A number in a corner can only grow in two directions, so each of its shapes fits in exactly one position. Numbers on an edge lose every option that would cross the border. That is why experienced solvers start around the outside of a Shikaku grid.
The idea
A rectangle must contain its number’s cell. In open space a shape can slide around that cell; at the border it cannot slide past the edge. Fewer positions means fewer options to rule out.
Counting options (computed by our solver)
On an empty 5×5 grid the 4 has 8 options in the centre, 5 on the top edge and only 3 in the corner. Add one neighbouring number and the corner 4 drops to 2:
The border-first method
- Walk around the four corners. For each corner cell, ask which numbers could cover it.
- Solve corner numbers that have one option left; mark shared cells when they have two.
- Move along each edge, treating placed rectangles as new walls.
- Only then move inwards — the solved border acts like a smaller puzzle’s edge.
Empty corners are just as useful as numbered ones. If only one number can reach an empty corner, it must — see unreachable cells.
Questions
Why start Shikaku at the corners?
A number in a corner has the fewest possible rectangles — one position per shape — so it is the most likely to be solved immediately.
Do placed rectangles count as edges?
Yes. Once a rectangle is drawn, its sides block every other number exactly like the border of the grid.