MathDB

6

Part of 2000 Portugal MO

Problems(1)

n players in a tournament, there can be only one champion

Source: Portugal OPM 2000 p6

5/18/2024
In a tournament, nn players participate. Each player plays each other exactly once, with no ties. A player AA is said to be champion if, for every other player BB, one of the following two situations occurs: (a) AA beat BB; (b) AA beat a player CC who in turn beat BB. Prove that in such a tournament there cannot be exactly two champions.
combinatorics