How to Solve Shikaku: Rectangles, Forced Cells, and Working the Corners

Updated August 2026

Shikaku asks you to cut a grid into rectangles, one per number, with each rectangle's area equal to its number. The trick is that you are really solving two puzzles at once: which shape each number takes, and which number claims each cell. Beginners work only the first; the second is where the fast deductions live.

List the shapes a number can take

Every number has a small set of possible rectangle dimensions. A 7 can only be 1×7 or 7×1, because 7 is prime — that makes prime clues the best possible starting point, since their orientation is often forced by the grid edges. A 12 can be 1×12, 2×6, 3×4 and their transposes, which is much looser. Do the primes and the large awkward numbers first, and leave the flexible middling numbers until the board has tightened.

A 1 is instant: it is its own cell and nothing else. Sweep every 1 before doing anything else, and mark its four neighbours as belonging to some other rectangle.

No rectangle may contain two numbers

This constraint does more work than it seems. When you are testing whether a number can extend in some direction, check whether that extension would swallow another clue — if it would, that direction is dead. Numbers sitting close together mutually restrict each other, so pairs of nearby clues are usually the first thing to resolve on a board.

Every cell belongs to exactly one rectangle

Switch perspective and look at cells rather than numbers. For a given empty cell, which clues could possibly reach it? Reaching means there is a rectangle of the right area, containing that clue and that cell, with no other clue inside. If exactly one number can reach a cell, that cell is settled — and often that settles the whole rectangle, because it pins one of its corners.

This cell-first view is what breaks boards that look stuck. Scan for cells with a single possible owner after every rectangle you draw.

Start in the corners

A corner cell has to belong to some rectangle, and its options are the most limited on the board because two sides are walls. Work all four corners early, then the edges. The same is true for any cell hemmed in by rectangles you have already drawn — each completed rectangle turns its neighbours into corners of the remaining space.

Count the area you have left

The clue numbers add up to exactly the number of cells in the grid. That gives you a running check: if the region you have carved out so far has an area that cannot be covered by the remaining numbers, something earlier was wrong. More usefully, when a pocket of empty cells is isolated by finished rectangles, only numbers touching that pocket can fill it, and their areas must sum to the pocket's size exactly.

Watch the width

When a strip of free cells is only one or two cells wide, most rectangle shapes no longer fit. A 6 in a two-wide corridor must be 2×3; a 9 cannot fit at all unless the corridor is at least three wide. Narrow channels are the cheapest deductions on the board, and they appear constantly once you have drawn a few rectangles.

A reliable order of attack

1. Place every 1.
2. Resolve primes and large numbers whose orientation is forced by edges or other clues.
3. For nearby pairs of clues, rule out the extensions that would swallow the other.
4. Scan corners and edges for cells with only one possible owner.
5. After each rectangle, check the widths of the corridors it created.
6. Check that isolated pockets can still be covered exactly.

A good Shikaku never needs a guess. When you stall, run the cell-first scan again — the reachability of every cell changes each time you draw a rectangle.