Shikaku Puzzle Maker
Printable Shikaku sheets with a checked single answer, three difficulties, and the solutions on a toggle.
How to solve it
Divide the whole grid into rectangles. Every rectangle must contain exactly one number, and that number must equal the rectangle’s area in cells. Every cell ends up inside exactly one rectangle, so nothing is left over and nothing overlaps. A 6 is a 1 × 6, a 2 × 3, a 3 × 2 or a 6 × 1 — choosing between those is the whole puzzle, and the corner a number sits in is usually the thread to pull first.
⭐The difficulty is where the number sits, not how big the grid is
A Shikaku is generated by cutting the grid into rectangles and then writing each rectangle’s area into one of its own cells. Which cell you choose looks cosmetic. It is not — it decides whether the puzzle has one answer at all. Same rectangles, same numbers, three different choices of which cell carries the number, 200 boards per measurement:
| Grid | Corner of its rectangle | Middle | Anywhere inside |
|---|---|---|---|
| 7 × 7 | 100% | 98% | 67% |
| 10 × 10 | 100% | 97% | 51% |
| 12 × 12 | 100% | 96% | 37% |
| 14 × 14 | 100% | 90% | 24% |
Read the first column downward: it does not move. Every board tested was uniquely solvable at every size, so putting the number in its rectangle’s corner removes grid size from the question entirely. Read the last column and size is suddenly the dominant term, falling away steadily as the board grows. At 14 × 14 the two choices are 4.2× apart.
The mechanism is structural rather than lucky, which is why it holds so flatly. Scanning the grid row by row, the first cell you meet that is not yet covered can only ever be the top-left corner of whichever rectangle covers it — everything above and to its left is already spoken for. So if the number is sitting on that cell, its rectangle’s corner is pinned before you start, and the only freedom left is which factorisation of the area to use. That resolves, pins the next corner, and cascades.
Which makes the obvious assumption wrong, and it is worth stating as an assumption that failed rather than quietly not making it. "Bigger grids are harder to pin down" is true only if the clues are placed badly. A 14 × 14 with corner clues is exactly as determined as a 7 × 7. The difficulty selector above is therefore not a size control wearing a different label — it genuinely moves the clue inside its rectangle, and the middle setting lands between the two ends at every size.
Every puzzle here is checked before you see it
A generated board is only printed once the solver has confirmed it has exactly one answer — the search counts solutions and stops at two, because two is all a uniqueness check ever needs to find. The cutting step cannot fail either: the same row-by-row argument above guarantees there is always at least a 1 × 1 rectangle available, so the grid is always tiled exactly, with no overlaps and nothing left over. That is verified by tiling boards and counting cells rather than by argument. A board carrying a number no rectangle could satisfy is refused outright instead of being searched forever.
⚠️Honest limit on the table above: 200 boards per row, one generator, one distribution of rectangle shapes. The 100% column is 100% of what was tested — the structural argument is the reason to believe it generalises, not the sample. Sizes 12 and 14 are measured once and frozen into the page rather than recomputed on every build, and the test suite re-derives them at full sample so they cannot quietly drift.
How to use
- Pick a grid size and a difficulty, and how many puzzles you want on the sheet.
- Press New sheet — every board is checked for a single answer before it appears.
- Print the sheet; the controls and notes are left off the page.
- Toggle Show solutions when you want the rectangle divisions revealed.
Frequently asked questions
What is Shikaku?
A Japanese logic puzzle, also called Rectangles or Divide by Squares. You cut the whole grid into rectangles so that each rectangle contains exactly one number and that number equals the rectangle area in cells. Every cell ends up in exactly one rectangle, so nothing overlaps and nothing is left over.
How do you solve a Shikaku puzzle?
Start with the numbers that have the fewest possible shapes. A prime number like 7 can only be a 1 by 7 or a 7 by 1, so it is nearly pinned already, while a 12 has six shapes and many positions. Corners and edges cut the options further, and every rectangle you place removes cells from its neighbours, which cascades.
Does every puzzle here have only one answer?
Yes, and it is checked rather than assumed. Each board is generated and then solved by an exact cover search that counts solutions and stops at two, because two is all a uniqueness check needs to find. Only boards with exactly one answer are printed.
What makes a Shikaku harder or easier?
Where the number sits inside its own rectangle, far more than how big the grid is. With every number at its rectangle top-left corner, every board tested was uniquely solvable at every size from 7 by 7 to 14 by 14. With the numbers placed anywhere inside their rectangles, that falls away steadily as the grid grows.
Why does the corner position matter so much?
Scanning the grid row by row, the first cell you meet that is not yet covered can only be the top-left corner of whichever rectangle covers it, because everything above and to the left is already taken. So a number sitting on that cell pins its rectangle corner before you start, and the only freedom left is which factorisation of the area to use.
Is a bigger grid a harder puzzle?
Not on its own, which surprises people. Under corner placement a 14 by 14 is exactly as determined as a 7 by 7 — the size simply does not enter. Grid size only becomes the dominant term once the clues are placed loosely inside their rectangles. Size changes how long a puzzle takes, not how pinned down it is.
How do I print these?
Use the Print button, which hides the controls and the explanation and leaves the sheet. You can put one, two or four puzzles on a page, and each puzzle is kept whole rather than split across a page break. Toggle the solutions on first if you want them printed underneath.
Can I get the solutions?
Yes. Show solutions reveals the rectangle divisions under each puzzle, drawn as coloured borders over the same grid. Toggle it off before printing if you want blank sheets to hand out.
What size should I choose?
7 by 7 is a few minutes. 10 by 10 is the standard sheet and the best starting point. 12 by 12 and 14 by 14 are long sittings, and at the harder difficulties they take noticeably more attempts to generate because far fewer random boards come out with a single answer.
Is Shikaku the same as Sudoku?
No. They share nothing but a square grid. Sudoku fills every cell with a digit under row, column and box constraints; Shikaku writes nothing at all and instead draws boundaries, cutting the grid into rectangles whose areas are given. Shikaku is a partition problem, which is why it is solved here as exact cover rather than by candidate elimination.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.