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In this paper we demonstrate a method for counting the number of solutions tovarious logic puzzles. Specifically, we remove all of the "clues" from thepuzzle which help the solver to a unique solution, and instead start from anempty grid. We then count the number of ways to fill in this empty grid to avalid solution. We fix the number of rows $r$, vary the number of columns $k$,and then compute the sequence $A_r(k)$, which gives the number of solutions onan empty grid of size $r \times k$.

Enumerating solutions to grid based puzzles with a fixed number of rows