MathDB

In a tournament, every two of the

n

players played exactly one match with each other (no draws). Prove that it is possible either (i) to partition the league in two groups

A

and

B

such that everybody in

A

defeated everybody in

B

; or (ii) to arrange all the players in a chain

x_1, x_2, . . . , x_n, x_1

in such a way that each player defeated his successor.

Problem Statement