Nurikabe is NP-Complete

Brandon McPhail
Reed College

Abstract: Nurikabe is one of many paper-and-pencil puzzles recently popular in Japan (and now elsewhere). The question, "Is this Nurikabe puzzle solvable?" turns out to be very "hard" to answer quickly. We construct a polynomial-time reduction from Circuit-SAT to Nurikabe to show that Nurikabe belongs to the hardest of its class. The construction, built of grid-based puzzle boards, is largely visual and should be fun.