When placed rectangles and the border enclose a region, the numbers inside it must add up to exactly its number of cells — unless a number from outside reaches in. Comparing the two totals tells you what must happen.
The rule
Every cell is covered once, so the numbers of any Shikaku always sum to the grid area (25 on a 5×5, 100 on a 10×10). The same is true of any area that is fully sealed off.
A verified example
Once the 4 runs down the middle column, the left side is a closed 2×4 pocket of 8 cells containing a 6 and a 2. Since 6 + 2 = 8, neither may leave — so the 6 is the 2×3 block and the 2 is the bottom domino. Our solver confirms this puzzle has exactly one solution.
Three possible outcomes
| Sum of numbers inside | What it means |
|---|---|
| Equal to the region’s area | Every number inside stays inside, and nothing from outside enters. |
| Less than the area | Some number from outside must reach into the region to cover the gap. |
| More than the area | Some number inside must reach out — or, if it can’t, an earlier rectangle is wrong. |
A mistake detector
If a sealed pocket has more area than its numbers can fill and nothing outside can reach in, the position is impossible. Region counting is one of the fastest ways to catch an error before it spreads.
Questions
Do Shikaku numbers always add up to the grid size?
Yes. Because rectangles cover every cell exactly once, the clues always sum to the number of cells — 100 on a 10×10 grid.
When is region counting useful?
Mid-solve, once rectangles start walling off pockets of the grid, and on large boards where pockets are common.