IMO 1966 LL CZS43

Origin: CZS

Problem

Five points in a plane are given, no three of which are collinear. Every two of them are joined by a segment, colored either red or gray, so that no three segments form a triangle colored in one color. (a) Prove that (1) every point is a vertex of exactly two red and two gray segments, and (2) the red segments form a closed path that passes through each point. (b) Give an example of such a coloring.