Non-orientable Nurikabe

Abstract

We study Nurikabe puzzles on non-orientable surfaces. Specifically, we propose two versions of non-orientable Nurikabe and investigate their combinatorics on Möbius strips, Klein bottles, and projective planes of size $1\times n$. Our results establish new connections among the OEIS sequences A101946, A213387, A123203, and A001045 (the Jacobsthal sequence).

v2: improvements following referee feedback; published version