Tatamibari Font

by Aviv Adler, Jeffrey Bosboom, Erik Demaine, and Martin Demaine, Quanquan Liu, and Jayson Lynch, 2020

 


In a Tatamibari puzzle, you are given a grid of unit squares, some of which have a clue icon of , , or . The goal is to decompose the grid into rectangles, each containing exactly one clue icon, where rectangles containing are squares, rectangles containing are wider than they are tall, and rectangles containing are taller than they are wide. Furthermore, at most three rectangles can meet at any grid intersection.

Tatamibari (タタミバリ in Japanese) is one of the many pencil-and-paper puzzles designed for the Japanese puzzle magazine and publisher Nikoli, Like most Nikoli puzzles, Tatamibari is NP-complete, meaning that there is no efficient algorithm to solve them, assuming P ≠ NP. Unusually, it took 16 years for this puzzle to be proved NP-complete.

This typeface features 26 uniquely solvable Tatamibari puzzles, one for each letter of the alphabet. The puzzle font shows just the clues. We introduce clues of two different colors, black and white; after solving the puzzle, the corresponding rectangle should be filled the same color. The black rectangles then form a letter. The solved font illustrates these solutions. See our paper for details, including how we designed the typeface.

In the puzzle font, you can try your hand at solving the puzzles by clicking on grid edges to toggle whether they are edges of a rectangle (black). If you Enable third “connected” state, then you can click on an edge a second time to make it gray and perpendicular to indicate that the two connected grid squares belong to the same rectangle. The rectangles will fill in when you solve the puzzle. Click Reset all puzzles to start over.

This font was designed using a custom design tool which uses our Tatamibari solver built on the Z3 engine. You can use it to design your own 10×10 Tatamibari puzzles and check for unique solutions. As possible starting points, here are links to load each letter into the design tool: .

Check out other mathematical and puzzle fonts. • Feedback or not working? Email Erik. • Source code on GitHub.