NP-Completeness Proofs of Puzzles using the T-Metacell Framework

Nattapol Kiatchaipipat; Suthee Ruangwises

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arXiv · 2508.11570

NP-Completeness Proofs of Puzzles using the T-Metacell Framework

Nattapol Kiatchaipipat·Suthee Ruangwises

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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.

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Nattapol Kiatchaipipat, Suthee Ruangwises. 2025-08-15. NP-Completeness Proofs of Puzzles using the T-Metacell Framework. https://arxiv.org/abs/2508.11570

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