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Shikaku Rules: How to Play (With Examples)

Shikaku, also called Rectangles, is a logic puzzle about dividing a grid. Some squares hold numbers. Cut the whole grid into rectangles so that each one holds exactly one number, and the number is how many squares the rectangle covers.

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The rules

Divide the grid into rectangles so that:

  1. Every rectangle holds exactly one number.
  2. The number is the rectangle’s area. A 6 covers six squares: two by three, three by two, one by six or six by one.
  3. The rectangles cover the whole grid, without overlapping.
A Shikaku to solve A 5 by 5 grid with 7 numbers. 2 2 6 6 4 2 3
A 5×5 with seven numbers.
The same grid, solved The grid divided into rectangles, each holding one number equal to its area. 2 2 6 6 4 2 3
The same grid divided into seven rectangles: each holds one number, equal to its area.

What breaks a rule

A rectangle of the wrong size. Stretch the rectangle of the 2 in row 1, column 2 by one square and it covers three: its number no longer matches its area.

A rectangle that breaks the rules A rectangle of 3 squares: its number isn't its area. 2 2 6 6 4 2 3
Three squares for a 2: not allowed.

A rectangle with two numbers, or none, and rectangles that overlap or leave a gap. In the game, a rectangle with the wrong area, two numbers or none is outlined in red. Drawing a new rectangle over old ones replaces them, so rectangles never overlap.

A puzzle from the game, solved

This is the first level in the game: Easy level 1, a 7×7 with nine numbers.

Easy level 1, before you start A 7 by 7 grid with 9 numbers. 7 2 8 7 5 4 2 7 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7
Easy level 1, before you start.

It takes 9 steps, and every one is the same idea: a number with only one rectangle left that fits. Here are the first three.

Step 1: the 7 in the corner

A 7 can only be a straight line, one by seven, since 7 doesn’t divide any other way. Along the top row it would take in the 2, so it must run down the first column. That’s the only rectangle that fits.

Easy level 1, step 1 only-fit: the 7 in row 1, column 1 is 7x1 from row 1, column 1 7 2 8 7 5 4 2 7 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7
The 7 has only one rectangle that fits (dashed): down the first column.

Steps 2 and 3: two more lines

The 7 in row 5, column 6 can’t run along row 5, where the 5 is, so it runs down column 6. Then the 5 in column 7 can’t take in the 2 below it, so it runs up from row 5 to row 1.

Easy level 1, step 2 only-fit: the 7 in row 5, column 6 is 7x1 from row 1, column 6 7 2 8 7 5 4 2 7 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7
The second 7 runs down column 6.
Easy level 1, step 3 only-fit: the 5 in row 5, column 7 is 5x1 from row 1, column 7 7 2 8 7 5 4 2 7 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7
The 5 runs up column 7, clear of the 2 below it.

The rest

Each rectangle drawn takes squares away from the others, so the remaining numbers fit one way each, one after another: 9 steps in all.

Easy level 1, solved The grid divided into rectangles. 7 2 8 7 5 4 2 7 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7
Easy level 1, solved.

Where to start in any puzzle

Look for numbers that can only be one shape: numbers like 5 and 7 can only be straight lines, and numbers in corners or beside other numbers often have just one rectangle that fits. On the game’s levels, 20% of the numbers on Easy fit only one way from the start, 10% on Medium and 7% on Hard, and 19 of the 50 Easy levels need nothing else from start to finish.

Common mix-ups

  • Count squares, not length. A 6 can be two by three; it doesn’t have to be six long.
  • Squares count as rectangles. A 4 can be two by two.
  • Every square belongs to a rectangle. There are no empty gaps.

Next steps

Questions

Is Shikaku the same as Rectangles?

Yes. Shikaku is the Japanese name (it means a four-cornered shape); in English it’s often called Rectangles. The rules are the same.

Can a rectangle be a square?

Yes. A square is a rectangle: a 4 can be two by two, and a 9 three by three.

Can a rectangle hold no number?

No. Every rectangle holds exactly one number, so there are exactly as many rectangles as numbers.

Does every puzzle have one solution?

Yes. Every puzzle on PeerPuzzles has exactly one solution, and can be finished by logic alone, without guessing.