THE SETUP
A Shikaku grid is an N×M rectangle with some cells containing numbers. Your goal is to partition the entire grid into rectangular regions such that:
- Every cell belongs to exactly one rectangle.
- Each rectangle contains exactly one given number.
- That number equals the area of the rectangle (number of cells it covers).
A clue of 6 in a 10×10 grid could be a 1×6, 2×3, 3×2, or 6×1 rectangle — any shape whose area is 6. Finding which of those shapes actually fits, given the grid boundaries and surrounding clues, is the puzzle.
FACTOR THE CLUE FIRST
The first step for any clue is to list its factor pairs. A clue of 12 could be 1×12, 2×6, 3×4, 4×3, 6×2, or 12×1. Many of those are immediately eliminated by the grid boundary — if the clue sits in the middle of an 8×8 grid, a 1×12 rectangle cannot fit in any direction.
After eliminating impossible orientations, count how many valid shapes remain. A clue with only one valid shape is forced — place it immediately. A clue with two or three shapes is worth revisiting after its neighbours are placed.
Primes are powerful: a clue of 7 can only be 1×7 or 7×1. If neither fits, the puzzle has an error. If only one fits, it's instantly placed.
WALLS AND CORNERS ARE YOUR FRIENDS
A clue touching a wall can only extend in a limited number of directions. A clue in a corner is even more constrained — the rectangle must fit entirely within the two sides it's pressed against.
Corner clues often have only one valid rectangle: a clue of 4 in a corner of a 6×6 grid must be either a 1×4, 2×2, or 4×1, and the corner walls eliminate anything that would extend beyond the grid. On smaller grids or with larger numbers, the corner might force a unique shape immediately.
Edge clues (not in corners) have one wall to lean against. The rectangle can extend along the edge or away from it, but it cannot cross the wall. This reduces the number of valid orientations from four directions to two or three.
NEIGHBOUR CLUES CONSTRAIN EACH OTHER
Two nearby clues cannot have overlapping rectangles. If clue A is placed and its rectangle covers a row, no other rectangle can use those cells. This eliminates shapes for clue B that would require the same cells.
This cascading effect is where Shikaku gets its depth. Placing one forced rectangle often narrows the valid shapes for two or three adjacent clues, which in turn may force those, which narrows their neighbours. The puzzle unravels from the most-constrained positions outward.
When a region of the grid is nearly fully partitioned, leftover cells may force the shape of the last rectangle in that region even before you've checked its factor pairs — the only remaining shape that fills exactly the right cells becomes the answer.
HOW IT DIFFERS FROM OTHER NUMBER PUZZLES
Most number puzzles — Sudoku, Kakuro, Calcudoku — are about placing digits. Shikaku places shapes. There is no candidate list, no digit elimination, no arithmetic. The reasoning is purely spatial: does this rectangle fit here given what's already placed?
This makes Shikaku unusually accessible as a logic puzzle. You don't need to track which numbers have appeared in a row or column — you just need to see whether a rectangle fits in the available space. But "easier to understand" doesn't mean "easier to solve": on larger grids, the spatial constraint chains become just as complex as digit-based logic.
Shikaku is often paired with Hitori as a "spatial constraint" puzzle — both ask you to make decisions about regions or cells based on local constraints that interact globally. But Shikaku's constraints are purely geometric, while Hitori's are rule-based.
THE SOLVE ORDER
- For each clue, list its valid factor pairs. Eliminate those that don't fit in the grid at that position.
- Place all clues with only one valid shape immediately — these are your anchors.
- For each newly placed rectangle, check its neighbours: which of their shapes now overlap the placed rectangle? Remove those shapes.
- If a neighbour clue now has only one valid shape, place it.
- Repeat until all rectangles are placed. If stuck, look at nearly- partitioned regions where leftover cells constrain the last rectangle.