NP-Completeness Proofs of Puzzles using the T-Metacell Framework
Computational Complexity
2026-01-15 v2
Abstract
Pencil puzzles are puzzles that can be solved by writing down solutions on a paper, using only logical reasoning. In this paper, we utilize the "T-metacell" framework developed by Tang and the MIT Hardness Group to prove the NP-completeness of four new pencil puzzles: Grand Tour, Entry Exit, Zahlenschlange, and Yagit. Additionally, the first three are also proven to be ASP-complete. The results demonstrate how versatile the framework is, offering new insights into the computational complexity of problems with various constraints.
Cite
@article{arxiv.2508.11570,
title = {NP-Completeness Proofs of Puzzles using the T-Metacell Framework},
author = {Nattapol Kiatchaipipat and Suthee Ruangwises},
journal= {arXiv preprint arXiv:2508.11570},
year = {2026}
}
Comments
16 pages, 20 figures