Problem 271. N-Cards Problem

Created by @bmtran (Bryant Tran)

Solve Later

{"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":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>You have a deck of</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>N</w:t></w:r><w:r><w:t> cards numbered in order from 1 to</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>N</w:t></w:r><w:r><w:t>. You discard the top card (card 1) and place the next card (card 2) at the bottom of the deck. Then you discard the top card of the remaining deck (card 3), and place the next card (card 4) at the bottom of the deck. We repeat the procedure: discarding the top card and placing the next card at the bottom of the deck. Eventually, you will have one card left. What is the number of that card?</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Example</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[    nCardsProblem(5)\n\n    deck = [ 1 2 3 4 5 ]\n    deck = [ 2 3 4 5 ]\n    deck = [ 3 4 5 2 ]\n    deck = [ 4 5 2 ]\n    deck = [ 5 2 4 ]\n    deck = [ 2 4 ]\n    deck = [ 4 2 ]\n    deck = [ 2 ]]]></w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

351 Solutions
188 Solvers

Last Solution submitted on Aug 10, 2020

Last 200 Solutions

Problem Comments

1 Comment

1 Comment

Peter Wittenberg on 29 Aug 2012

What an interesting pattern!

Solution Comments

Solution 31960

2 Comments

2 Comments

@bmtran (Bryant Tran) on 7 Feb 2012

love it

Kuifeng on 13 Apr 2012

This is so mathematical!

Problem Recent Solvers188

Problem Tags

loop math

Problem 271. N-Cards Problem

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers188

Suggested Problems

More from this Author56

Problem Tags

Problem 271. N-Cards Problem

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers188

Suggested Problems

More from this Author56

Problem Tags

Players