conditions: last digit of the first prime equals to the first digit of the second prime also last two digits of the first prime equals to the first two digits of the first prime.\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 70.5px 8px; transform-origin: 70.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eFor 4 digit numbers:\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 244.5px 8px; transform-origin: 244.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1-) 1637 and 7549 are pair primes. First ends with 7 and second starts with 7.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 252px 8px; transform-origin: 252px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2-) 6221 and 2113 are pair primes. First ends with 21 and second starts with 21.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 383px 8px; transform-origin: 383px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3-) 1429 and 4297 are pair primes. First ends with 429 and second starts with 429. You should be careful. 2111 and 1117 are also four digit pair primes. It satisfies three conditions. First ends with 1 and second starts with 1. First ends with 11 and second starts with 11. First ends with 111 and second starts with 111. [2111 1117] pair should be counted for once.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 279px 8px; transform-origin: 279px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGiven the digit counts, can you determine how many unique pair primes are there (a~=b)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = pairPrimes(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nfiletext = fileread('pairPrimes.m');\r\nillegal = contains(filetext, 'regexp') || contains(filetext, 'interp1') || ...\r\n          contains(filetext, 'elseif') || contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = 2;\r\ny_correct = 51;\r\nassert(isequal(pairPrimes(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[51,2485,136162,8578934]),regexp(fileread('pairPrimes.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 2485;\r\nassert(isequal(pairPrimes(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[51,2485,136162,8578934]),regexp(fileread('pairPrimes.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 4;\r\ny_correct = 136162;\r\nassert(isequal(pairPrimes(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[51,2485,136162,8578934]),regexp(fileread('pairPrimes.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 5;\r\ny_correct = 8578934;\r\nassert(isequal(pairPrimes(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[51,2485,136162,8578934]),regexp(fileread('pairPrimes.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n","published":true,"deleted":false,"likes_count":9,"comments_count":5,"created_by":8703,"edited_by":223089,"edited_at":"2022-10-11T06:50:24.000Z","deleted_by":null,"deleted_at":null,"solvers_count":105,"test_suite_updated_at":"2022-10-11T06:50:24.000Z","rescore_all_solutions":false,"group_id":35,"created_at":"2017-09-22T08:07:44.000Z","updated_at":"2026-02-03T07:36:30.000Z","published_at":"2017-10-16T01:50:59.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eLet's define pair primes as follow;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFor 2 digits numbers:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 11 and 17 are pair primes because both of them are 2 digits prime numbers and last digit of the first prime equals to the first digit of second prime number. 11 and 11 are not pair primes because a = b.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFor 3 digit numbers:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e 389 and 967 are pair primes because both of them are 3 digits prime numbers and last digit of the first prime equals to the first digit of the second prime number (797 and 797 are not pair primes because a = b). 467 and 673 are pair primes too because the last two digits of the first prime number (67) equals to the first two digit (67) of the second prime number. 211 and 113 are pair primes too but they satisfy two conditions: last digit of the first prime equals to the first digit of the second prime also last two digits of the first prime equals to the first two digits of the first prime.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eFor 4 digit numbers:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1-) 1637 and 7549 are pair primes. First ends with 7 and second starts with 7.