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In this paper, we present Demystify, a general tool for creatinghuman-interpretable step-by-step explanations of how to solve a wide range ofpen and paper puzzles from a high-level logical description. Demystify is basedon Minimal Unsatisfiable Subsets (MUSes), which allow Demystify to solvepuzzles as a series of logical deductions by identifying which parts of thepuzzle are required to progress. This paper makes three contributions overprevious work. First, we provide a generic input language, based on the Essenceconstraint language, which allows us to easily use MUSes to solve a much widerrange of pen and paper puzzles. Second, we demonstrate that the explanationsthat Demystify produces match those provided by humans by comparing our resultswith those provided independently by puzzle experts on a range of puzzles. Wecompare Demystify to published guides for solving a range of different pen andpaper puzzles and show that by using MUSes, Demystify produces solvingstrategies which closely match human-produced guides to solving those samepuzzles (on average 89% of the time). Finally, we introduce a new randomisedalgorithm to find MUSes for more difficult puzzles. This algorithm is focusedon optimised search for individual small MUSes.

Using Small MUSes to Explain How to Solve Pen and Paper Puzzles