Shikaku Puzzle

Shikaku is a region puzzle. Numbers sit on the grid, and you draw rectangles so each number equals the area of its rectangle and every cell belongs to exactly one rectangle. You can play grids from 5×5 up to 10×10, and every puzzle here has exactly one solution that you can reach by logic, with no guessing.

Rules

The board is an n×n grid with a few positive integers printed in some of the cells. Empty cells have no number.

Divide the board into axis-aligned rectangles. Rectangles do not overlap, and together they cover every cell. Each rectangle contains exactly one of the printed numbers, and that number equals the area of the rectangle (width × height). A square counts as a rectangle. A one-cell rectangle is legal when its number is 1.

The puzzle is solved when every cell is covered, no rectangles overlap, and every number matches its area.

Controls

Drag from one cell to another to draw a rectangle. The yellow badge shows the area of the preview so you can match it to a number before you let go. Dragging the same bounds again erases that rectangle.

Erase mode under the board removes the topmost rectangle under the pointer. With a mouse you do not need to switch: left-drag draws and right-drag erases.

On a keyboard, the arrow keys move around the grid. Space, Enter, D or 1 draws a one-cell rectangle on the selected cell (or erases in Erase mode). Backspace, Delete, X, E or 0 erases the rectangle covering the selected cell.

Overlapping rectangles, a rectangle with no number, two numbers, or a number that is not the area all turn red at once. Press Hint for one rectangle the rules already force, with a sentence saying why. Press Check when you want the board checked against the rules. Undo and Redo step through your moves, and Reset clears every rectangle. When the division is right, the borders turn teal.

Techniques

Easy grids follow from numbers with only one legal area:

• Forced one: a printed 1 covers only its own cell.
• Only rectangle: after earlier placements, a number has exactly one remaining rectangle that fits its area, stays on the board, and leaves other numbers outside.
• Corner and edge squeeze: a number on a corner or a short edge often has only one rectangle that fits its area once neighbours are taken.

Medium grids also need reachability:

• Only reach: a cell that only one unfinished number can cover must belong to that number’s rectangle.

Hard grids need a wider view:

• Reserved cells: cells common to every remaining rectangle of a number belong to it.
• Contradiction: drop an area that immediately leaves a cell or a number with nothing left.
• Chain: placing one forced rectangle can leave the next number with only one rectangle; keep following those knock-ons before you try a harder step.

Beginner tips

Start with the largest numbers and with numbers in corners or on edges. They often have fewer legal rectangles.

When you place a rectangle, look at the cells it touches. Neighbouring numbers may suddenly have only one area left.

If you are new to Shikaku, start with the daily 7×7 easy grid, and move up once forced ones and only-rectangle steps feel natural.