How to Solve Shikaku Puzzles
Shikaku, invented by Yoshi Anpuku, and originally published by Nikoli, a game and puzzle magazine in Japan, is an area-division type of puzzle.
Your goal is to divide the grid into rectangles, in which every rectangle contains one and only one of the number clues, and has an area equal to that number. For example, the number 8 will be in a rectangle containing 8 squares. It might be a 2×4 shape, or a 1×8 shape, in either a horizontal or vertical orientation. All grid squares must be used.
Rectangles may only border each other – they cannot cross. Some knowledge of multiplication and a few prime numbers can help, but is not required to solve the puzzle.
Let’s start in the upper left corner, where we have a 3 and a 5 given as clues. Neither of these can be more than 1 square wide, because they are both prime numbers – nothing divides into them evenly, so a rectangle can only be 1×3 and 1×5 for them.
Using blue for the 3 and red for the 5, you can see where the different placement options would cross each other. Because that is not allowed, we only have a few possible placements for these rectangles which do not cross.
Next, let’s look at these two squares. Remember that every square in the grid must be used in a solution rectangle.
The only nearby numbers are 6 and 16. While the 16 could be part of a 4×4 square to reach them, it would have to cover the 6 to do so. Therefore the 6 must be the clue we will use.
Because the rectangle must include the number, and the total number of squares from the top row to the 6 is three, we must conclude that it is a 3-square tall by 2-square wide rectangle.
The same concept applies to this cluster of squares. They have to be covered by a rectangle, and the only nearby number which won’t cross another rectangle is the 20.
Because this gap is only 2 squares wide, it means the entire rectangle must be 2 squares across. Fortunately, the grid is 10 squares tall, so we know we have a narrow rectangle that is 2×10 containing 20 squares.
After drawing in the 20-square rectangle, it’s easy to see that the entire bottom row follows the same pattern. The only numbers close enough to reach those squares without crossing other rectangles can only do so by creating a rectangle that is 2-squares wide.
The sixes are each 3 squares away, while the eights are each 4 squares away. 6/3 = 2, and 8/4 = 2, so we can fill this area with four different rectangles, each two squares wide.
Once we draw all those in, we see that the 16 is now boxed into an area that is only 4 spaces tall.
We can either work this out with math – 16/4 = 4, or younger solvers can simply count the spaces, making sure to keep a rectangular shape.
Just make sure to include the cells to the right of the clue.
We only have two clues left to use, and the way the other rectangles border them makes it obvious how to draw around their required areas.
The 10 is in a place that is 5 spaces wide by 2 spaces tall, and the 12 must cover an area that is 3 spaces tall and 4 spaces wide.
And here is the completed puzzle.
