Solving Tantrix via Integer Programming

Abstract

Tantrix is a puzzle to make a loop by connecting lines drawn on hexagonal tiles, and the objective of this research is to solve it by a computer. For this purpose, we give a problem setting of solving Tantrix as arranging tiles in an appropriate shape and making a loop at the same time within a given hexagonal lattice board. We then formulate it as an integer program by expressing the rules of Tantrix as its constraints, and solve it by a mathematical programming solver to have a solution. As a result, we establish a formulation that solves Tantrix of moderate sizes, and even when the solutions are invalid only by elementary constraints, we achieved it by introducing additional constraints and an artificial objective function to avoid flaws in invalid solutions. By this approach we are successful in solving Tantrix of size up to 50.