MathDB

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.

Problem Statement