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The firm has given a tester two identical eggs to experiment with. The same egg can be dropped multiple times unless it breaks. \r\n\r\nFor a _n_ floor story building, what is the minimum number of droppings _d_ that is guaranteed to determine the highest safe floor in all cases?\r\n","description_html":"\u003cp\u003eConsider the following problem, a popular Google interview question:\u003c/p\u003e\u003cp\u003eA firm has invented a super-strong egg. For publicity purposes, it wants to determine the highest floor in a story building of \u003ci\u003en\u003c/i\u003e floors from which such an egg can fall without breaking. The firm has given a tester two identical eggs to experiment with. The same egg can be dropped multiple times unless it breaks.\u003c/p\u003e\u003cp\u003eFor a \u003ci\u003en\u003c/i\u003e floor story building, what is the minimum number of droppings \u003ci\u003ed\u003c/i\u003e that is guaranteed to determine the highest safe floor in all cases?\u003c/p\u003e","function_template":"function d = Google(h)\r\n  \r\nend","test_suite":"%%\r\nassert(isequal(Google(1),1))\r\n\r\n%%\r\nassert(isequal(Google(5),3))\r\n\r\n%%\r\nassert(isequal(Google(20),6))\r\n\r\n%%\r\nassert(isequal(Google(50),10))\r\n\r\n%%\r\nassert(isequal(Google(75),12))\r\n\r\n%%\r\nassert(isequal(Google(100),14))\r\n\r\n%%\r\nassert(isequal(Google(120),15))\r\n\r\n%%\r\nassert(isequal(Google(180),19))\r\n\r\n%%\r\nassert(isequal(Google(250),22))\r\n\r\n%%\r\nassert(isequal(Google(320),25))\r\n\r\n%%\r\nassert(isequal(Google(360),27))\r\n\r\n%%\r\nassert(isequal(Google(410),29))\r\n\r\n%%\r\nassert(isequal(Google(500),32))\r\n\r\n%%\r\nassert(isequal(Google(610),35))\r\n\r\n%%\r\nassert(isequal(Google(1000),45))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":178544,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2018-09-07T17:47:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-08-03T21:41:09.000Z","updated_at":"2026-01-20T13:52:14.000Z","published_at":"2018-08-04T01:39:07.000Z","restored_at":"2018-10-10T14:58:01.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"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 following problem, a popular Google interview question:\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\u003eA firm has invented a super-strong egg. For publicity purposes, it wants to determine the highest floor in a story building 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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e floors from which such an egg can fall without breaking. The firm has given a tester two identical eggs to experiment with. The same egg can be dropped multiple times unless it breaks.\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 a\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 floor story building, what is the minimum number of droppings\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\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that is guaranteed to determine the highest safe floor in all cases?\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":44714,"title":"The Generalized-N Eggs Problem","description":"A firm has invented a super-strong egg. For publicity purposes, it wants to determine the highest floor in a story building with _N_f_ floors from which such an egg can fall without breaking. The firm has given a tester _N_ identical eggs to experiment with. The same egg can be dropped multiple times unless it breaks. \r\n\r\nWhat is the minimum number of droppings _d_ that is guaranteed to determine the highest safe floor in all cases for a given number of floors _N_f_, and eggs _N_ ?