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2-) 6221 and 2113 are pair primes. First ends with 21 and second starts with 21.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3-) 1429 and 4297 are pair primes. First ends with 429 and second starts with 429. You should be careful. 2111 and 1117 are also four digit pair primes. It satisfies three conditions. First ends with 1 and second starts with 1. First ends with 11 and second starts with 11. First ends with 111 and second starts with 111. [2111 1117] pair should be counted for once.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven the digit counts, can you determine how many unique pair primes are there (a~=b)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44341,"title":"Hexagonal numbers on a spiral matrix","description":"Put hexagonal numbers in a ( m x m ) spiral matrix and return the sum of its diagonal elements.\r\n\r\nFormula of hexagonal numbers h(n) = 2n^2 - n\r\n\r\nIf m = 5;\r\n\r\n  spiral(5) =   \r\n    21    22    23    24    25\r\n    20     7     8     9    10\r\n    19     6     1     2    11\r\n    18     5     4     3    12\r\n    17    16    15    14    13\r\n\r\nFirst 5x5=25 hexagonal numbers are;\r\n\r\n  h = [1 6 15 28 45 66 91 120 153 190 231 276 325 378 435 496 561 630 703 780 861 946 1035 1128 1225]\r\n\r\nWe put them in a spiral format;\r\n\r\n   spiralHex = [\r\n861\t946\t1035\t1128\t1225\r\n780\t91\t120\t153\t190\r\n703\t66\t1\t6\t231\r\n630\t45\t28\t15\t276\r\n561\t496\t435\t378\t325\r\n\r\nAnd sum its diag = 861 + 91 + 1 + 15 + 325 = 1293.\r\n\r\nReturn the output as char.","description_html":"\u003cp\u003ePut hexagonal numbers in a ( m x m ) spiral matrix and return the sum of its diagonal elements.\u003c/p\u003e\u003cp\u003eFormula of hexagonal numbers h(n) = 2n^2 - n\u003c/p\u003e\u003cp\u003eIf m = 5;\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003espiral(5) =   \r\n  21    22    23    24    25\r\n  20     7     8     9    10\r\n  19     6     1     2    11\r\n  18     5     4     3    12\r\n  17    16    15    14    13\r\n\u003c/pre\u003e\u003cp\u003eFirst 5x5=25 hexagonal numbers are;\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003eh = [1 6 15 28 45 66 91 120 153 190 231 276 325 378 435 496 561 630 703 780 861 946 1035 1128 1225]\r\n\u003c/pre\u003e\u003cp\u003eWe put them in a spiral format;\u003c/p\u003e\u003cpre\u003e   spiralHex = [\r\n861\t946\t1035\t1128\t1225\r\n780\t91\t120\t153\t190\r\n703\t66\t1\t6\t231\r\n630\t45\t28\t15\t276\r\n561\t496\t435\t378\t325\u003c/pre\u003e\u003cp\u003eAnd sum its diag = 861 + 91 + 1 + 15 + 325 = 1293.\u003c/p\u003e\u003cp\u003eReturn the output as char.\u003c/p\u003e","function_template":"function y = hexagonalSpiral(m)\r\n  \r\nend","test_suite":"%%\r\nm = 1;\r\ny_correct = '1';\r\nassert(isequal(hexagonalSpiral(m),y_correct))\r\n\r\n%%\r\nm = 2;\r\ny_correct = '16';\r\nassert(isequal(hexagonalSpiral(m),y_correct))\r\n\r\n%%\r\nm = 5;\r\ny_correct = '1293';\r\nassert(isequal(hexagonalSpiral(m),y_correct))\r\n\r\n%%\r\nm = 16;\r\ny_correct = '420800';\r\nassert(isequal(hexagonalSpiral(m),y_correct))\r\n\r\n%%\r\nm = 100;\r\ny_correct = '4000333360';\r\nassert(isequal(hexagonalSpiral(m),y_correct))\r\n\r\n%%\r\nm = 1295;\r\ny_correct = '1456830580539887';\r\nassert(isequal(hexagonalSpiral(m),y_correct))\r\n\r\n%%\r\nm = 2500;\r\ny_correct = '39062505208334000';\r\nassert(isequal(hexagonalSpiral(m),y_correct))\r\n\r\n%%\r\nm = 5000;\r\ny_correct = '1250000041666668000';\r\nassert(isequal(hexagonalSpiral(m),y_correct))\r\n\r\n%%\r\nm = 8000;\r\ny_correct = '13107200170666668800';\r\nassert(isequal(hexagonalSpiral(m),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":164,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":35,"created_at":"2017-09-19T08:06:36.000Z","updated_at":"2025-12-26T10:11:44.000Z","published_at":"2017-10-16T01:50:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePut hexagonal numbers in a ( m x m ) spiral matrix and return the sum of its diagonal elements.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFormula of hexagonal numbers h(n) = 2n^2 - n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIf m = 5;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[spiral(5) =   \\n  21    22    23    24    25\\n  20     7     8     9    10\\n  19     6     1     2    11\\n  18     5     4     3    12\\n  17    16    15    14    13]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFirst 5x5=25 hexagonal numbers are;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[h = [1 6 15 28 45 66 91 120 153 190 231 276 325 378 435 496 561 630 703 780 861 946 1035 1128 1225]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe put them in a spiral format;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[   spiralHex = [\\n861  946  1035  1128  1225\\n780  91  120  153  190\\n703  66  1  6  231\\n630  45  28  15  276\\n561  496  435  378  325]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAnd sum its diag = 861 + 91 + 1 + 15 + 325 = 1293.