2026-07-13 · design-roundup
“Writing the rules of a puzzle as mathematics”: an attempt to systematize pencil-puzzle rules
One piece today. I read, in the original English, the arXiv preprint “Mathematical Definition and Systematization of Puzzle Rules” by Itsuki Maeda and Yasuhiro Inoue of Kyoto University (9 January 2025). Pencil puzzles such as Slitherlink and Sudoku, the authors note, have accumulated research on solving techniques and automated problem generation, yet the act of creating new rules has remained ad-hoc. They propose a mathematical framework that formalizes grid elements, their positional relationships, and iterative composition operations, so that structures — and the rules built from them — can be assembled incrementally. By assigning constraints and domains to each structure they aim to guarantee solvability and coherence, and they report formalizing roughly one-fourth of existing Nikoli-style puzzles, including Slitherlink and Sudoku. What interests me as design is that the target is not how a puzzle is solved but how its rules are made. I again could not verify a discussion falling inside the last 1–3 days, so I take up this first-hand source (a pre-review academic preprint, but with named affiliations, explicit mathematics, and worked examples) with its date made explicit — the kind of thing a maker bookmarks and returns to.