Possible Duplicate:
A less challenging trivia problem
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 was thinking that after a few moves, the 25-25 are in different hands and stationary. 24-24 is also in different hands and stationary. ect. until card 13. I'm stuck on this part. I can't find a way to garuntee that one will get a match