  In this paper, we present Demystify, a general tool for creating
human-interpretable step-by-step explanations of how to solve a wide range of
pen and paper puzzles from a high-level logical description. Demystify is based
on Minimal Unsatisfiable Subsets (MUSes), which allow Demystify to solve
puzzles as a series of logical deductions by identifying which parts of the
puzzle are required to progress. This paper makes three contributions over
previous work. First, we provide a generic input language, based on the Essence
constraint language, which allows us to easily use MUSes to solve a much wider
range of pen and paper puzzles. Second, we demonstrate that the explanations
that Demystify produces match those provided by humans by comparing our results
with those provided independently by puzzle experts on a range of puzzles. We
compare Demystify to published guides for solving a range of different pen and
paper puzzles and show that by using MUSes, Demystify produces solving
strategies which closely match human-produced guides to solving those same
puzzles (on average 89% of the time). Finally, we introduce a new randomised
algorithm to find MUSes for more difficult puzzles. This algorithm is focused
on optimised search for individual small MUSes.
