Coloring problem in 2019 China Second Round(B)
Source: 2019 China Second Round(B) P4
September 8, 2019
combinatoricsColoring
Problem Statement
Each side of a convex -gon polygon is dyed with red, yellow and blue, and there are exactly sides of each kind of color. Prove that there exists at least one way to draw diagonals to divide the convex -gon polygon into triangles, such that any two of the diagonals don't have intersection inside the -gon polygon,and for any triangle in all the triangles, the colors of the three sides of the triangle are all the same, either totally different.