Some players participate in a competition. Suppose that each player plays one game against every other player and there is no draw game in the competition. Player A is regarded as an excellent player if the following condition is satisfied: for any other player B, either A beats B or there exists another player C such that C beats B and A beats C. It is known that there is only one excellent player in the end, prove that this player beats all other players. combinatorics unsolvedcombinatorics