Tuesday, March 9, 2010

Tennis tournament

In a tennis tournament of 100 people, each player plays every other players exactly once. There is no draw in a tennis game, one side always wins.

Given that no player loses all of his games, prove that there is a cycle of exactly 3 players. That is, there are players A,B, and C such that A defeats B, B defeats C, and C defeats A.

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