Subcontests
(3)Tournament and diving into groups
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 x1,x2,...,xn,x1 in such a way that each player defeated his successor.