IMO 1970 LL BUL13

Origin: BUL

Problem

A triangle ABC is given. Each side of ABC is divided into equal parts, and through each of the division points are drawn lines parallel to AB, BC, and CA, thus cutting ABC into small triangles. To each of the vertices of these triangles is assigned 1, 2, or 3, so that: (1) to A, B, C are assigned 1, 2 and 3 respectively; (2) points on AB are marked by 1 or 2; (3) points on BC are marked by 2 or 3; (4) points on CA are marked by 3 or 1. Prove that there must exist a small triangle whose vertices are marked by 1, 2, and 3.