How to play Shikaku

Shikaku is a rectangle-partitioning puzzle. The finished grid is divided into rectangles, and every printed number describes exactly one of them.

The rules

1. Every region must be a rectangle with horizontal and vertical sides.
2. Each rectangle contains exactly one numbered clue.
3. The clue equals the rectangle’s area in grid cells.
4. Rectangles may not overlap.
5. Every cell must belong to a rectangle; no gaps are allowed.

A clue of 6, for example, could belong to a 1×6, 2×3, 3×2, or 6×1 rectangle if that shape fits the grid and contains no other clue.

Your first deductions

List the factor pairs of a clue, then eliminate rectangles that run outside the grid or enclose another number. Edge and corner clues often have very few legal shapes. Prime numbers are especially constrained because their only dimensions are 1×n and n×1.

A rectangle is not proved merely because its area is correct. It must also contain exactly one clue and leave the remaining cells partitionable by the other clues.

A reliable solving routine

1. Start with clues near corners and edges, plus large or prime clues.
2. Sketch every legal rectangle for the most constrained clue.
3. Fill a rectangle when only one placement remains.
4. Use its boundary to reduce the choices for neighbouring clues.
5. Check uncovered pockets: their area and shape must fit the clues left inside them.

Controls on this site

Drag from one corner of a proposed rectangle to its opposite corner. You may drag in any direction and across more than two cells. Tap or click an existing rectangle to remove it. Progress is saved automatically in this browser.

Play the Great Patchwork or continue with the Shikaku solving techniques.