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eReturn the output as char.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44340,"title":"Recaman Sequence - III","description":"I want to create a Recaman sequence where there is a \"1\" in the n-th position. So from which integer should I start the Recaman sequence? If there are more than one starting integer that generates a sequence with a 1 in the n-th position, return the lowest one.\r\nFor example if I want to place the digit 1 in the 7th place in the sequence then I should start the sequence from six as follow;\r\nseq = [6 5 3 6 2 7 1 8 16]\r\nYou can also start the sequence with 12 and obtain a series where there is a 1 in 7th position;\r\nseq = [12 11 9 6 2 7 1]\r\nRelated Challenges :\r\nRecaman Sequence - I\r\nRecaman Sequence - II\r\nRecaman Sequence - III","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 308.167px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 154.083px; transform-origin: 407px 154.083px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 371.5px 8px; transform-origin: 371.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eI want to create a Recaman sequence where there is a \"1\" in the n-th position. So from which integer should I start the Recaman sequence? If there are more than one starting integer that generates a sequence with a 1 in the n-th position, return the lowest one.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 368.5px 8px; transform-origin: 368.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor example if I want to place the digit 1 in the 7th place in the sequence then I should start the sequence from six as follow;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 104px 8.5px; tab-size: 4; transform-origin: 104px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eseq = [6 5 3 6 2 7 1 8 16]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 294.5px 8px; transform-origin: 294.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYou can also start the sequence with 12 and obtain a series where there is a 1 in 7th position;\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"background-color: rgb(247, 247, 247); block-size: 20.4333px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; \"\u003e\u003cdiv style=\"background-color: rgba(0, 0, 0, 0); border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; white-space: nowrap; \"\u003e\u003cspan style=\"block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 92px 8.5px; tab-size: 4; transform-origin: 92px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; \"\u003e\u003cspan style=\"margin-inline-end: 0px; margin-right: 0px; \"\u003eseq = [12 11 9 6 2 7 1]\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 72.5px 8px; transform-origin: 72.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eRelated Challenges :\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003col style=\"block-size: 61.3px; counter-reset: list-item 0; font-family: Helvetica, Arial, sans-serif; list-style-type: decimal; margin-block-end: 20px; margin-block-start: 10px; margin-bottom: 20px; margin-top: 10px; perspective-origin: 391px 30.65px; transform-origin: 391px 30.65px; margin-top: 10px; margin-bottom: 20px; \"\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44338\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eRecaman Sequence - I\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003ca target='_blank' href = \"https://www.mathworks.com/matlabcentral/cody/problems/44339\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eRecaman Sequence - II\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003c/li\u003e\u003cli style=\"block-size: 20.4333px; counter-reset: none; display: list-item; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-start: 56px; margin-left: 56px; margin-top: 0px; perspective-origin: 363px 10.2167px; text-align: left; transform-origin: 363px 10.2167px; white-space: pre-wrap; margin-left: 56px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-inline-start: 