Puzzle guide
How to solve Shikaku
Shikaku is a cutting puzzle. You split the whole grid into rectangles, and every rectangle holds exactly one number: how many cells it has. It sounds like guessing shapes, but there is almost always one rectangle that has only one way to fit. Here is how to find it.
The rules
- Cut the whole grid into rectangles (squares count too). Every cell belongs to exactly one.
- Every rectangle contains exactly one number.
- That number is the rectangle's area, in cells: a 6 is a rectangle of six cells.
A solved puzzle
Your first moves
- Draw every 1 right away: it is its own one-cell square.
- Look at numbers squeezed against an edge or between other numbers. They often have only one rectangle that fits.
- Think about the shapes a number can take: a 6 can be 1 × 6, 2 × 3, 3 × 2 or 6 × 1, but a 5 can only be a straight line of five.
- Check empty cells too: a cell that only one number can reach belongs to that number.
Techniques, step by step
Only one rectangle fits
The 4 in the bottom-left corner could be a 2 × 2 square, but that would swallow the 4 above it. A column of four does not fit, the puzzle is only three cells tall. So the only rectangle left is the whole bottom row. Every number that has just one shape left can be drawn at once.
Every cell must be covered
The top 4 could look like a 2 × 2 square around itself. But then a cell in the top corner would be left that no other rectangle can reach, and the puzzle could not be finished. So the top 4 has to be the whole top row, and the two 4s below sit side by side as two squares. Before you draw a rectangle, check that it does not leave any cell stranded.
Only one number can reach this cell
Start from an empty cell instead of a number. Which numbers could have a rectangle that covers the top-left corner? Only the 4 next to it: all the others are too far away or blocked. So the corner belongs to that 4, and here that means its 2 × 2 square. This is the idea the harder boards need most.
Every shape covers the same cell
Sometimes a number still has a few rectangles it could be. Look at all of them: if every one covers the same cell, that cell is part of the number's rectangle, whichever shape it takes. For example, a 4 in a corridor three cells wide can slide up or down, but it always covers the cells right next to the number.
Count the shapes
A number's area limits its shapes. A 5 or a 7 can only be a straight line, because they cannot be split into rows of equal length. A 4 is a line of four or a 2 × 2 square. An 8 is a line, 2 × 4 or 4 × 2. Listing the shapes first makes it much quicker to see which ones still fit.
Common mistakes
- Two numbers in one rectangle. Every rectangle holds exactly one number, so a rectangle may never stretch over a second one.
- A rectangle with no number. Every cell must belong to a numbered rectangle; there are no empty areas left at the end.
- Shapes that are not rectangles. An L-shape or a cross is never allowed, even if its area is right.
- Drawing the big numbers first. Big numbers have the most shapes. Start with small numbers and tight spots, and leave the big ones for later.
Questions and answers
Ready to play?
Draw the rectangles that have only one way to fit, never leave a cell stranded, and ask which number can reach an empty cell. That is how every Shikaku gets cut.