n players in a tournament, there can be only one champion
Source: Portugal OPM 2000 p6
May 18, 2024
combinatorics
Problem Statement
In a tournament, players participate. Each player plays each other exactly once, with no ties. A player is said to be champion if, for every other player , one of the following two situations occurs:
(a) beat ;
(b) beat a player who in turn beat .
Prove that in such a tournament there cannot be exactly two champions.