Solving Tantrix via Integer Programming

TL;DR

This paper presents an integer programming approach to solve the Tantrix puzzle by formulating its rules as constraints, enabling the solution of moderate-sized instances up to 50 tiles.

Contribution

It introduces a novel integer programming formulation for Tantrix, including additional constraints and an objective to handle invalid solutions effectively.

Findings

Successfully solved Tantrix puzzles up to 50 tiles.

Developed a formulation that handles invalid solutions with additional constraints.

Demonstrated the effectiveness of mathematical programming for puzzle solving.

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.