Problem 272. Generalized 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>Preface: This is a generalized version of the problem I presented</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://www.mathworks.com/matlabcentral/cody/problems/271-n-cards-problem\"><w:r><w:t>here</w:t></w:r></w:hyperlink><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>You have a deck of N cards numbered in order from 1 to N. You are given a pattern to discard a certain number of cards and move a number of cards to 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:t>The sequence of discarding/moving cards will be given in a row vector of 1s and -1s where 1 represents moving a card to the bottom of the deck and -1 represents discarding a card. This sequence should be repeated until there is only one card left (e.g. [-1 1] would return this problem to the non-generalized case).</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[ generalNCardsProblem(5,[-1 1])\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 ]\n\n generalNCardsProblem(5,[-1 1 1 -1])\n deck = [ 1 2 3 4 5 ]\n deck = [ 2 3 4 5 ]\n deck = [ 3 4 5 2 ]\n deck = [ 4 5 2 3 ]\n deck = [ 5 2 3 ]\n deck = [ 2 3 ]\n deck = [ 3 2 ]\n deck = [ 2 3 ]\n deck = [ 3 ]]]></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>"}]}

Preface: This is a generalized version of the problem I presented <a href="http://www.mathworks.com/matlabcentral/cody/problems/271-n-cards-problem">here</a>.You have a deck of N cards numbered in order from 1 to N. You are given a pattern to discard a certain number of cards and move a number of cards to the bottom of the deck. Eventually, you will have one card left. What is the number of that card?The sequence of discarding/moving cards will be given in a row vector of 1s and -1s where 1 represents moving a card to the bottom of the deck and -1 represents discarding a card. This sequence should be repeated until there is only one card left (e.g. [-1 1] would return this problem to the non-generalized case).Example<pre> generalNCardsProblem(5,[-1 1])
 deck = [ 1 2 3 4 5 ]
 deck = [ 2 3 4 5 ]
 deck = [ 3 4 5 2 ]
 deck = [ 4 5 2 ]
 deck = [ 5 2 4 ]
 deck = [ 2 4 ]
 deck = [ 4 2 ]
 deck = [ 2 ]</pre><pre> generalNCardsProblem(5,[-1 1 1 -1])
 deck = [ 1 2 3 4 5 ]
 deck = [ 2 3 4 5 ]
 deck = [ 3 4 5 2 ]
 deck = [ 4 5 2 3 ]
 deck = [ 5 2 3 ]
 deck = [ 2 3 ]
 deck = [ 3 2 ]
 deck = [ 2 3 ]
 deck = [ 3 ]</pre>

Preface: This is a generalized version of the problem I presented <http://www.mathworks.com/matlabcentral/cody/problems/271-n-cards-problem here>.

You have a deck of N cards numbered in order from 1 to N. You are given a pattern to discard a certain number of cards and move a number of cards to the bottom of the deck. Eventually, you will have one card left. What is the number of that card?

The sequence of discarding/moving cards will be given in a row vector of 1s and -1s where 1 represents moving a card to the bottom of the deck and -1 represents discarding a card. This sequence should be repeated until there is only one card left (e.g. [-1 1] would return this problem to the non-generalized case).

*Example*

generalNCardsProblem(5,[-1 1])
    deck = [ 1 2 3 4 5 ]
    deck = [ 2 3 4 5 ]
    deck = [ 3 4 5 2 ]
    deck = [ 4 5 2 ]
    deck = [ 5 2 4 ]
    deck = [ 2 4 ]
    deck = [ 4 2 ]
    deck = [ 2 ]

generalNCardsProblem(5,[-1 1 1 -1])
    deck = [ 1 2 3 4 5 ]
    deck = [ 2 3 4 5 ]
    deck = [ 3 4 5 2 ]
    deck = [ 4 5 2 3 ]
    deck = [ 5 2 3 ]
    deck = [ 2 3 ]
    deck = [ 3 2 ]
    deck = [ 2 3 ]
    deck = [ 3 ]

Solve

Solution Stats

61 Solutions
25 Solvers

Last Solution submitted on Jan 21, 2022

Last 200 Solutions

Problem Comments

Problem Recent Solvers25

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 272. Generalized N-Cards Problem

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers25

Suggested Problems

More from this Author56

Problem Tags

Community Treasure Hunt

Problem 272. Generalized N-Cards Problem

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers25

Suggested Problems

More from this Author56

Problem Tags

Community Treasure Hunt

Players