Solving Shisen-Sho boards

Abstract

We give a simple proof of that determining solvability of Shisen-Sho boards is NP-complete. Furthermore, we show that under realistic assumptions, one can compute in logarithmic time if two tiles form a playable pair. We combine an implementation of the algoritm to test playability of pairs with my earlier algorithm to solve Mahjong Solitaire boards with peeking, to obtain an algorithm to solve Shisen-Sho boards. We sample several Shisen-Sho and Mahjong Solitaire layouts for solvability for Shisen-Sho and Mahjong Solitaire.