0px; margin-left: 0px; perspective-origin: 75px 8px; transform-origin: 75px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eRecaman Sequence - III\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function startPoint = RecamanIII(onesplace)\r\n\r\nend","test_suite":"%%\r\nfiletext = fileread('RecamanIII.m');\r\nillegal = contains(filetext, 'assignin') || contains(filetext, 'str2num'); \r\nassert(~illegal)\r\n\r\n%%\r\nx = 1;\r\ny_correct = 1;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 2;\r\ny_correct = 0;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 3;\r\ny_correct = 4;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 9;\r\ny_correct = 13;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 13;\r\ny_correct = 15;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 15;\r\ny_correct = 26;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 26;\r\ny_correct = 54;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 54;\r\ny_correct = 208;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n%%\r\nx = 208;\r\ny_correct = 2485;\r\nassert(isequal(RecamanIII(x),y_correct))\r\nassert(~any(cellfun(@(x)ismember(max([0,str2num(x)]),[13 15 26 54 208 2485]),regexp(fileread('RecamanIII.m'),'[\\d\\.\\+\\-\\*\\/]+','match'))))\r\n\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":12,"created_by":8703,"edited_by":223089,"edited_at":"2022-10-11T07:22:46.000Z","deleted_by":null,"deleted_at":null,"solvers_count":89,"test_suite_updated_at":"2022-10-11T07:22:46.000Z","rescore_all_solutions":false,"group_id":35,"created_at":"2017-09-19T07:36:19.000Z","updated_at":"2026-03-22T11:36:50.000Z","published_at":"2017-10-16T01:50:59.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eI want to create a Recaman sequence where there is a \\\"1\\\" in the n-th position. So from which integer should I start the Recaman sequence? If there are more than one starting integer that generates a sequence with a 1 in the n-th position, return the lowest one.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor example if I want to place the digit 1 in the 7th place in the sequence then I should start the sequence from six as follow;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[seq = [6 5 3 6 2 7 1 8 16]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou can also start the sequence with 12 and obtain a series where there is a 1 in 7th position;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[seq = [12 11 9 6 2 7 1]]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eRelated Challenges :\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44338\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eRecaman Sequence - I\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.mathworks.com/matlabcentral/cody/problems/44339\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eRecaman Sequence - II\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRecaman Sequence - III\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":44337,"title":"Sums of Distinct Powers","description":"You will be given three numbers: base, nstart, and nend.  Write a MATLAB script that will compute the sum of a sequence of both the distinct powers of base as well as sums of distinct powers of base.  Your sequence should start with the 'nstart'th term and end with the 'nend'th term.  For example:\r\n\r\n* base=4\r\n* nstart=2\r\n* nend=6\r\n\r\nThe first several sums of the distinct powers of 4 are:\r\n\r\n* 1 (4^0)\r\n* 4 (4^1)\r\n* 5 (4^1 + 4^0)\r\n* 16 (4^2)\r\n* 17 (4^2 + 4^0)\r\n* 20 (4^2 + 4^1)\r\n* 21 (4^2 + 4^1 + 4^0)\r\n* 64 (4^3)\r\n* 65 (4^3 + 4^0)\r\n\r\nSince nstart=2 and nend=6 in this example, you take the second through the sixth terms of this sequence.  The correct output would be 4+5+16+17+20, or 62.  Notice that the number 8 does not occur in this pattern.  While 8 is a multiple of 4, 8=4^1+4^1.  Because there are two 4^1 terms in the sum, 8 does not qualify as a sum of *distinct* powers of 4.  You can assume that all three will be integers, base\u003e1, and that nstart\u003cnend.  Good luck!","description_html":"\u003cp\u003eYou will be given three numbers: base, nstart, and nend.  Write a MATLAB script that will compute the sum of a sequence of both the distinct powers of base as well as sums of distinct powers of base.  Your sequence should start with the 'nstart'th term and end with the 'nend'th term.  