IMO 1971 LL YUG54

Origin: YUG

Problem

A set M is formed of
2n n  men, n = 1, 2, . . .. Prove that we can choose a subset P of the set M consisting of n + 1 men such that one of the following conditions is satisfied: (1) every member of the set P knows every other member of the set P; (2) no member of the set P knows any other member of the set P.