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

DOI10.1007/S11786-022-00530-XarXiv2202.06234MaRDI QIDQ6390959

George Spahn

Publication date: 13 February 2022

Abstract: In this paper we demonstrate a method for counting the number of solutions to various logic puzzles. Specifically, we remove all of the "clues" from the puzzle which help the solver to a unique solution, and instead start from an empty grid. We then count the number of ways to fill in this empty grid to a valid 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 on an empty grid of size $rimesk$.

Mathematics Subject Classification ID

Computational methods for problems pertaining to combinatorics (05-08)

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