For example:\u003c/p\u003e\u003cul\u003e\u003cli\u003ebase=4\u003c/li\u003e\u003cli\u003enstart=2\u003c/li\u003e\u003cli\u003enend=6\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eThe first several sums of the distinct powers of 4 are:\u003c/p\u003e\u003cul\u003e\u003cli\u003e1 (4^0)\u003c/li\u003e\u003cli\u003e4 (4^1)\u003c/li\u003e\u003cli\u003e5 (4^1 + 4^0)\u003c/li\u003e\u003cli\u003e16 (4^2)\u003c/li\u003e\u003cli\u003e17 (4^2 + 4^0)\u003c/li\u003e\u003cli\u003e20 (4^2 + 4^1)\u003c/li\u003e\u003cli\u003e21 (4^2 + 4^1 + 4^0)\u003c/li\u003e\u003cli\u003e64 (4^3)\u003c/li\u003e\u003cli\u003e65 (4^3 + 4^0)\u003c/li\u003e\u003c/ul\u003e\u003cp\u003eSince nstart=2 and nend=6 in this example, you take the second through the sixth terms of this sequence.  The correct output would be 4+5+16+17+20, or 62.  Notice that the number 8 does not occur in this pattern.  While 8 is a multiple of 4, 8=4^1+4^1.  Because there are two 4^1 terms in the sum, 8 does not qualify as a sum of \u003cb\u003edistinct\u003c/b\u003e powers of 4.  You can assume that all three will be integers, base\u0026gt;1, and that nstart\u0026lt;nend.  Good luck!\u003c/p\u003e","function_template":"function y = sum_distinct_powers(base,nstart,nend)\r\n  y = base*nstart*nend;\r\nend","test_suite":"%%\r\nbase=4;nstart=2;nend=6;y_correct=62;\r\nassert(isequal(sum_distinct_powers(base,nstart,nend),y_correct))\r\n%%\r\nbase=5;nstart=1;nend=1000;y_correct=1193853250;\r\nassert(isequal(sum_distinct_powers(base,nstart,nend),y_correct))\r\n%%\r\nbase=3;nstart=1;nend=1000;y_correct=14438162;\r\nassert(isequal(sum_distinct_powers(base,nstart,nend),y_correct))\r\n%%\r\nbase=3;nstart=100;nend=1000;y_correct=14397354;\r\nassert(isequal(sum_distinct_powers(base,nstart,nend),y_correct))\r\n%%\r\nbase=2;nstart=1;nend=2017;y_correct=2035153;\r\nassert(isequal(sum_distinct_powers(base,nstart,nend),y_correct))\r\n%%\r\nbase=7;nstart=1234;nend=2345;y_correct=843569026324;\r\nassert(isequal(sum_distinct_powers(base,nstart,nend),y_correct))\r\n%%\r\nbase=7;nstart=1;nend=10;y_correct=1265;\r\nassert(isequal(sum_distinct_powers(base,nstart,nend),y_correct))\r\n%%\r\nnstart=1;nend=50;\r\njunk=arrayfun(@(base) sum_distinct_powers(base,nstart,nend),2:10);\r\ny_correct=[1275 7120 26365 75000 178591 374560 714465 1266280 2116675];\r\nassert(isequal(junk,y_correct))\r\n","published":true,"deleted":false,"likes_count":6,"comments_count":9,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":156,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":35,"created_at":"2017-09-18T16:30:15.000Z","updated_at":"2026-02-03T09:26:51.000Z","published_at":"2017-10-16T01:50:59.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou will be given three numbers: base, nstart, and nend. Write a MATLAB script that will compute the sum of a sequence of both the distinct powers of base as well as sums of distinct powers of base. Your sequence should start with the 'nstart'th term and end with the 'nend'th term. For example:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ebase=4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003enstart=2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003enend=6\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe first several sums of the distinct powers of 4 are:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1 (4^0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4 (4^1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e5 (4^1 + 4^0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e16 (4^2)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e17 (4^2 + 4^0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e20 (4^2 + 4^1)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e21 (4^2 + 4^1 + 4^0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e64 (4^3)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"1\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e65 (4^3 + 4^0)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSince nstart=2 and nend=6 in this example, you take the second through the sixth terms of this sequence. The correct output would be 4+5+16+17+20, or 62. Notice that the number 8 does not occur in this pattern. While 8 is a multiple of 4, 8=4^1+4^1. Because there are two 4^1 terms in the sum, 8 does not qualify as a sum of\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003edistinct\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e powers of 4. You can assume that all three will be integers, base\u0026gt;1, and that nstart\u0026lt;nend. Good luck!