\r\n\r\n*APPLICATION:* This problem has many applications in the real world such as avoiding a call out to the slow HDD, or attempting to minimize cache misses, or running a large number of expensive queries on a database.","description_html":"\u003cp\u003eA firm has invented a super-strong egg. For publicity purposes, it wants to determine the highest floor in a story building with \u003ci\u003eN_f\u003c/i\u003e floors from which such an egg can fall without breaking. The firm has given a tester \u003ci\u003eN\u003c/i\u003e identical eggs to experiment with. The same egg can be dropped multiple times unless it breaks.\u003c/p\u003e\u003cp\u003eWhat is the minimum number of droppings \u003ci\u003ed\u003c/i\u003e that is guaranteed to determine the highest safe floor in all cases for a given number of floors \u003ci\u003eN_f\u003c/i\u003e, and eggs \u003ci\u003eN\u003c/i\u003e ?\u003c/p\u003e\u003cp\u003e\u003cb\u003eAPPLICATION:\u003c/b\u003e This problem has many applications in the real world such as avoiding a call out to the slow HDD, or attempting to minimize cache misses, or running a large number of expensive queries on a database.\u003c/p\u003e","function_template":"function y = N_GeneralizedEggs(N_f, N)\r\n % N_f Number of story building floors\r\n % N   Number of eggs\r\nend","test_suite":"assert(isequal(N_GeneralizedEggs(0, 1),0))\r\n\r\nassert(isequal(N_GeneralizedEggs(10, 2),4))\r\n\r\nassert(isequal(N_GeneralizedEggs(10, 3),4))\r\n\r\nassert(isequal(N_GeneralizedEggs(50, 1),50))\r\n\r\nassert(isequal(N_GeneralizedEggs(50, 2),10))\r\n\r\nassert(isequal(N_GeneralizedEggs(50, 3),7))\r\n\r\nassert(isequal(N_GeneralizedEggs(50, 50),6))\r\n\r\nassert(isequal(N_GeneralizedEggs(50, 51),6))\r\n\r\nassert(isequal(N_GeneralizedEggs(100, 1),100))\r\n\r\nassert(isequal(N_GeneralizedEggs(100, 2),14))     % The famous two eggs problem.\r\n\r\nassert(isequal(N_GeneralizedEggs(100, 3),9))\r\n\r\nassert(isequal(N_GeneralizedEggs(100, 10),7))\r\n\r\nassert(isequal(N_GeneralizedEggs(100, 100),7))\r\n\r\nassert(isequal(N_GeneralizedEggs(250, 2),22))\r\n\r\nassert(isequal(N_GeneralizedEggs(250, 4),9))\r\n\r\nassert(isequal(N_GeneralizedEggs(500, 2),32))\r\n\r\nassert(isequal(N_GeneralizedEggs(500, 5),10))\r\n\r\nassert(isequal(N_GeneralizedEggs(500, 6),10))\r\n\r\nassert(isequal(N_GeneralizedEggs(1000, 2),45))\r\n\r\nassert(isequal(N_GeneralizedEggs(1000, 3),19))\r\n\r\nassert(isequal(N_GeneralizedEggs(1000, 7),11))\r\n\r\nassert(isequal(N_GeneralizedEggs(1000, 10),10))\r\n\r\nassert(isequal(N_GeneralizedEggs(100000, 2),447))\r\n\r\nassert(isequal(N_GeneralizedEggs(100000, 3),85))\r\n\r\nassert(isequal(N_GeneralizedEggs(100000, 5),27))\r\n\r\nassert(isequal(N_GeneralizedEggs(100000, 7),20))\r\n\r\nassert(isequal(N_GeneralizedEggs(100000, 10),17))\r\n\r\nassert(isequal(N_GeneralizedEggs(1000000, 2),1414))\r\n\r\nassert(isequal(N_GeneralizedEggs(1000000, 3),182))\r\n\r\nassert(isequal(N_GeneralizedEggs(1000000, 4),71))\r\n\r\nassert(isequal(N_GeneralizedEggs(1000000, 10),21))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":178544,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2018-08-04T01:43:53.000Z","updated_at":"2025-06-17T06:09:27.000Z","published_at":"2018-08-04T13:00:01.000Z","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\u003eA firm has invented a super-strong egg. For publicity purposes, it wants to determine the highest floor in a story building with\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_f\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e floors from which such an egg can fall without breaking. The firm has given a tester\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 identical eggs to experiment with. The same egg can be dropped multiple times unless it breaks.\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\u003eWhat is the minimum number of droppings\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\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that is guaranteed to determine the highest safe floor in all cases for a given number of floors\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_f\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, and eggs\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 ?