How to Solve Shikaku Puzzles

1. The rules in 60 seconds

Shikaku is a Japanese logic puzzle published by Nikoli — the same company behind Sudoku. The goal is simple: divide the entire grid into non-overlapping rectangles so that each rectangle contains exactly one number, and that number equals the area of the rectangle.

• Every cell in the grid must belong to exactly one rectangle.
• Each rectangle contains exactly one clue number.
• The clue number equals the area of its rectangle — width × height.
• Rectangles cannot overlap or extend outside the grid.

That is the entire ruleset. A cell showing the number 6 must belong to a rectangle with area 6 — that could be 1×6, 6×1, 2×3, or 3×2. A cell showing 1 is a rectangle all by itself. There is no arithmetic, no guessing, and every puzzle has exactly one solution.

2. Where to start — your first moves

The biggest mistake beginners make is trying to solve Shikaku left-to-right, top-to-bottom. That approach quickly leads to contradictions. Instead, look for the most constrained cells first — the ones that have only one or two possible rectangle shapes.

Scan for prime numbers

Prime numbers (2, 3, 5, 7, 11, 13...) can only form rectangles in one orientation: 1×N or N×1. A cell containing 7 must be part of a 1×7 or 7×1 rectangle — there is no 2×3.5. This dramatically limits your options and makes primes one of the easiest places to start.

Look for 1s and 2s

A cell containing 1 is already solved — it is a 1×1 rectangle. Mark it immediately. A cell containing 2 can only be 1×2 or 2×1. In many positions, one of those orientations will be blocked by the grid boundary or another clue, leaving only one possibility.

3. Corner and edge clues

The grid boundary is your friend. A clue in the corner of the grid has far fewer possible rectangle positions than a clue in the middle, because the rectangle cannot extend beyond the edge.

Corner clues

A clue in the top-left corner can only extend right or downward. If the number is 4 and the corner is at position (0,0), the possible rectangles are 1×4, 4×1, or 2×2 — and the rectangle must stay within the grid. Many corner positions have only one valid option once you account for neighbouring clues.

Edge clues

A clue on the top edge can only extend downward or sideways — not upward. This halves the number of possible orientations compared to a centre clue. Always check edge clues early: they are often the most constrained cells on the board.

4. Large numbers first

Counter-intuitively, large numbers are often easier to place than medium-sized ones. A large rectangle takes up a lot of space, which means it quickly conflicts with neighbouring clues — and those conflicts narrow down your options fast.

On a 10×10 grid, a clue showing 10 could be 1×10, 10×1, 2×5, or 5×2. But once you account for the grid boundary and nearby clues, often only one or two orientations remain. Place large rectangles early to carve the grid into smaller, more manageable sections.

On 20×20 and 25×25 grids this becomes even more important. Large clues (20, 25, 30+) divide the grid into distinct regions. Solve them first and the puzzle breaks into independent sub-problems.

5. Elimination and forced cells

Once you have placed several rectangles, you can use the filled space to force the remaining ones. This is the core technique for intermediate and hard puzzles.

Look for isolated cells

As rectangles fill the grid, watch for cells that become surrounded on multiple sides. If a small region of unfilled cells can only be covered by one specific rectangle configuration, that configuration is forced — place it immediately.

Count remaining space

If a clue has only one possible rectangle that fits in the remaining unfilled space around it, that rectangle is placed. Systematically count available cells around each unsolved clue as the grid fills up.

Two clues, one gap

When two unsolved clues are adjacent with a small gap between them, their rectangles must together cover exactly the cells between them. This often forces both orientations simultaneously. Work these paired-clue situations carefully — they are frequent sources of progress on harder grids.

6. Advanced techniques

For hard and expert grids, the basic strategies above will take you most of the way — but some puzzles require more systematic thinking.

Parity analysis

Count the total area of all clues in a region. If the sum must equal the number of cells in that region, and only one rectangle configuration achieves that sum, the placement is forced. This is especially useful when a large rectangle has been placed, splitting the grid into distinct areas.

Rectangle shape constraints

Some numbers have very few valid rectangle shapes. 4 can be 1×4, 4×1, or 2×2. If the available space near a clue of 4 is too narrow for 1×4 but too short for 4×1, only 2×2 remains. Build a mental catalogue of which numbers have limited shapes — it speeds up scanning significantly.

Work backwards from near-complete rows

On larger grids, when a row or column is almost fully covered, the remaining gap must be exactly filled by the unsolved clue adjacent to it. This is a fast way to force placements without checking every option.

7. Strategy by difficulty level

Level	Grid	Best approach	Typical solve time
Starter	5×5	Primes and edges are almost always enough. Each puzzle can usually be solved in 2–3 moves.	Under 1 min
Classic	10×10	Start with corners and large numbers. Use elimination once about half the grid is filled.	2–6 min
Hard	20×20	Place large numbers first to divide the grid into regions. Treat each region as an independent sub-puzzle.	10–25 min
Expert	25×25	Requires systematic elimination and parity analysis. Work section by section. Expect to revisit earlier decisions as constraints propagate.	20–60 min

8. Common mistakes to avoid

Solving left-to-right

Do not work through the grid in reading order. Always seek out the most constrained cell — the one with fewest valid rectangle options — regardless of where it sits on the board.

Forgetting that every cell must be covered

A rectangle does not just need to contain its clue number — it must cover an exact area with no gaps. Beginners sometimes place rectangles that are too small, leaving isolated cells that cannot later be assigned to any remaining clue.

Overlooking small clues

A clue of 2 or 3 in the middle of the grid looks harmless, but it can block several larger rectangles. Resolve small clues as soon as their placement is forced — do not leave them until the end.

Ignoring the grid boundary

New solvers often mentally treat the grid as infinite. Always check whether a rectangle would extend off the edge — that eliminates many orientations automatically.