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44316,"title":"Pandigital Multiples of 11 (based on Project Euler 491)","description":"A \"Pandigital number of order X\" is one that contains all of the numbers from 0 to X, but with no leading zeroes. If X\u003e9, the cycle 0-9 repeats itself. For example, 2310 is a Pandigital number of order 3 (0-3), while 120345678901 is a Pandigital number of order 11, with the \"01\" at the end of the number representing 10 and 11, respectively (10 and 11 mod 10, essentially). 0321 is not a Pandigital number, as it has a leading zero.\r\n\r\nGiven a number X, determine how many pandigital numbers of that order are divisible by 11.  You do not need to return the numbers themselves, just how many of them there are.","description_html":"\u003cp\u003eA \"Pandigital number of order X\" is one that contains all of the numbers from 0 to X, but with no leading zeroes. If X\u0026gt;9, the cycle 0-9 repeats itself. For example, 2310 is a Pandigital number of order 3 (0-3), while 120345678901 is a Pandigital number of order 11, with the \"01\" at the end of the number representing 10 and 11, respectively (10 and 11 mod 10, essentially). 0321 is not a Pandigital number, as it has a leading zero.\u003c/p\u003e\u003cp\u003eGiven a number X, determine how many pandigital numbers of that order are divisible by 11.  You do not need to return the numbers themselves, just how many of them there are.\u003c/p\u003e","function_template":"function y = pandigitalby11(x)\r\n  y = x;\r\nend","test_suite":"%%\r\nx = 2;y_correct = 0;\r\nassert(isequal(pandigitalby11(x),y_correct))\r\n%%\r\nx = 3;y_correct = 6;\r\nassert(isequal(pandigitalby11(x),y_correct))\r\n%%\r\nx = 7;y_correct = 4032;\r\nassert(isequal(pandigitalby11(x),y_correct))\r\n%%\r\np6=pandigitalby11(6);\r\np8=pandigitalby11(8);\r\np9=pandigitalby11(9);\r\n\r\nassert(p8\u003ep6);\r\nassert(p9\u003ep8);\r\n\r\nf6=factor(p6);\r\nf8=factor(p8);\r\nf9=factor(p9);\r\nf9e1=f9(end-1);\r\n\r\nassert(p6\u003e256);\r\nassert(max(f9)\u003cmax(f8));\r\nassert(f9e1\u003emax(f6));\r\nassert(numel(f9)\u003enumel(f8));\r\n%%\r\nx = 11;y_correct = 9072000;\r\nassert(isequal(pandigitalby11(x),y_correct))\r\n%%\r\nx = 14;y_correct = 3216477600;\r\nassert(isequal(pandigitalby11(x),y_correct))\r\n%%\r\nassert(isequal(pandigitalby11(16),222911740800))","published":true,"deleted":false,"likes_count":5,"comments_count":15,"created_by":1615,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":53,"test_suite_updated_at":"2017-10-23T01:32:05.000Z","rescore_all_solutions":false,"group_id":35,"created_at":"2017-09-12T15:26:05.000Z","updated_at":"2026-02-03T09:29:47.000Z","published_at":"2017-10-16T01:50:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA \\\"Pandigital number of order X\\\" is one that contains all of the numbers from 0 to X, but with no leading zeroes. If X\u0026gt;9, the cycle 0-9 repeats itself. For example, 2310 is a Pandigital number of order 3 (0-3), while 120345678901 is a Pandigital number of order 11, with the \\\"01\\\" at the end of the number representing 10 and 11, respectively (10 and 11 mod 10, essentially). 0321 is not a Pandigital number, as it has a leading zero.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGiven a number X, determine how many pandigital numbers of that order are divisible by 11. You do not need to return the numbers themselves, just how many of them there are.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44311,"title":"Number of Even Elements in Fibonacci Sequence","description":"Find how many even Fibonacci numbers are available in the first d numbers.\r\n\r\nConsider the following first 14 numbers\r\n\r\n  1 1 2 3 5 8 13 21 34 55 89 144 233 377 ...\r\n\r\n4 of them are even. ","description_html":"\u003cp\u003eFind how many even Fibonacci numbers are available in the first d numbers.\u003c/p\u003e\u003cp\u003eConsider the following first 14 numbers\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003e1 1 2 3 5 8 13 21 34 55 89 144 233 377 ...\r\n\u003c/pre\u003e\u003cp\u003e4 of them are even.