\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\u003eAPPLICATION:\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e This problem has many applications in the real world such as avoiding a call out to the slow HDD, or attempting to minimize cache misses, or running a large number of expensive queries on a database.\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\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":44713,"title":"The Google Interview: Two Eggs Problem","description":"Consider the following problem, a popular Google interview question:\r\n\r\nA firm has invented a super-strong egg. For publicity purposes, it wants to determine the highest floor in a story building of _n_ floors from which such an egg can fall without breaking. The firm has given a tester two identical eggs to experiment with. The same egg can be dropped multiple times unless it breaks. \r\n\r\nFor a _n_ floor story building, what is the minimum number of droppings _d_ that is guaranteed to determine the highest safe floor in all cases?\r\n","description_html":"\u003cp\u003eConsider the following problem, a popular Google interview question:\u003c/p\u003e\u003cp\u003eA firm has invented a super-strong egg. For publicity purposes, it wants to determine the highest floor in a story building of \u003ci\u003en\u003c/i\u003e floors from which such an egg can fall without breaking. The firm has given a tester two identical eggs to experiment with. The same egg can be dropped multiple times unless it breaks.\u003c/p\u003e\u003cp\u003eFor a \u003ci\u003en\u003c/i\u003e floor story building, what is the minimum number of droppings \u003ci\u003ed\u003c/i\u003e that is guaranteed to determine the highest safe floor in all cases?\u003c/p\u003e","function_template":"function d = Google(h)\r\n  \r\nend","test_suite":"%%\r\nassert(isequal(Google(1),1))\r\n\r\n%%\r\nassert(isequal(Google(5),3))\r\n\r\n%%\r\nassert(isequal(Google(20),6))\r\n\r\n%%\r\nassert(isequal(Google(50),10))\r\n\r\n%%\r\nassert(isequal(Google(75),12))\r\n\r\n%%\r\nassert(isequal(Google(100),14))\r\n\r\n%%\r\nassert(isequal(Google(120),15))\r\n\r\n%%\r\nassert(isequal(Google(180),19))\r\n\r\n%%\r\nassert(isequal(Google(250),22))\r\n\r\n%%\r\nassert(isequal(Google(320),25))\r\n\r\n%%\r\nassert(isequal(Google(360),27))\r\n\r\n%%\r\nassert(isequal(Google(410),29))\r\n\r\n%%\r\nassert(isequal(Google(500),32))\r\n\r\n%%\r\nassert(isequal(Google(610),35))\r\n\r\n%%\r\nassert(isequal(Google(1000),45))","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":178544,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":22,"test_suite_updated_at":"2018-09-07T17:47:50.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2018-08-03T21:41:09.000Z","updated_at":"2026-01-20T13:52:14.000Z","published_at":"2018-08-04T01:39:07.000Z","restored_at":"2018-10-10T14:58:01.000Z","restored_by":null,"spam":false,"simulink":false,"admin_reviewed":true,"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 following problem, a popular Google interview question:\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\u003eA firm has invented a super-strong egg. For publicity purposes, it wants to determine the highest floor in a story building 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:i/\u003e\u003c/w:rPr\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e floors from which such an egg can fall without breaking. The firm has given a tester two identical eggs to experiment with. The same egg can be dropped multiple times unless it breaks.\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 a\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 floor story building, what is the minimum number of droppings\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\u003ed\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e that is guaranteed to determine the highest safe floor in all cases?