Triangulating three-coloured polygon
Source: IMOTC PT 2 2018 P3, India
July 18, 2018
combinatoricsconvex polygon
Problem Statement
A convex polygon has the property that its vertices are coloured by three colors, each colour occurring at least once and any two adjacent vertices having different colours. Prove that the polygon can be divided into triangles by diagonals, no two of which intersect in the interior of the polygon, in such a way that all the resulting triangles have vertices of all three colours.