THE CORE CONSTRAINT
Every clue number is the area of the rectangle that contains it. A clue of 6 means its rectangle has 6 cells — which could be 1×6, 6×1, 2×3, or 3×2. A clue of 4 could be 1×4, 4×1, or 2×2.
The rectangle must be axis-aligned (no diagonals, no L-shapes) and must contain the clue number as its only clue. Every cell in the grid belongs to exactly one rectangle.
Solving Shikaku is about eliminating impossible rectangle shapes until only one valid shape remains for each clue. You don't guess — you narrow.
START WITH THE MOST CONSTRAINED CLUES
Two types of clues are most constrained and should be handled first:
- Clue 1: the rectangle is a single cell — just the clue cell itself. These are immediately resolved with no logic needed.
- Prime-number clues: a prime N can only be 1×N or N×1 — two orientations. Compare them against the grid boundaries and nearby clues to rule one out, and the rectangle is forced.
After primes, look for clues near corners and edges — they have fewer spatial options than clues in the interior.
EDGE AND CORNER CLUES CONSTRAIN THEMSELVES
A clue touching the grid boundary can't extend beyond it. This cuts down the valid shapes immediately.
A clue of 6 in a corner of a 7×7 grid can't extend right beyond column 6, can't extend down beyond row 6, and must fit within the space available. Rectangles like 2×3 might only fit in one orientation given the corner. Work corner clues before interior clues of the same size.
Tip: when a clue sits on an edge, one dimension of the rectangle is capped. Count how many options remain — often just one or two — before moving on.
USE NEIGHBOURING CLUES AS WALLS
Every placed or partially-placed rectangle acts as a wall that neighbouring rectangles cannot cross. This is the main propagation mechanism in Shikaku.
When a rectangle is fixed, trace which cells it occupies and mark them off. Then revisit every neighbouring clue: its rectangle now can't extend into those cells. Some previously-valid shapes are now blocked — recount the remaining options.
The cascade often works in both directions: fixing clue A constrains clue B, whose rectangle then constrains clue C, and so on. In practice the grid solves faster than it looks once the first few rectangles lock in.
ASPECT RATIO LIMITS AND GRID COVERAGE
Some clues have many divisor pairs but the grid geometry eliminates most of them. A clue of 8 has divisors 1×8, 8×1, 2×4, 4×2 — but if the clue sits in row 2 of a 7-row grid, the 8×1 vertical option extends beyond the grid and is eliminated.
A useful check: after a rectangle is placed, verify that the remaining unassigned cells in the grid can still be covered by the remaining clues. An isolated pocket of cells too small or strangely shaped for any remaining clue signals an error earlier in the solve.
THE BEGINNER MISTAKE
The most common error is placing rectangles speculatively — choosing a shape that seems reasonable without verifying that it doesn't block a neighbouring clue. This creates contradictions several steps later that are hard to trace back.
The safe rule: only place a rectangle when it's the only valid shape remaining for that clue. If two or more shapes are still possible, leave it and work other clues until a wall or grid boundary eliminates one of the options. Patience in Shikaku beats optimism.