Same colour triangle
Source: Baltic Way 1994 - 20
February 24, 2005
combinatorics unsolvedcombinatorics
Problem Statement
An equilateral triangle is divided into congruent equilateral triangles by lines parallel to its sides. Each vertex of the small triangles is coloured in one of three colours. Prove that there exist three points of the same colour being the vertices of a triangle with its sides parallel to the lines of the original triangle.