The rules of Tatamibari
Tatamibari — 畳ばり — is a Japanese tiling puzzle about cutting a floor into mats.
- Divide the whole grid into rectangles. Every cell belongs to exactly one of them.
- Every rectangle holds exactly one symbol, and every symbol ends up in exactly one rectangle.
- The symbol says the shape. A plus means a square, equal in width and height. A vertical bar means taller than wide. A horizontal bar means wider than tall.
- Four rectangles may never meet at a single point, the way four tatami mats are never laid corner to corner.
- a square
- taller than wide
- wider than tall
Ways in
Start with the crowded corners
A cell in the corner of the grid can only be covered by a rectangle that reaches it from one direction. Work out which symbols are close enough to reach, then rule out the ones whose shape cannot stretch that far without swallowing a second symbol.
Two symbols in touching cells
Neighbouring symbols always sit in different rectangles, so the line between them is a boundary before you have drawn anything. On a dense grid that alone fixes a good deal of the answer.
A plus in a tight space
A plus needs equal width and height. If a symbol has only one free cell to its left and none above, its rectangle is a 1×1, and everything around it is then someone else's. Squares are the most constrained symbol and the best place to begin.
Count the cells a symbol can own
Every cell belongs to something. If a cell can only be reached by one symbol, it belongs to that symbol, and the rectangle has to stretch to cover it. Chasing the cells with fewest owners is exactly what the solver does.
Watch the four-way points
Whenever three boundaries already meet at a point, the fourth line through it is forbidden — the two rectangles on the remaining side must be one and the same. Late in a puzzle this rule closes more cells than the shapes do.