MathDB

n

players participated in a competition. Any two players have played exactly one game, and there was no tie game. For a set of

k(\le n)

players, if it is able to line the players up so that each player won every player at the back, we call the set ranked. For each player who participated in the competition, the set of players who lost to the player is ranked. Prove that the whole set of players can be split into three or less ranked sets.

3

Problems(1)