Solving General Lattice Puzzles

In this paper we describe implementations of two general methods for solving puzzles on any structured lattice. We define the puzzle as a graph induced by (finite portion of) the lattice, and apply a back-tracking method for iteratively find all solutions by identifying parts of the puzzle (or transformed versions of them) with subgraphs of the puzzle, such that the entire puzzle graph is covered without overlaps by the graphs of the parts. Alternatively, we reduce the puzzle problem to a submatrix-selection problem, and solve the latter problem by using the "dancing-links" trick of Knuth. A few expediting heuristics are discussed, and experimental results on various lattice puzzles are presented.