In the Nikoli pencil-and-paper game Tatamibari, a puzzle consists of an $m \times n$ grid of cells, where each cell possibly contains a clue among +, -, |. The goal is to partition the grid into disjoint rectangles, where every rectangle contains exactly one clue, rectangles containing + are square, rectangles containing - are strictly longer horizontally than vertically, rectangles containing | are strictly longer vertically than horizontally, and no four rectangles share a corner. We prove this puzzle NP-complete, establishing a Nikoli gap of 16 years. Along the way, we introduce a gadget framework for proving hardness of similar puzzles involving area coverage, and show that it applies to an existing NP-hardness proof for Spiral Galaxies. We also present a mathematical puzzle font for Tatamibari.
- Pub Date:
- March 2020
- Computer Science - Computational Complexity;
- Computer Science - Computational Geometry
- 26 pages, 21 figures. New discussion of safe placement of wires in Sections 3.2 and 3.5. To appear at the 10th International Conference on Fun with Algorithms (FUN 2020)