\u003c/p\u003e","function_template":"function y = evenFibo(d)\r\n  y = x;\r\nend","test_suite":"%%\r\nd = 14;\r\ny_correct = 4;\r\nassert(isequal(evenFibo(d),y_correct))\r\n\r\n%%\r\nd = 20;\r\ny_correct = 6;\r\nassert(isequal(evenFibo(d),y_correct))\r\n\r\n%%\r\nd = 50;\r\ny_correct = 16;\r\nassert(isequal(evenFibo(d),y_correct))\r\n\r\n%%\r\nd = 100;\r\ny_correct = 33;\r\nassert(isequal(evenFibo(d),y_correct))\r\n\r\n%%\r\nd = 150;\r\ny_correct = 50;\r\nassert(isequal(evenFibo(d),y_correct))\r\n\r\n%%\r\nd = 200;\r\ny_correct = 66;\r\nassert(isequal(evenFibo(d),y_correct))\r\n\r\n%%\r\nd = 500;\r\ny_correct = 166;\r\nassert(isequal(evenFibo(d),y_correct))\r\n\r\n%%\r\nd = 1000;\r\ny_correct = 333;\r\nassert(isequal(evenFibo(d),y_correct))\r\n\r\n%%\r\nd = 1e4;\r\ny_correct = 3333;\r\nassert(isequal(evenFibo(d),y_correct))\r\n\r\n%%\r\nd = 2e4;\r\ny_correct = 6666;\r\nassert(isequal(evenFibo(d),y_correct))\r\n\r\n%%\r\nd = 3e5;\r\ny_correct = 1e5;\r\nassert(isequal(evenFibo(d),y_correct))\r\n\r\n%%\r\nd = 6e6;\r\ny_correct = 2e6;\r\nassert(isequal(evenFibo(d),y_correct))\r\n% \r\n% %%\r\n% d = 9223372036854775807;\r\n% y_correct = 3074457345618258432;\r\n% assert(isequal(evenFibo(d),y_correct))\r\n","published":true,"deleted":false,"likes_count":21,"comments_count":9,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":1640,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":35,"created_at":"2017-09-11T12:36:15.000Z","updated_at":"2026-03-31T16:31:07.000Z","published_at":"2017-10-16T01:50:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFind how many even Fibonacci numbers are available in the first d numbers.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the following first 14 numbers\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[1 1 2 3 5 8 13 21 34 55 89 144 233 377 ...]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4 of them are even.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":44310,"title":"Digit concentration in Champernowne's constant","description":"Consider the first 50 digits of Champernowne's constant\r\n \r\n    0.12345678910111213141516171819202122232425262728293...\r\n  \r\nThere are two zeros (do not count the left side of \".\" (integer part) ) in this series. So the digit concentration for 0 for the first 50 digits is = 2 / 50 = 0.04.\r\n\r\nAlso the number of '2' (x) digit is counted as 13. So the digit concentration of number '2' for the first 50 (d) digit is = 13/50 = 0.26\r\n\r\nCalculate the digit concentration of number x for the first d digit of constant.\r\n","description_html":"\u003cp\u003eConsider the first 50 digits of Champernowne's constant\u003c/p\u003e\u003cpre\u003e    0.12345678910111213141516171819202122232425262728293...\u003c/pre\u003e\u003cp\u003eThere are two zeros (do not count the left side of \".\" (integer part) ) in this series. So the digit concentration for 0 for the first 50 digits is = 2 / 50 = 0.04.\u003c/p\u003e\u003cp\u003eAlso the number of '2' (x) digit is counted as 13. So the digit concentration of number '2' for the first 50 (d) digit is = 13/50 = 0.26\u003c/p\u003e\u003cp\u003eCalculate the digit concentration of number x for the first d digit of constant.\u003c/p\u003e","function_template":"function concentration = digitCon(d,x)\r\n  y = x;\r\nend","test_suite":"%%\r\nd = 1;\r\nx = 1;\r\ny_correct = 1;\r\nassert(abs(digitCon(d,x)-y_correct) \u003c 1e-4)\r\n\r\n%%\r\nd = 10;\r\nx = 5;\r\ny_correct = 0.1000;\r\nassert(abs(digitCon(d,x)-y_correct) \u003c 1e-4)\r\n\r\n%%\r\nd = 10;\r\nx = 1;\r\ny_correct = 0.2000;\r\nassert(abs(digitCon(d,x)-y_correct) \u003c 1e-4)\r\n\r\n%%\r\nd = 20;\r\nx = 9;\r\ny_correct = 0.0500;\r\nassert(abs(digitCon(d,x)-y_correct) \u003c 1e-4)\r\n\r\n\r\n%%\r\nd = 50;\r\nx = 0;\r\ny_correct = 0.0400;\r\nassert(abs(digitCon(d,x)-y_correct) \u003c 1e-4)\r\n\r\n%%\r\nd = 50;\r\nx = 2;\r\ny_correct = 0.2600;\r\nassert(abs(digitCon(d,x)-y_correct) \u003c 1e-4)\r\n\r\n%%\r\nd = 1000;\r\nx = 9;\r\ny_correct = 0.0670;\r\nassert(abs(digitCon(d,x)-y_correct) \u003c 1e-4)\r\n\r\n%%\r\nd = 1e4;\r\nx = 8;\r\ny_correct = 0.0747;\r\nassert(abs(digitCon(d,x)-y_correct) \u003c 1e-4)\r\n\r\n%%\r\nd = 1e5;\r\nx = 7;\r\ny_correct = 0.0864;\r\nassert(abs(digitCon(d,x)-y_correct) \u003c 1e-4)\r\n\r\n%%\r\nd = 1e6;\r\nx = 6;\r\ny_correct = 0.0935;\r\nassert(abs(digitCon(d,x)-y_correct) \u003c 1e-4)\r\n\r\n%%\r\nd = 1e6;\r\nx = 5;\r\ny_correct = 0.0937;\r\nassert(abs(digitCon(d,x)-y_correct) \u003c 1e-4)\r\n\r\n%%\r\nd = 2e6;\r\nx = 4;\r\ny_correct = 0.0903;\r\nassert(abs(digitCon(d,x)-y_correct) \u003c 1e-4)\r\n\r\n%%\r\nd = 2000124;\r\nx = 3;\r\ny_correct = 0.1162;\r\nassert(abs(digitCon(d,x)-y_correct) \u003c 1e-4)","published":true,"deleted":false,"likes_count":5,"comments_count":1,"created_by":8703,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":125,"test_suite_updated_at":"2017-10-25T07:12:47.000Z","rescore_all_solutions":true,"group_id":35,"created_at":"2017-09-11T10:35:46.000Z","updated_at":"2026-02-03T09:31:30.000Z","published_at":"2017-10-16T01:50:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the first 50 digits of Champernowne's constant\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[    0.12345678910111213141516171819202122232425262728293...]