Non-orientable Nurikabe
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).
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