Shikaku Solver, Step by Step
Type each number into its square. Each rectangle is shaded as it is found, with a heavy line where two meet.
How to use the shikaku solver
Set the width and height, then type each number into its square. Press Explain the next step: the solver gives the squares that are certain to the number they belong to, outlines what changed, and says why. Show the answer draws every rectangle at once and checks the solution is the only one. Grids up to 16 by 16 work, and numbers up to 99.
The rules of shikaku
Divide the grid into rectangles. Each rectangle holds exactly one number, and that number is its area, the count of squares inside it. Squares are rectangles too, and every square of the grid belongs to exactly one rectangle. So the numbers always add up to the size of the grid, which is the first thing the solver checks.
How to solve shikaku, step by step
List the shapes. A 6 can be 1 by 6, 2 by 3, 3 by 2 or 6 by 1, and each of those can sit in several places around its number. Rule out any that cover another number or run off the grid. Draw the rectangles with only one way to fit. Big numbers in tight corners and primes against an edge are the usual starts. Claim the overlap. When every rectangle a number could still take covers the same squares, those squares are its. Find the squares only one number can reach. They belong to it, which narrows its shapes again. When those run out, the solver tries each shape of the number with the fewest and drops the ones that lead to a square nothing can cover.
How it was checked
The solver was run on all 150 puzzles of the daily shikaku. It found each stored answer and found it to be the only one, and every step it explained was checked against those answers: it never gave a square to the wrong number. All 150 were explained from start to finish without needing a trial. It was also run on larger grids up to 16 by 16, including some that do need one.
More logic puzzles
There is a new daily shikaku every day. The nurikabe solver and the kakuro solver explain their steps the same way. For a puzzle you hold in your hands, see our brain teasers. There are more solvers on the puzzle tools page.
Frequently Asked Questions
How do you solve shikaku?
List the shapes each number could take and rule out any that cover another number. Draw the rectangles that have only one way to fit, then claim the squares every remaining shape of a number covers, and give a square to the only number that can still reach it.
What are the rules of shikaku?
Divide the grid into rectangles so that each holds exactly one number, and that number is the rectangle's area. Every square belongs to exactly one rectangle.
Do the numbers in a shikaku add up to the grid?
Always. Every square belongs to one rectangle and each rectangle's number is its area, so the numbers sum to the number of squares. The solver checks this first.
Can a shikaku rectangle be a square?
Yes. A square is a rectangle, so a 4 can be 2 by 2 as well as 1 by 4 or 4 by 1.
Does every shikaku have one solution?
A well-made one does. The solver checks, and says if the numbers you entered allow more than one.