A formal proof for the three-colored triangle problem on Coq

Abstract

The three-color triangle problem is a mathematical quiz: Consider regular hexagonal tiles arranged in an inverted triangle shape of n stages, and paint them in three colors so that any three adjacent tiles have the same color or all different colors. The quiz asks to determine the general form of n that satisfies the condition that the colors for the three vertices of the inverted triangle are always the same or different. This quiz was given in the column “Seeking an elegant answer” of the journal “Suugaku Seminar”, and it was shown that the general form of n is 3^k. The paper implements a formalized proof for the three-color triangle problem in Coq. It gives a proof for the problem on paper, and then discusses the devised points for formalization and the benefits obtained by the formal proof on Coq compared to the proof on paper.