Shikaku strategies

A useful move is more than a rectangle that fits. It is a rectangle you can explain. Work from the most constrained clues and keep an eye on the empty cells they leave behind.

1. List the possible shapes

Start with factor pairs. For 6, consider 1 × 6, 2 × 3, 3 × 2 and 6 × 1. On a 5 × 5 board the strips do not fit, so only the two compact shapes remain. A prime number such as 5 can only make a straight strip. Remember that the number need not sit at a corner: the same shape may have several legal positions.

2. Let edges and other clues rule shapes out

Edges cut off positions that run outside the grid. Other numbers cut off rectangles that would enclose a second clue. In the example above, these two checks force the 4 to be a 2 × 2 square. Fill it, then reconsider its neighbors: a new boundary often removes another possibility.

3. Look at cells, not just numbers

An empty corner or narrow gap must be covered somehow. Trace every clue that could legally reach it. If only one rectangle can cover that cell, that rectangle is forced—even if its number looked ambiguous on its own.

Only the top-row 2 can reach the top-right cell: the other 2 in column 3 is diagonally away, and a two-cell rectangle cannot turn a corner. The top-row 2 must extend right. This is a second way to justify the move, by looking at the cell that needs covering.

4. Recheck after each placement

Do not plan five uncertain rectangles at once. Place a justified region and make another pass over nearby clues. Count dimensions again, including the clue cell itself. In a 3 × 2 region, there are six cells—not the five cells surrounding the clue.

5. Recover from a blocked board

Local validity is not the same as a complete solution. Two individually legal rectangles can collectively prevent another number from getting its required area. If a hint reports a blocked cell, use Undo to return to your most recent uncertain choice. Erase a specific rectangle if you know which assumption needs to change.

Our explanation system looks first for a clue with one remaining legal rectangle, then for a cell covered by only one possible rectangle. If those tests find no forced step, it says so. A highlighted region is a suggestion with a reason, not a penalty or a score adjustment.

6. Practice a deliberate first move

Before drawing anything, name the reason for your first rectangle: an edge, a second clue, or an otherwise unreachable cell. Then check your reasoning using the explanation button. As boards grow from 5 × 5 to 9 × 9, the same rules apply; there are simply more relationships to manage.

Try a featured puzzle with a written first-step walkthrough, or put these ideas to work on today’s puzzle.