The Complexity of Tantrix Match Puzzles with Four Colors

Abstract

Tantrix Match is a puzzle in which hexagonal tiles are arranged within a hexagonal lattice board in which there are some fixed tiles. Each tile has painted lines in three of four possible colors, and it is required that all lines that touch on adjacent tiles must match in color. The aim of this research is to determine the computational complexity of this puzzle, and we prove that the generalized Tantrix Match is NP-complete by reduction from the circuit-satisfiability problem (Circuit-SAT).