a triangle is dissected into $25$ small triangle...
Source: Serbian Mathematical Olympiad 2007
June 10, 2007
combinatorics proposedcombinatorics
Problem Statement
Triangle is dissected into small triangles as shown. All vertices of these triangles are painted in three colors so that the following conditions are satisfied: Vertex is painted in green, vertex in red, and in blue; Each vertex on side is either green or red, each vertex on is either red or blue, and each vertex on is either green or blue. The vertices inside the big triangle are arbitrarily colored.
Prove that, regardless of the way of coloring, at least one of the small triangles has vertices of three different colors.