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are two zeros (do not count the left side of \\\".\\\" (integer part) ) in this series. So the digit concentration for 0 for the first 50 digits is = 2 / 50 = 0.04.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAlso the number of '2' (x) digit is counted as 13. So the digit concentration of number '2' for the first 50 (d) digit is = 13/50 = 0.26\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCalculate the digit concentration of number x for the first d digit of constant.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"},{"id":281,"title":"Acid and water","description":"\u0026#9878; \u0026#9878; \u0026#9878; \u0026#9878; \u0026#9878; \u0026#9878; \u0026#9878; \u0026#9878;\r\n\r\nAssume that there is a 100 liter tank. \r\n\r\nIt is initially filled with just distilled water. \r\n\r\nIt is continuously drained at R liters per minute. \r\n\r\nThis tank is always maintained full and homogeneous by continuously adding and stirring R liters per minute of an unknown acid (or some fancy oil if it helps you solving this problem). \r\n\r\nHow many liters W of water will be in the tank after M minutes?\r\n\r\nNeglect any expansion or contraction when the acid is mixed with water. ","description_html":"\u003cp\u003e\u0026#9878; \u0026#9878; \u0026#9878; \u0026#9878; \u0026#9878; \u0026#9878; \u0026#9878; \u0026#9878;\u003c/p\u003e\u003cp\u003eAssume that there is a 100 liter tank.\u003c/p\u003e\u003cp\u003eIt is initially filled with just distilled water.\u003c/p\u003e\u003cp\u003eIt is continuously drained at R liters per minute.\u003c/p\u003e\u003cp\u003eThis tank is always maintained full and homogeneous by continuously adding and stirring R liters per minute of an unknown acid (or some fancy oil if it helps you solving this problem).\u003c/p\u003e\u003cp\u003eHow many liters W of water will be in the tank after M minutes?\u003c/p\u003e\u003cp\u003eNeglect any expansion or contraction when the acid is mixed with water.\u003c/p\u003e","function_template":"function W = tank(R,M)\r\n  W = 100 * R * M;\r\nend","test_suite":"%%\r\nR=1; \r\nM=1;\r\nW=99;\r\nassert(tank(R,M)\u003eW)\r\n%%\r\nR=2; \r\nM=2;\r\nW=96;\r\nassert(tank(R,M)\u003eW)\r\n%%\r\nR=10; \r\nM=10;\r\nW=36;\r\nassert(tank(R,M)\u003eW)\r\n%%\r\nR=15; \r\nM=20;\r\nW=5;\r\nassert(tank(R,M)\u003cW)\r\n%%\r\nR=7; \r\nM=8;\r\nW=58;\r\nassert(tank(R,M)\u003cW)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":13,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":261,"test_suite_updated_at":"2012-02-07T16:08:37.000Z","rescore_all_solutions":false,"group_id":35,"created_at":"2012-02-07T16:08:37.000Z","updated_at":"2026-03-26T15:49:26.000Z","published_at":"2017-10-16T01:50:58.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u0026#9878; \u0026#9878; \u0026#9878; \u0026#9878; \u0026#9878; \u0026#9878; \u0026#9878; \u0026#9878;\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssume that there is a 100 liter tank.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt is initially filled with just distilled water.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt is continuously drained at R liters per minute.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis tank is always maintained full and homogeneous by continuously adding and stirring R liters per minute of an unknown acid (or some fancy oil if it helps you solving this problem).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHow many liters W of water will be in the tank after M minutes?\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNeglect any expansion or contraction when the acid is mixed with water.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"no_progress_badge":{"id":53,"name":"Unknown","symbol":"unknown","description":"Partially completed groups","description_html":null,"image_location":"/images/responsive/supporting/matlabcentral/cody/badges/problem_groups_unknown_2.png","bonus":null,"players_count":0,"active":false,"created_by":null,"updated_by":null,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"created_at":"2018-01-10T23:20:29.000Z","updated_at":"2018-01-10T23:20:29.000Z","community_badge_id":null,"award_multiples":false}}