GMP: Gratuitous Math Post

I love my math senior seminar a lot, and had an obscene amount of fun with one of the problems due next Tuesday.

7. In a round-robin tennis tournament with n players, each player plays every other player exactly once. Can one always rank the players in such a way that the player ranked 1st has beaten the player ranked 2nd, the player ranked 2nd has beaten the player ranked 3rd, …, the player ranked (n-1)st has beaten the player ranked nth?

( Solution )