How to play Shikaku

Cut the grid into rectangles. Each one holds a single number, and that number is exactly how many squares the rectangle covers.

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Shikaku, sometimes called Divide by Squares or Rectangles, is a puzzle of pure spatial deduction. There is no arithmetic beyond multiplication tables up to nine, no hidden information, and no guessing. Every board has exactly one answer, and every step toward it can be argued.

The rule, in full

The grid must be cut into rectangles so that:

- Each rectangle contains exactly one of the numbers on the board - Each number equals the area of the rectangle containing it, counted in squares - The rectangles fit together with no gaps and no overlaps, covering every square of the grid

That is all of it. The count of numbers on the board is therefore also the count of rectangles in the answer, and the numbers always add up to the total number of squares.

Why the covering rule matters most

Beginners read the first two rules and start hunting for rectangles that fit each number. The third rule is where the real leverage is. Every square has to be covered by something, so any square that only one possible rectangle can reach settles that rectangle immediately, no matter how many other placements its number might have had in isolation.

This is why corners are the traditional opening. The square in a corner can only be covered by a rectangle running along one of the two edges that meet there. Usually only one number is close enough along either edge, and often only one shape of rectangle reaches. The same argument works, slightly weaker, all along the borders, and it works again in the middle of the board once a few rectangles are down and the remaining space is broken up.

Reading a number

A number's area tells you its possible shapes, and the shapes are the factor pairs.

- 1 is one square, its own - 2, 3, 5 and 7 are prime: one row or one column, nothing else - 4 is one by four, two by two, or four by one - 6 is one by six, two by three, three by two, or six by one - 8 and 9 have their own short lists, and on the sizes played here the very long thin ones usually run off the edge

For each shape, the rectangle must still cover the number's own square, so the shape can be slid along until it does. Placements that would swallow a second number are out, because a rectangle may only contain one.

Grades

Boards are graded by the deduction they actually need, not by size.

- **Gentle** boards can be finished by counting placements. Take each number in turn, list the placements still open to it, and whenever one number is down to a single placement, draw it. That single placement removes squares from the board, which shortens other numbers' lists, and the board unravels - **Hard** boards reach a point where every number still has two or more placements open and nothing is forced that way. The extra step is to turn the question round: instead of asking where this number can go, ask which rectangles could possibly cover this particular square. When only one can, that rectangle is settled — because the square has to be covered by something

A board is labelled Hard only once that harder step has been shown to be necessary. The generator solves the board a second time with the step switched off, and if the board still falls, it is not Hard and does not claim to be. The Grade panel reads Grade when the claim was proved and Aim when it was only sought.

No guessing, ever

Every board is checked before it is dealt by a solver that never guesses — it only ever draws a rectangle that has been forced, and it must finish the entire grid or the board is discarded and another one cut. That is a stronger promise than a unique answer, because a puzzle can have exactly one answer that no person could find without trial and error. If you are stuck here, there is a square somewhere whose covering options you have not counted.

The daily board

Everyone gets the same 9x9 board each day, cut from the date in your own browser, and it is always a Hard one. Finish it to build a streak, which survives as long as you do not miss a day. Times and streaks are stored in this browser only.

Controls

Drag from one square to another to draw the rectangle between them. The running area is shown while you drag, so you never have to count squares by eye.

Tap a rectangle you have already drawn to take it back
Drawing across an existing rectangle replaces it, so a correction is one gesture rather than three
Undo steps back through your rectangles, as does Z
The Size button cycles 7x7, 9x9 and 12x12

Strategy tips

Start in a corner, every time. The corner square can only be covered by a rectangle running along one of the two edges that meet there, which is the shortest list of options anywhere on the board. Work the four corners, then the edges, and only then the middle.
## Count placements, not shapes
For each number, the useful question is how many rectangles of that area both cover its square and swallow no other number. If the answer is one, draw it and move on
Every rectangle you draw shortens the lists of its neighbours, because the squares it took are no longer available. After each one, re-check the numbers nearest to it rather than starting again from the top
Primes are gifts. A 5, 7 or 3 is a straight line in one of two directions, so it has far fewer placements than a composite of similar size
## Turn the question round when you stall
The move that unlocks a Hard board is asking which rectangles could cover a given empty square, rather than where a given number could go. Every square must be covered by something, so a square with only one possible coverer settles that rectangle even when its number still looked free
Isolated pockets are the place to try this. A square hemmed in by rectangles you have already drawn usually has very few numbers still able to reach it
## Read the neighbours
Two numbers close together restrict each other hard. A rectangle may only contain one number, so no placement can reach across its neighbour
A number sitting immediately beside another cannot extend in that direction beyond the gap between them
Large numbers in tight spaces are more constrained than they look: an 8 with three squares of clearance on one side has to run the other way
## Habits that save time
Draw the ones you are certain about straight away, even if they look unhelpful. Territory removed is information gained
If a rectangle turns red, fix it before doing anything else. A wrong rectangle steals squares from its neighbours and every deduction you make afterwards is built on it
On the 12x12, finish one region completely rather than scattering rectangles across the board. A solid block of settled squares gives the covering argument something to push against