Evolomino is NP-complete
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908639449579520 |
|---|---|
| author | Nikolaev, Andrei V. |
| author_facet | Nikolaev, Andrei V. |
| contents | Evolomino is a pencil-and-paper logic puzzle popularized by the Japanese publisher Nikoli (like Sudoku, Kakuro, Slitherlink, Masyu, and Fillomino). The puzzle's name reflects its core mechanic: the shapes of polyomino-like blocks that players must draw gradually "evolve" in the directions indicated by pre-drawn arrows. We prove, by reduction from 3-SAT, that the question of whether there exists at least one solution to an Evolomino puzzle satisfying the rules is NP-complete. Since our reduction is parsimonious, i.e., it preserves the number of distinct solutions, we also prove that counting the number of solutions to an Evolomino puzzle is #P-complete. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Evolomino is NP-complete Nikolaev, Andrei V. Computational Complexity Combinatorics 68Q25, 03D15 F.2.2 Evolomino is a pencil-and-paper logic puzzle popularized by the Japanese publisher Nikoli (like Sudoku, Kakuro, Slitherlink, Masyu, and Fillomino). The puzzle's name reflects its core mechanic: the shapes of polyomino-like blocks that players must draw gradually "evolve" in the directions indicated by pre-drawn arrows. We prove, by reduction from 3-SAT, that the question of whether there exists at least one solution to an Evolomino puzzle satisfying the rules is NP-complete. Since our reduction is parsimonious, i.e., it preserves the number of distinct solutions, we also prove that counting the number of solutions to an Evolomino puzzle is #P-complete. |
| title | Evolomino is NP-complete |
| topic | Computational Complexity Combinatorics 68Q25, 03D15 F.2.2 |
| url | https://arxiv.org/abs/2503.07611 |