THE ONE RULE
Every number in the grid is the area of the rectangle that contains it. Each rectangle is axis-aligned, contains exactly one number, and every cell belongs to exactly one rectangle.
Solving Shikaku = eliminating impossible rectangle shapes until only one remains for each number. You never guess — you narrow.
TECHNIQUE 1 — FACTOR EVERY CLUE FIRST
Before placing anything, write down the divisor pairs for each number. These are the only possible rectangle shapes:
- 2: 1×2 or 2×1
- 4: 1×4, 4×1, or 2×2
- 6: 1×6, 6×1, 2×3, or 3×2
- Prime (3, 5, 7, 11…): only 1×N or N×1 — two options total.
Fewer divisor pairs = more constrained clue = solve it first.
TECHNIQUE 2 — FORCED CLUES: PLACE THESE IMMEDIATELY
Three situations give you a rectangle with no guesswork:
- Clue = 1: the rectangle is just that one cell. Done instantly.
- Prime clue on an edge or near a corner: the rectangle is 1×N or N×1 — one orientation is cut off by the grid boundary or a nearby clue. The other is forced.
- Any clue where grid boundary eliminates all but one shape: a clue of 4 in a 1-row-high strip can only be 1×4 or 4×1. If one extends off the grid, the other is forced.
Scan the entire grid for these before attempting any harder deductions.
TECHNIQUE 3 — PLACED RECTANGLES AS WALLS
Every rectangle you place removes cells from the board. Any neighbouring clue whose rectangle would have extended into those cells now has fewer valid shapes.
After each placement, revisit every clue adjacent to the new rectangle. Recount its valid shapes given the new wall. Often one or two previously-valid orientations are now blocked — and the remaining shape is forced.
This cascade is the main engine of Shikaku. One forced rectangle forces the next, which forces the next. Work the boundary of your placed region outward.
TECHNIQUE 4 — ORPHAN CELL CHECK
When you have several placed rectangles and a few unresolved clues, scan for "orphan" cells — isolated pockets of unassigned cells that are not adjacent to any unresolved clue. If such a pocket exists, you've placed a rectangle incorrectly somewhere.
Also check: can the remaining unresolved clues cover all remaining unassigned cells exactly? If the total of the remaining clue numbers doesn't match the remaining cell count, there's an error. This check costs a few seconds and catches placement mistakes before they cascade.
THE SOLVING ORDER
- Factor all clues and note their divisor pairs.
- Place all clue-1 cells immediately.
- Identify primes and clues near edges/corners — place all forced ones.
- For each newly placed rectangle, re-evaluate neighbouring clues for newly-blocked shapes.
- Repeat until stuck. If truly stuck: find the clue with the fewest remaining valid shapes (usually 2) and pick the option that avoids creating orphan cells.
Most Shikaku puzzles at beginner and intermediate level solve completely via steps 1–4. You'll rarely reach step 5.
THE BEGINNER TRAP
Starting with the largest numbers. Large clues have the most divisor pairs and are almost never forced early — they're the hardest cells to resolve at the start and the easiest to resolve once walls narrow them from multiple sides.
Start with the most constrained clues (clue-1, primes, edge clues) and work outward. The large-number rectangles almost always fall into place once their neighbours are resolved.