Problem 271. N-Cards Problem

Created by @bmtran (Bryant Tran)

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{"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>"}]}

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350 Solutions
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Last Solution submitted on May 28, 2020

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Peter Wittenberg on 29 Aug 2012

What an interesting pattern!

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Solution 31960

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2 Comments

@bmtran (Bryant Tran) on 7 Feb 2012

love it

Kuifeng on 13 Apr 2012

This is so mathematical!

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Problem 271. N-Cards Problem

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Problem 271. N-Cards Problem

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Last 200 Solutions

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