The Computational Complexity of Creek Puzzles on Several Grids

Abstract

The Creek puzzle is a pencil-and-paper puzzle developed by Japanese puzzle publisher Nikoli, usually played on a square grid. We study the computational complexity of the Creek puzzle, and first it is shown that deciding whether a given instance of this puzzle on a square grid has a solution is NP-complete by a reduction from the Circuit-SAT problem. In addition, we prove the NP-completeness for the Creek puzzle on triangular grids in the same way.