How to play Rectangles

Split the grid into rectangles so each holds exactly one number, and that number is its area. Also known as Shikaku, Divide by Box.

▶ Play Rectangles ⊞ Open the solver

The rules

Divide the whole grid into rectangles (squares are rectangles too).
Every rectangle contains exactly one number.
The number is the rectangle’s area — how many squares it covers.
Every puzzle has exactly one solution.

Playing Rectangles on Puzzle Solvers

Choose a size, square or wide grid, and a difficulty, then press New Puzzle.
Drag from corner to corner to draw a rectangle. While you drag, the label shows width × height = area and turns green when it fits the number inside.
Tap a rectangle (or right-click) to remove it. Numbers turn green when their rectangle is right.
Show factor pairs lists every shape the number could take. Hint draws one rectangle and explains why.

Open the Rectangles game →

Using the Rectangles solver

Choose the number of rows and columns, then click each numbered square and type its number (or press Sample).
Press Solve and step through: one shape left, only one number can reach a square, squares every shape shares, and shapes that would block another number.

Open the solver →

A worked example

A 3 sits in the top-left corner and a 4 is two squares to its right. The 3 can be a row of three (which would hit the 4) or a column of three going down. So it is the column.

That leaves the 4: it cannot reach back into the corner column any more, so it must be the 2×2 to its right or a strip going down — and the squares around decide which.

Strategies

Factor pairs. List the shapes a number can take: 12 is 1×12, 2×6, 3×4, 4×3, 6×2 or 12×1. Shapes that run off the grid or swallow another number are out.
Primes are strips. A prime number like 5 or 7 can only be a straight line, one square thick.
Corners and edges. A square in a corner may be reachable by only one number — that number’s rectangle must stretch to it.
Shared squares. If every possible shape for a number covers the same squares, those squares are its, and no other rectangle can use them.
Big numbers first. Large numbers have few shapes that fit; placing them early shrinks everyone else’s options.

Common mistakes

Forgetting that 1×n strips count — a 6 can be a long thin line.
Drawing a rectangle that contains two numbers.
Leaving a gap that no number can reach.

Where it comes from

Rectangles was popularised in Japan under the name Shikaku (‘divide by squares’) and is known in many puzzle collections as Rectangles or Divide by Box. It turns times tables into a spatial puzzle.

Frequently asked questions

Is this the same as Shikaku?

Yes — Shikaku is the Japanese name for the same puzzle.

What maths does it practise?

Multiplication facts and factor pairs (which widths and heights make each number), area, and checking with addition: all the numbers together add up to the size of the grid.

Can a rectangle be a square?

Yes. A 4 can be a 2×2 square, a 9 can be 3×3.

How do I enter a puzzle from a book?

Open the Rectangles Solver, choose the rows and columns, click each numbered square and type its number, then press Solve.

Keep going

All guides: How to play every puzzle and game.