\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":44714,"title":"The Generalized-N Eggs Problem","description":"A firm has invented a super-strong egg. For publicity purposes, it wants to determine the highest floor in a story building with _N_f_ floors from which such an egg can fall without breaking. The firm has given a tester _N_ identical eggs to experiment with. The same egg can be dropped multiple times unless it breaks. \r\n\r\nWhat is the minimum number of droppings _d_ that is guaranteed to determine the highest safe floor in all cases for a given number of floors _N_f_, and eggs _N_ ?\r\n\r\n*APPLICATION:* This problem has many applications in the real world such as avoiding a call out to the slow HDD, or attempting to minimize cache misses, or running a large number of expensive queries on a database.","description_html":"\u003cp\u003eA firm has invented a super-strong egg. For publicity purposes, it wants to determine the highest floor in a story building with \u003ci\u003eN_f\u003c/i\u003e floors from which such an egg can fall without breaking. The firm has given a tester \u003ci\u003eN\u003c/i\u003e identical eggs to experiment with. The same egg can be dropped multiple times unless it breaks.\u003c/p\u003e\u003cp\u003eWhat is the minimum number of droppings \u003ci\u003ed\u003c/i\u003e that is guaranteed to determine the highest safe floor in all cases for a given number of floors \u003ci\u003eN_f\u003c/i\u003e, and eggs \u003ci\u003eN\u003c/i\u003e ?\u003c/p\u003e\u003cp\u003e\u003cb\u003eAPPLICATION:\u003c/b\u003e This problem has many applications in the real world such as avoiding a call out to the slow HDD, or attempting to minimize cache misses, or running a large number of expensive queries on a database.\u003c/p\u003e","function_template":"function y = N_GeneralizedEggs(N_f, N)\r\n % N_f Number of story building floors\r\n % N   Number of eggs\r\nend","test_suite":"assert(isequal(N_GeneralizedEggs(0, 1),0))\r\n\r\nassert(isequal(N_GeneralizedEggs(10, 2),4))\r\n\r\nassert(isequal(N_GeneralizedEggs(10, 3),4))\r\n\r\nassert(isequal(N_GeneralizedEggs(50, 1),50))\r\n\r\nassert(isequal(N_GeneralizedEggs(50, 2),10))\r\n\r\nassert(isequal(N_GeneralizedEggs(50, 3),7))\r\n\r\nassert(isequal(N_GeneralizedEggs(50, 50),6))\r\n\r\nassert(isequal(N_GeneralizedEggs(50, 51),6))\r\n\r\nassert(isequal(N_GeneralizedEggs(100, 1),100))\r\n\r\nassert(isequal(N_GeneralizedEggs(100, 2),14))     % The famous two eggs problem.\r\n\r\nassert(isequal(N_GeneralizedEggs(100, 3),9))\r\n\r\nassert(isequal(N_GeneralizedEggs(100, 10),7))\r\n\r\nassert(isequal(N_GeneralizedEggs(100, 100),7))\r\n\r\nassert(isequal(N_GeneralizedEggs(250, 2),22))\r\n\r\nassert(isequal(N_GeneralizedEggs(250, 4),9))\r\n\r\nassert(isequal(N_GeneralizedEggs(500, 2),32))\r\n\r\nassert(isequal(N_GeneralizedEggs(500, 5),10))\r\n\r\nassert(isequal(N_GeneralizedEggs(500, 6),10))\r\n\r\nassert(isequal(N_GeneralizedEggs(1000, 2),45))\r\n\r\nassert(isequal(N_GeneralizedEggs(1000, 3),19))\r\n\r\nassert(isequal(N_GeneralizedEggs(1000, 7),11))\r\n\r\nassert(isequal(N_GeneralizedEggs(1000, 10),10))\r\n\r\nassert(isequal(N_GeneralizedEggs(100000, 2),447))\r\n\r\nassert(isequal(N_GeneralizedEggs(100000, 3),85))\r\n\r\nassert(isequal(N_GeneralizedEggs(100000, 5),27))\r\n\r\nassert(isequal(N_GeneralizedEggs(100000, 7),20))\r\n\r\nassert(isequal(N_GeneralizedEggs(100000, 10),17))\r\n\r\nassert(isequal(N_GeneralizedEggs(1000000, 2),1414))\r\n\r\nassert(isequal(N_GeneralizedEggs(1000000, 3),182))\r\n\r\nassert(isequal(N_GeneralizedEggs(1000000, 4),71))\r\n\r\nassert(isequal(N_GeneralizedEggs(1000000, 10),21))\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":178544,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2018-08-04T01:43:53.000Z","updated_at":"2025-06-17T06:09:27.000Z","published_at":"2018-08-04T13:00:01.000Z","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\u003eA firm has invented a super-strong egg. 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