Shikaku

How to play Shikaku (rectangle division puzzle)

Shikaku — Japanese for "four quarters" — is a rectangle-division logic puzzle. A grid is scattered with numbered clues, and your job is to partition the entire grid into rectangles so that every rectangle contains exactly one clue and that rectangle's area — its width times its height — equals the clue's number. Every cell in the grid must end up inside exactly one rectangle: no gaps, no overlaps, no cell left over. Every puzzle here is generated and then proven, by an independent solver, to have exactly one correct dissection, so a logical path to the finish always exists — you never have to guess.

The goal

Cover the whole board with non-overlapping rectangles, one per clue, where each rectangle's area exactly matches the number it contains. When every cell belongs to a correctly sized rectangle and nothing is left uncovered, the puzzle is solved. You are timed, and any rectangle you draw that breaks the rules — wrong size, wrong clue count, or overlapping another rectangle — counts as a mistake, so precision matters as much as speed.

The grid and the clues

The board is a square grid — 6×6, 8×8 or 10×10 depending on the difficulty you choose. A handful of cells show a bold number; every other cell starts blank. Each number is the area of the single hidden rectangle that must be built around it — a clue of 6 might end up as a 1×6 strip, a 2×3 block, or a 3×2 block, and part of the challenge is figuring out which shape actually fits alongside its neighbours. Once the grid is fully tiled by correctly sized rectangles, each covering exactly one clue, the puzzle is complete.

Rules

• Every rectangle you draw must be axis-aligned — its sides run along the rows and columns of the grid, never diagonally.
• A rectangle must contain exactly one numbered clue cell — never zero, never two or more.
• A rectangle's area (its width multiplied by its height, in cells) must exactly equal the number inside it.
• Rectangles may never overlap. Every cell belongs to exactly one rectangle once the puzzle is solved.
• The whole grid must be covered — no cell may be left outside every rectangle.
• There is always exactly one way to dissect the grid that satisfies every clue at once; every puzzle is checked by a solver before it is served to you.

Solving techniques

• Start with the largest and smallest numbers. A very large clue has few possible shapes that fit inside the grid, and a clue of 2 or 3 sitting near an edge or corner is often forced into a single orientation immediately.
• Work the corners and edges first. A clue in a corner has fewer directions it can expand into, so its rectangle is usually easier to pin down than one in the open middle of the board.
• Watch the gaps between clues. If two clue cells sit close together, the space between them limits how far either rectangle can stretch before it would swallow its neighbour's number — use that spacing to rule out shapes.
• Count remaining cells. Once most of the board is tiled, the few uncovered cells left over must belong to whichever clues remain, which often forces the final rectangles into a single possible shape.
• Never guess. Every puzzle has one provably unique dissection, so if a shape feels ambiguous you have not yet used all the information nearby — look again before committing.

Controls

Press and drag from one cell to another; the rectangle spanning your drag is previewed live, tinted green if it would be a legal placement and red if it would not. Release to commit it — a legal rectangle locks into place, while an illegal one is rejected and counted as a mistake. To remove a rectangle you have already placed, simply tap (or click) once anywhere inside it; it is cleared instantly so you can redraw it differently. Use New Puzzle at any time for a fresh random grid, Daily for the puzzle everyone gets on today's date, and the size selector to switch between the 6×6, 8×8 and 10×10 boards.

Scoring and the leaderboard

Your score is calculated the moment the whole grid is correctly tiled: score = 10000 − seconds × 5 − mistakes × 200. Every second on the clock trims five points, and every rejected rectangle — wrong area, wrong clue count, or an overlap — costs 200 points, so a fast, clean solve scores highest. The result is clamped between 1 and 99,999 and recorded per difficulty, so easy, medium and hard each keep their own leaderboard.

Frequently asked questions