Shikaku is also called Rectangles or Divide by Box. It is a calm puzzle about shapes and simple counting.
The rules
- Cut the whole board into rectangles along the lines.
- Every box belongs to exactly 1 rectangle. There are no gaps and no overlaps.
- Each rectangle holds exactly 1 number.
- The number tells how many boxes the rectangle covers.
- A square counts as a rectangle too.
Quirk uses the classic rules. A rectangle can also be long and thin, like a strip of 1 by 5 boxes.
A worked example
Here is a small board with 3 rows and 3 columns. Three boxes hold a number, and the rest are empty.
| Column 1 | Column 2 | Column 3 | |
|---|---|---|---|
| Row 1 | 2 | 3 | |
| Row 2 | 4 | ||
| Row 3 |
The numbers add up to 9, the same as the 9 boxes on the board.
- Start with the 2 in the top left corner. It needs 2 boxes, so it goes across or down.
- Going down would cover the 4 below it. A rectangle may hold only 1 number, so the 2 goes across.
- The 2 now covers row 1, columns 1 and 2.
- Next, look at the 3 in row 1, column 3. A 3 can only be a straight line of 3 boxes.
- Across would run into the 2. So the 3 goes down and covers all of column 3.
- Four boxes are left: rows 2 and 3, columns 1 and 2. They make a 2 by 2 square with the 4 inside.
- Draw that square, and every box is covered.
Here is a second board with 3 rows and 4 columns. Every number on it is a 4.
| Column 1 | Column 2 | Column 3 | Column 4 | |
|---|---|---|---|---|
| Row 1 | 4 | |||
| Row 2 | 4 | 4 | ||
| Row 3 |
- A 4 can be a line of 4 boxes or a 2 by 2 square.
- Look at the 4 in row 1, column 1. A line down does not fit, because the board has only 3 rows.
- A square from that corner would cover the 4 in row 2. So this 4 takes the whole top row.
- Now the 4 in row 2, column 1. A line across row 2 would cover the other 4 in that row.
- The top row is already taken. So this 4 makes a square in rows 2 and 3, columns 1 and 2.
- The last 4 boxes are rows 2 and 3, columns 3 and 4. They make a square around the last 4.
Beginner techniques
Know the shapes for each number
Each number allows only a few shapes. A 6 can be 1 by 6, 2 by 3, 3 by 2 or 6 by 1.
Some numbers, like 2, 3, 5 and 7, can only be straight lines. They are often a good place to start.
Never cover a second number
Try each shape for a number. Throw out any shape that covers another number or runs off the board. Often only 1 shape is left.
Work around rectangles you already drew
Rectangles cannot overlap. After you draw one, check the numbers next to it. Any shape that would overlap it is out.
Ask which number can reach a box
Look at an empty box, often a corner. If only 1 number can reach it, that number's rectangle must cover it.
This often leaves just 1 shape for that number.
Find the boxes every shape shares
Sometimes a number still has a few shapes left. If all of them cover the same box, that box belongs to this number.
Common mistakes
- Drawing a rectangle that holds 2 numbers.
- Leaving a box uncovered. Every box must end up in a rectangle.
- Counting along the sides instead of counting boxes. A 2 by 3 rectangle covers 6 boxes.
- Forgetting that a long, thin strip is a rectangle too.
- Trying an L shape. Only rectangles and squares are allowed.
Questions
Is Shikaku the same as Rectangles?
Yes. Rectangles and Divide by Box are other names for the same puzzle. The rules are the same.
Does every puzzle have one solution?
Yes. Quirk checks that each board can be cut in exactly 1 way.
What sizes are there?
Quirk keeps the boards small, up to 8 by 8 boxes. Easier boards are smaller and have fewer numbers.
Is Shikaku good for beginners?
Yes. You only need to count boxes. The first boards are small, and a hint can explain the next step.
What can I do when I am stuck?
Ask for a hint. It marks a rectangle and tells you why it is the only one that fits. You can also undo a move or reset the board.
Related puzzles
Playing it in Quirk
To draw a rectangle, drag from 1 corner box to the opposite corner. You can also tap 1 corner and then the opposite corner.
While you draw, Quirk shows the size, like 2 × 3 = 6. Tap a rectangle to remove it. Quirk tells you when rectangles overlap or have the wrong size.
