Shikaku

How to play shikaku

Every cell ends up in exactly one rectangle, and every rectangle holds exactly one number. Squares count as rectangles. Start with the numbers that have the fewest possible shapes and work outwards from there.

Here’s a small one. The 1 in the corner is a rectangle on its own. The 4 can’t run along the top row, down its column, or into a square to its right without covering another number, so it takes the square in the top-left corner. Any shape for the 3 that reaches the bottom row covers the 1, and going left covers the 6, so the 3 runs up the right edge. That leaves the 2 one way to go: down. The 6 takes the six cells that are left.

Beginner techniques

Prime numbers run straight

A 2, 3, 5 or 7 can’t make a rectangle more than one cell thick, so it’s always a straight line, across or down. Check both directions: one of them often hits another number or the edge of the grid.

Count the possible shapes

Bigger numbers have more shapes. A 6 can be 2 by 3, 3 by 2 or 1 by 6, and each shape can sit in several places. Go through them and drop any that covers another number or a cell that’s already taken. Often only one is left.

Every cell needs a number

Every cell has to belong to some rectangle. When only one number can reach a cell, that number’s rectangle has to cover it. Corners are the best place to look, because they have the fewest neighbours.

Difficulty and grid sizes

Every Owlpuzzles shikaku puzzle has exactly one solution. The grids grow through the week:

Days	Level	Grid	Largest rectangle
Monday, Tuesday	Easy	8×8	8 cells
Wednesday, Thursday	Medium	12×12	14 cells
Friday to Sunday	Hard	16×16	20 cells, and no 1s

Bigger rectangles have more possible shapes, and that’s most of what makes the hard grids slower. The logic steps up too. On easy days each rectangle fits only one way by the time you reach it. Midweek, some cells can only belong to one number. At the weekend you’ll rule out shapes that would block a neighbour.

Where shikaku comes from

Shikaku is an original puzzle from Nikoli, the Japanese puzzle publisher that also named sudoku. It first appeared in Nikoli’s magazine in 1989. Shikaku (四角) means a four-sided shape, and the full Japanese title, shikaku ni kire (四角に切れ), asks you to cut the grid into them. Nikoli’s English name for it is Divide by Box, and you’ll also see it called Rectangles or Divide by Squares.

Shikaku questions

How do you solve a shikaku puzzle?

Start with the numbers that have the fewest shapes: 1s, prime numbers and numbers in corners. Each rectangle you place takes cells away from its neighbours, which cuts down their shapes in turn.

Can a shikaku rectangle be a square?

Yes. A 4 can be a 2 by 2 square and a 9 can be 3 by 3. Squares count as rectangles.

Does every shikaku puzzle have only one solution?

A well-made one does. Every Owlpuzzles shikaku puzzle has exactly one solution.

Can kids play shikaku puzzles?

Yes. The rules only need counting cells, and the 8×8 grids on Mondays and Tuesdays are a good size to start with.

Is shikaku like sudoku?

Both are Japanese grid puzzles with number clues, and both came through the puzzle publisher Nikoli. In shikaku you don’t place digits: you draw rectangles, and the only maths is working out areas.

Puzzles like shikaku

If you like the counting, try a nonogram, where number clues tell you which cells to fill. Killer sudoku adds sums to sudoku, and star battle is pure placement with no numbers at all.