MathDB
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 20192019-gon polygon is dyed with red, yellow and blue, and there are exactly 673673 sides of each kind of color. Prove that there exists at least one way to draw 20162016 diagonals to divide the convex 20192019-gon polygon into 20172017 triangles, such that any two of the 20162016 diagonals don't have intersection inside the 20192019-gon polygon,and for any triangle in all the 20172017 triangles, the colors of the three sides of the triangle are all the same, either totally different.