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There are 25 people sitting around a table and each person has two cards. One of the numbers 1,2,..., 25 is written on each card, and each number occurs on exactly two cards. At a signal, each person passes one of her cards, the one with the smaller number to her right hand neighbor. Prove that sooner or later, one of the players will have two cards with the same numbers.

I am thinking it will have to do with the 12 and 13 card because there is a 50% chance of giving it to their partner but I can't find a way to back that up

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    I don't know the original source of this problem, but I first saw it in the Australian Math Society Gazette, http://www.austms.org.au/Publ/Gazette/2008/Mar08/PuzzleCorner.pdf --- solutions would be in a later issue.2012-11-20
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    Adding an exactly equal problem (http://math.stackexchange.com/questions/241409/card-game-problem) do not help. Just ask where are you stuck here, there are no problem in giving more hint.2012-11-20
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    A generalization on the no.of players will give us that it should always be an odd number to achieve the required state. Isn't it ?2012-11-21
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    @GerryMyerson: Actually, your solution was published in the later issue :-) http://www.austms.org.au/Publ/Gazette/2008/Jul08/PuzzleCorner.pdf2015-10-09
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    See also my anwer to [Ross's follow-up question](http://math.stackexchange.com/questions/245310) on the maximum length of the game.2015-10-09

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