Non-orientable Nurikabe

TL;DR

This paper explores Nurikabe puzzles on non-orientable surfaces like Möbius strips and Klein bottles, establishing new combinatorial connections and proposing two variants of the puzzle.

Contribution

It introduces two versions of non-orientable Nurikabe and investigates their combinatorics on various non-orientable surfaces.

Findings

Established connections with OEIS sequences A101946, A213387, A123203, and A001045.

Analyzed combinatorics of non-orientable Nurikabe on different surfaces.

Proposed two variants of Nurikabe for non-orientable surfaces.

Abstract

We study Nurikabe puzzles on non-orientable surfaces. Specifically, we propose two versions of non-orientable Nurikabe and investigate their combinatorics on M\"obius 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).