Problem 44797. Cannibal eating odd and even numbered men

Created by PE

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{"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":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><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>There are N men in a queue. A cannibal eats either all odd-numbered or all even-numbered men in the queue at a time. In the first round he eats all the odd-numbered. In the next round he eats all even-numbered. This goes on repeating (with odd or even toggling after every round) till there is only 1 man in the queue. What would be the original number of this man in the queue? e.g. If N = 6,</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Men remaining after round 1: 2, 4, 6</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Men remaining after round 2: 2, 6</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Men remaining after round 3: 6</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Hence answer = 6</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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Last Solution submitted on Sep 22, 2020

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Solution 1684038

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3 Comments

James on 11 Dec 2018

OK. I'll bite. Where did this formula come from?

Tim on 16 Dec 2018

Just from calculating a number of values and figuring out the pattern.

goc3 on 25 Apr 2019

That's quite the pattern to figure out...

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Problem 44797. Cannibal eating odd and even numbered men

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Problem 44797. Cannibal eating odd and even numbered men

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