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