Eight proven techniques for solving Shikaku puzzles, from absolute beginner to advanced. Each one includes a concrete grid example so you can see it in action.
| Technique | Level | When to Use | Core Idea |
|---|---|---|---|
| 1. Start with "1" | Beginner | Any grid | 1×1 = done instantly |
| 2. Corner-First | Beginner | Numbers in corners | Only 2 directions possible |
| 3. Count Shapes | Beginner | Large numbers | List all valid rectangles first |
| 4. Factor Decomposition | Intermediate | Any number | N = a × b, enumerate pairs |
| 5. Edge Framing | Intermediate | Border numbers | Fill edges, shrink interior |
| 6. Area Arithmetic | Intermediate | Mid-solve check | Areas must sum to grid total |
| 7. Chain Reasoning | Advanced | Complex grids | One placement forces the next |
| 8. Hypothetical Reasoning | Advanced | Stuck | Try both ways, contradiction eliminates one |
A cell numbered 1 is already a complete 1×1 rectangle. No dragging needed — it's done. Mark it and move on. These freebies reduce the grid fast.
Why it works: 1 has only one factor (itself), so there's exactly one possible shape.
Corner cells have fewer possible rectangle shapes. A "2" in a corner can only extend in one direction. A "3" in a corner has only two options. Start here.
Why it works: Corners have 2 edges blocked, drastically reducing possibilities.
Before dragging, list all rectangle shapes for a number. A "6" can be 1×6, 2×3, 3×2, or 6×1. Check which ones fit the available space.
Why it works: Eliminating impossible shapes early prevents dead ends.
For any number N, list all factor pairs: N = a × b. Each pair gives two rectangle orientations (a×b and b×a). This is the systematic version of "count possible shapes."
Why it works: Gives you a complete, systematic list instead of guessing.
Work inward from edges. Place rectangles along the border first — they constrain the interior and make remaining placements easier.
Why it works: Edge rectangles have fewer degrees of freedom, making them easier to place correctly.
All rectangle areas must sum to the total grid cells. A 5×5 grid = 25 cells. If you've placed rectangles totaling 20, the remaining numbers must sum to 5.
Why it works: Catches errors early — if the math doesn't add up, something is wrong.
Placing one rectangle forces or eliminates options for neighbors. Follow the chain: "If I place this 2×3 here, then that 4 must be 2×2, which means..."
Why it works: One correct placement cascades through the grid, solving multiple cells at once.
Stuck? Try: "What if this 3 goes horizontal?" If that leads to a contradiction (overlap, gap, or impossible shape), then it must go vertical.
Why it works: Eliminates possibilities by proving alternatives wrong. The most powerful technique for hard puzzles.
Start with numbers that have only one possible rectangle shape — primes like 2, 3, 5, 7. Then work from corners and edges inward, since boundary positions have fewer options.
Depends on grid size and difficulty. A 5×5 puzzle takes 2-5 minutes for experienced solvers. A 9×9 puzzle might take 15-30 minutes. Speed comes with practice.