Completing a colorful hexagon
Source: 2022 Grosman Mathematical Olympiad P6
September 22, 2022
combinatoricsColoringcombinatorics unsolved
Problem Statement
In the following image is a beehive lattice of hexagons. Each cell is colored in one of three colors Red, Blue, or Green (denoted by the letters ). The frame is colored according to the instructions in the image, and the rest of the hexagons are colored however one wants.
Is there necessarily a point where three hexagons of different colors meet?