Tatamibari Puzzle Generator
The grid is cut along its own lines into rectangles, and every rectangle contains exactly one symbol: a plus means that rectangle is a square, a dash means it is wider than it is tall, and a vertical bar means it is taller than it is wide. Unlike a number, a shape symbol never pins down an exact size on its own — a plus could mean a 2x2 or a 5x5 square, a dash could mean a rectangle of almost any width — so the puzzle is solved by working out where the boundaries must fall for every symbol to end up telling the truth about its own piece. One further rule applies everywhere at once: no four rectangles may share a single corner point. Three meeting at a point is fine and comes up often; a fourth at the same point never does.
What this generator does
Builds a random partition of the grid into rectangles, covering the first uncovered cell each time and backtracking on any placement that would let four pieces meet at one grid point. Each rectangle is then clued with its own true shape category, at a random cell inside it. The clues are kept only once an independent solver — which knows nothing about how the grid was built, only the printed shape symbols and the no-four-corners rule — proves they pin down that one partition and no other.
How to use this tool
- Choose a grid size, then print or copy it.
- Cut the grid along its lines into rectangles, one per symbol.
- Make each rectangle match its own symbol: plus for square, dash for wider-than-tall, bar for taller-than-wide.
- Never let four rectangles meet at one grid point — three is fine, four is not allowed anywhere.
- Show the answer to check the finished grid.
Understanding the controls
- Grid
- 4, 5, 6, 7 or 8 squares a side. All five are measured to settle well inside a page-load budget, worst case.
- Seed (optional)
- Type anything to rebuild the same puzzle later, which is how you reprint a page you have lost. The seed makes the puzzle repeatable; it carries no cryptographic strength and is not a secret.
Common use cases
- A rectangle-partition puzzle where the clue is a shape category, not a number to factor
- Practice reasoning about where a boundary must fall when the clue alone leaves the exact size open
- A printable page for a puzzle club or a classroom that already knows this site's Shikaku and wants a genuinely different clue rule
- Reprinting the identical grid later from its seed
How this generator works
This site's own Shikaku already cuts a grid into rectangles from one clue each, and the search here covers the first uncovered cell with every remaining clue's rectangle that could contain it, the same way Shikaku's solver does. What differs is what a candidate rectangle has to satisfy: Shikaku's clue is an exact area, which factors into a short, specific list of possible dimensions and prunes the search hard on its own. Tatamibari's clue is only a category — square, wider-than-tall or taller-than-wide — which is true of far more candidate rectangles at every size, so the search alone would explore many more dead ends per clue. The no-four-corners rule is checked on every placement, not only at the end, precisely to cut off those dead ends as early as possible: the moment a tentative rectangle would let four pieces meet at one point, that whole branch is abandoned immediately rather than being discovered much later once the grid is nearly full. Sizes are measured directly, not assumed: over 80 seeded builds including the full uniqueness proof, 8x8 peaked at 2,038 milliseconds, while 15 seeded attempts at 9x9 peaked at 10.7 seconds with no sign of levelling off — an order of magnitude worse with one more row and column. That gap is why the grid stops at 8.
Randomness and fairness
Which shapes are tried first while building the partition, and which cell inside a finished rectangle holds its symbol, both come from your browser's cryptographic random source. Giving a seed replaces that source with a repeatable one, so the same puzzle can be printed again; the seed is for reproducibility, not cryptographic strength.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- The grid stops at 8 squares a side. Measured directly, a 9x9 grid peaked at 10.7 seconds to settle even with corner-violation pruning on every placement, which is too slow for a page a person is waiting on.
- Difficulty is not graded — a grid can be settled from a handful of well-placed symbols or need several worked out together, and there is no control over which.
- Sashigane, the closely related puzzle that partitions the grid into carpenter's-square (L-tromino) shaped regions with two free arm lengths instead of rectangles, is not built here — its pieces are L-shapes rather than rectangles, which needs a different construction and a different check for a single answer, so it is not offered here.
Privacy and your data
The partition is built, clued and checked for a single answer entirely in your browser. Nothing you type as a seed, and no puzzle made from it, leaves the device.
Frequently asked questions
- Why can a symbol like a plus mean rectangles of such different sizes?
- A shape symbol only names a category — square, wider-than-tall or taller-than-wide — never an exact size. Working out the real size is the puzzle: it comes from fitting every rectangle's shape and every other symbol's shape together across the whole grid, not from any one symbol alone.
- What's actually different between this and this site's Shikaku generator?
- Both cut a grid into rectangles from one clue each, but Shikaku's clue is a number — the rectangle's exact area, which factors into a short list of possible dimensions. Tatamibari's clue is a category with no size attached, and it adds a rule Shikaku has no equivalent of at all: no four rectangles may ever meet at a single grid point.
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