Shikaku
Play Shikaku puzzles online. Divide the grid into rectangles so each one contains a single number whose value equals its area. Drag to draw, 5×5 to 10×10.
The rules
Shikaku — from the Japanese shikaku ni kire (“divide into squares”) — is a pure-logic dissection puzzle. The grid hides a tiling of axis-aligned rectangles. Your job is to recover it.
Three rules, no exceptions:
- Every cell belongs to exactly one rectangle — no gaps, no overlaps.
- Each rectangle contains exactly one number.
- The rectangle's area equals that number.
Click two opposite corners to draw a rectangle — the live size readout shows its width and height as you go. Tap an existing rectangle to erase it. New rectangles can't overlap old ones, so your finished work is always safe.
This 4×4 grid is fully split into five rectangles. Every cell belongs to exactly one box:
- The two 3s become a 1×3 strip and a 3×1 strip — same area, different shapes.
- The 4s are a 2×2 square and a 1×4 strip.
- The 2 can only be a domino — here, a 2×1.
Decomposing the number
A number tells you the area but not the shape. Every Shikaku deduction starts by listing the rectangles a number could live in, then intersecting that with what its position allows.
| Number | Possible shapes (w×h) | Why it's useful |
|---|---|---|
| 2 | 1×2, 2×1 | Forced to a domino; only orientation is open. |
| 3 | 1×3, 3×1 | Always a straight tromino — never bends. |
| 4 | 1×4, 4×1, 2×2 | First number with two distinct shapes — aspect matters. |
| 5, 7 | 1×n only (primes) | Primes are 1-wide strips — easy to place. |
| 6 | 1×6, 6×1, 2×3, 3×2 | Four orientations — the workhorse of mid-game tension. |
| 8 | 1×8, 8×1, 2×4, 4×2 | No square option; one dimension is always ≤ 4. |
| 9 | 1×9, 9×1, 3×3 | Square or long strip — corners decide. |
Solving techniques
- Corners and edges first. A number in a corner only has one direction to extend in each axis — usually forcing the shape immediately. The same logic narrows numbers on the outer edges.
- Reach analysis. A number at position
(r, c)with value n can only sit inside a rectangle whose top-left corner is at most n−1 cells away (horizontally or vertically). Two numbers whose reach areas don't overlap can't share a rectangle — that's often the first elimination. - Pairwise separation. Two adjacent numbers must end up in different rectangles, so a boundary line must run between them. Sometimes that boundary forces a whole column or row of cuts.
- Count the cells. All the numbers add up to the total cell count. If a region you can isolate has, say, 12 cells and only contains numbers summing to 12, the puzzle factorises — solve each region independently.
- Avoid forbidden 1×1s. No number 1 means no 1×1 rectangle — so a lone unfilled cell is always a sign you've drawn one of your neighbours wrong.
About the puzzle
Shikaku was first published by Nikoli — the same Tokyo-based magazine that popularised Sudoku, Slitherlink and Kakuro — in 1989. It is sometimes sold as Divide by Squares or Divide by Box in English. Unlike Sudoku, Shikaku has zero arithmetic and zero pencil-marks: every step is a geometric deduction about which rectangles can still fit, which is why it feels so different despite a similar level of difficulty. Well-formed Shikaku always has exactly one solution reachable by logic alone.