revenge of the 2009-gon, game of coloring green diagonals
Source: Bulgaria 2009 NMO p5
May 28, 2019
combinatoricsconvex polygonColoringColor problemdiagonal
Problem Statement
We divide a convex -gon in triangles using non-intersecting diagonals. One of these diagonals is colored green. It is allowed the following operation: for two triangles and from the dividing/separating with a common side if the replaced diagonal was green it loses its color and the replacing diagonal becomes green colored. Prove that if we choose any diagonal in advance it can be colored in green after applying the operation described finite number of times.