Shikaku strategy: 9 techniques, beginner to expert

Before you start: think in options

For any number n, its rectangle has a width and height whose product is n, and it must contain the number’s cell. A 6 has four shapes (1×6, 6×1, 2×3, 3×2) and each shape can sit in several positions around the number. Solving Shikaku is the process of eliminating those options until one is left.

1. Prime numbers are straight lines

A prime number can only be written as 1 × itself, so its rectangle must be a single row or column. That instantly halves the options and often more: if the number is too close to a wall for a vertical strip, it must be horizontal.

2. Corners and edges cut the options

A number in a corner can only extend in two directions, so each shape has just one position. Numbers on an edge lose every position that would cross the border. Always solve around the edges first.

3. Other numbers block shapes

A rectangle can never contain two numbers. Any option that would swallow a second number is impossible — and so is any option overlapping a rectangle you have already placed.

4. The only option left

When blocking and borders leave a number with one possible rectangle, draw it. This is the most common deduction in easy puzzles.

5. Cells only one number can reach

Flip the question around: instead of asking where a number can go, ask which numbers can cover a particular empty cell. If only one number has any option covering it, that cell belongs to that number — which in turn removes every option of that number that misses the cell.

6. Overlap: cells every option shares

If every remaining option of a number covers the same cell, that cell belongs to the number even though you do not yet know the exact shape. Other numbers can no longer use it, which often unlocks them.

7. Region counting

When placed rectangles wall off an area, the numbers inside it must add up to exactly that area. If a sealed pocket has 10 cells and contains a 4 and a 6, both must stay inside it. If the sum is too small, a number from outside must be reaching in; if it is too big, something is wrong — a powerful mistake detector.

8. A good order of attack

1. Place every 1 and any number with an obvious single option.
2. Work around the edges and corners.
3. Handle large numbers and primes next to walls.
4. Scan for empty cells that only one number can reach.
5. Apply overlap to numbers with two or three options.
6. Count areas of closed-off regions.

9. Contradiction (for the hardest grids)

On hard puzzles you may reach a position where each number has two or more options. Pick a number with exactly two options and imagine one of them. Follow the consequences: if they lead to an impossible cell (no number can reach it) or a number with no options, the other choice must be right. Because every puzzle here has a unique solution, this always resolves without luck.

How our difficulty levels work

We grade puzzles by running our solver with limited techniques:

Common mistakes

• Drawing the “obvious” shape too early. A 4 next to a wall is not automatically 2×2 — check 1×4 too.
• Forgetting squares. 4, 9, 16 and 25 can all be squares.
• Ignoring empty cells. An uncovered cell no number can reach means an earlier rectangle is wrong.