Solving techniques from easy puzzles to nightmare difficulty.
Shikaku is a constraint-satisfaction puzzle. Every clue restricts where rectangles can go, and those restrictions ripple across the grid. The strategies below teach you how to read those constraints and use them to make progress — from your first easy puzzle to the toughest extreme grids.
For any clue, there are a finite number of valid rectangles that could contain it: rectangles of the right area, positioned so the clue cell is inside, that fit within the grid boundaries. These are the clue's candidates.
Your job is to eliminate candidates using two kinds of logic:
Reducing candidates eventually forces placements: when a clue has only one valid candidate left, that's where its rectangle goes.
The smaller the clue number, the fewer valid rectangles exist for it. Start here:
A clue in the corner of the grid can only place its rectangle in one quadrant. A clue on an edge has its rectangle options cut roughly in half. These heavily constrained positions are easy wins.
For example, a clue of 6 in the top-left corner of a 10×10 grid can be: 1×6, 6×1, 2×3, or 3×2 — but all must start at or include the corner cell, which means only orientations extending right or downward are valid. Compare that to the same clue in the center of the grid, where all orientations and many positions are valid.
After resolving small clues, look for any clue that now has only one valid candidate left. Placing a rectangle often eliminates candidates for neighboring clues, which in turn may force their placements. Follow this chain as far as it goes before switching to more complex analysis.
Look at any unoccupied cell and ask: which clues have candidates that cover this cell? If only one clue's candidates ever touch this cell, that clue must own it. This immediately eliminates all of that clue's candidates that don't cover the cell.
This technique is powerful near the edges of large clue rectangles, where grid boundaries limit coverage.
If a clue has multiple candidates but all of them overlap a specific set of cells, those cells are committed — they must belong to this clue regardless of which candidate is chosen. You can treat them as placed and use them to block candidates for neighboring clues.
Example: A clue of 6 can only fit as 2×3 or 3×2 in a tight area, and both orientations share 3 cells in common. Those 3 cells must belong to this clue — mark them and eliminate conflicting candidates for all nearby clues.
Two clues whose candidate rectangles would always conflict with each other provide useful information. If candidate A for clue X would block all candidates for clue Y, then candidate A can be eliminated.
This kind of "if I place this here, it makes something else impossible" reasoning is the core of intermediate-level Shikaku.
Constraint propagation means systematically applying the above techniques in a loop until no more progress can be made. After every placement or elimination, re-check all affected clues. Placements cascade: a new rectangle eliminates candidates, which forces new placements, which eliminate more candidates.
On hard and extreme puzzles, a single forced placement can trigger a chain of 10+ further deductions. Always follow the chain completely before looking for new starting points.
Consider an isolated region of the grid (bounded by placed rectangles or grid edges). Count the total cells in it and the sum of all clues with candidates inside it. If they match, every cell in the region is accounted for — any candidates extending outside the region can be eliminated.
This is especially useful when a solved section of the grid creates a new bounded area.
On the hardest puzzles, pure logical deduction sometimes leaves two or more equally valid-looking options. At this point, pick the most constrained clue, assume one of its candidates is correct, and follow the implications. If you reach a contradiction, the assumed candidate is wrong — eliminate it.
This is a last resort. On well-designed hard puzzles, it's rarely needed; on extreme and nightmare difficulty it may be required once or twice per puzzle.
Nearly all placements are forced. Use strategies 1–3 and you'll solve every easy puzzle without needing anything more complex. Focus on building your pattern recognition for small clues and corner/edge constraints.
Expect one or two spots where forced placements run out and you need to look at cell ownership or candidate intersections. Strategies 4 and 5 are your main tools here.
The entire intermediate toolkit is needed. Mutual exclusion analysis becomes essential. Expect constraint chains of moderate length. Slow down and be systematic rather than relying on quick visual scans.
All strategies apply. Constraint propagation is crucial — always drain every implication before looking for new entry points. You may occasionally need hypothesis testing, but try constraint propagation thoroughly first.
Grid sizes scale up to 21×24. The logic is the same but the volume is much higher. Managing your working memory across a large grid is itself part of the challenge. Consider dividing the grid into quadrants and ensuring each is progressing before moving on.
Like any logic puzzle, Shikaku rewards repeated play. After solving enough puzzles, you'll start pattern-matching common configurations: a 4-clue in a corner is almost always 2×2, a 6-clue between two 2-clues needs to bridge around them, and so on. These intuitions speed up your solving significantly.
The best way to improve is to play puzzles one step above your comfort level. Medium puzzles teach the techniques that make hard puzzles approachable. Start with hints enabled if you get stuck — after a few puzzles the patterns become clear.