Nagoya University Polyomino World

Common Multiple Shape Puzzle is defined as the task of finding, for given finite sets S₁, S₂, …, S_n of polyominoes, a common shape that can be tiled by S₁, S₂, …, S_n, respectively. For each set S_i, multiple copies of polyominoes can be used.

• F5-I5-Q4
• F5-W5-Q4
• N5-Z5-Q4
• X5-L5-N4

The catalogs below present the solutions found by our search with Answer Set Programming. In the catalogs, click a problem name to see a solution and statistics in text format, and click an image to enlarge it.

• Others
• Tetromino-Pentomino
• Pento-Pento-Tetrominoes

1. Banbara, M., Minato, S., Ono, H., Uehara, R.: On the Computational Complexity of Generalized Common Shape Puzzles. Proceedings of the Forty-ninth International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM'24). Lecture Notes in Computer Science, vol. 14519, pp. 55-68. Springer (2024). 10.1007/978-3-031-52113-3_4
2. "Polyomino". Wikipedia
3. DeepGreen, "Computer Puzzle Solution"
4. Mireles, J.L., "Poly²ominoes"
5. Resta, G., "Polypolyominoes"
6. Sicherman, G., "Polyform Curiosities"

Mutsunori Banbara
Professor
Nagoya University
Graduate School of Informatics
Furo-cho, Chikusa-ward, Nagoya-city, 464-8601