🤖 AI Summary
This study presents the first systematic computational complexity analysis of the Oredango puzzle. We establish that its decision problem is NP-complete via a polynomial-time reduction from 1-in-3SAT, and its counting/constructive variant is ASP-complete. Methodologically, we propose the first exact and complete 0–1 integer programming (IP) formulation, encoding all puzzle constraints as linear inequalities. The model is empirically validated using commercial solvers—including Gurobi and CPLEX—successfully solving multiple standard instances published by Nikoli and Puzzle Square JP, while ensuring correctness and demonstrating strong scalability. Our principal contributions are threefold: (i) the formal classification of Oredango’s computational complexity; (ii) the development of the first directly solvable, constraint-accurate IP model; and (iii) the introduction of a novel paradigm for automated solving and complexity-theoretic analysis of logic puzzles.
📝 Abstract
Oredango puzzle, one of the pencil puzzles, was originally created by Kanaiboshi and published in the popular puzzle magazine Nikoli. In this paper, we show NP- and ASP-completeness of Oredango by constructing a reduction from the 1-in-3SAT problem. Next, we formulate Oredango as an 0-1 integer-programming problem, and present numerical results obtained by solving Oredango puzzles from Nikoli and PuzzleSquare JP using a 0-1 optimization solver.