In short. Shikaku is played on a grid where a few squares carry a number. You cut the whole grid into rectangles so that each rectangle holds exactly one number, and its area in squares equals that number. No rectangle may overlap another, and no square may be left out. A correct grid has exactly one solution, and that solution is reached by deduction: guessing is never required.
- 1Number per rectangle. Never two, never none.
- 4Deductions are enough to solve a whole grid.
- 0Guesses required. Every grid is checked before it ships.
The rule, in three lines
Cut the whole grid into rectangles. Each rectangle holds exactly one number. That number is its area, its count of squares.
So a 6 is a rectangle of six squares: 1 × 6, 2 × 3, 3 × 2 or 6 × 1. A square counts as a rectangle, and so does a strip one square wide.
Nothing overlaps, nothing is left over. When the last square is taken the grid is done, and there was only one way to get there.
The four deductions that are enough
A Shikaku is not solved by picturing the whole partition. It is solved by elimination, number by number and square by square. Four lines of reasoning are enough, and they are exactly the four the game's solver applies to check a grid before serving it to you.
1. The only rectangle that fits
Take a number and count the rectangles of the right area that contain it without swallowing another number or leaving the board. If one is left, it is placed. This is what happens to prime numbers against an edge: a 5 has only two shapes, 1 × 5 and 5 × 1, and an edge often kills one of them.
2. The square with a single cover
Look at an empty square and ask which rectangles, across all numbers, can still cover it. If only one can, it is placed, whatever room it takes elsewhere.
3. The square only one number can reach
The most rewarding of the four, and the least practised. The square may have several covers, but if they all belong to the same number, then that number will take it: every one of its rectangles that misses the square can be thrown away.
. . . . . 6 . . . . . 3 ? . . .
The 3 cannot get down to the corner: its three-square rectangles stay too high. The 6 can, with a 2 × 3 along the left edge. The corner therefore belongs to the 6, and every layout of the 6 that avoids it is eliminated at once.
4. The forced crossing
The reverse move. Take a number and mentally stack all the rectangles it can still take. If a square turns out to be covered in every case, it already belongs to that number, even though its final shape is still unknown. No other number can claim it.
Where to start
- Corners and edges first. A corner square can be reached by very few rectangles, often from a single number. That is where the third deduction pays best.
- Then the primes. 2, 3, 5, 7, 11: two orientations only, and an edge regularly kills one.
- Big numbers after that. A 12 has many shapes but needs a lot of room: on a crowded grid it often finds only one.
- Sweep the lonely squares again. After each piece, look at the squares that just lost candidates. That is where the grid starts unfolding on its own.
The mistake that costs the game: placing a rectangle because it fits, without checking that it is the only one that fits. The game accepts it, since the area is right, and the error only surfaces ten pieces later, when a square has no taker left. By then, finding which of the ten is wrong costs more than the deduction you saved.
Never ask "where can this number go?". Ask "who can cover this square?". Both questions are about the same grid, but the second one has far fewer answers.
Why you never guess
A correct Shikaku has a unique solution and, more importantly, a path to it: at every step at least one deduction is available. Without that guarantee the game becomes a bet, and a bet lost after twenty minutes is not forgiven.
Here every level is generated and then put through the solver before it ships. If the slightest assumption is needed to move forward, the grid is thrown away and another is generated. Uniqueness follows: when every step is forced, no branch ever existed.
Where Shikaku comes from
The puzzle was invented in 1989 by Yoshinao Anpuku, a mathematics student at Kyoto University, and published by Nikoli, the Japanese house that made sudoku famous. Its full name, 四角に切れ, shikaku ni kire, means "cut into rectangles".
It also travels as "Rectangles" and "Divide by Box", and sometimes "Cell Block". Same game, same rules.
In this game
The gesture
Put your finger on a square and drag: the rectangle draws itself. A badge shows the running area against the target, 4 / 6, and it sits above your finger, never below: on a phone your hand covers exactly what you are trying to read. Let go when the count is right. To lift a piece already set, tap inside it.
What the game refuses, and why it says so
A rectangle of the wrong size is refused with its reason: "the 6 needs 6 squares, you drew 8". Two numbers inside, it says that too. This is deliberate: a silent refusal reads as a bug, a refusal that explains itself teaches the rule in one session.
The hint explains before it answers
The first press sets nothing. It marks a square and states the deduction in plain words: "only the 6 can reach this square, so its rectangle has to cover it". The second press places the piece, if you want the answer after all. Hints cost no stars.
The stars
Three stars are earned by a clean run. Mistakes are: a rectangle refused for the wrong area or for holding two numbers, and above all a piece set and then lifted, which is admitting it was wrong. A finger sliding off the board is not.
The silhouettes
Some grids are not rectangles but cut-out shapes, a heart, a key, a cat. They are not harder, quite the opposite: every hollow edge removes possible rectangles, so there is less to examine. They are the campaign's breathing room.
Frequently asked questions
What is Shikaku?
A Japanese logic puzzle published by Nikoli. You cut a grid into rectangles so that each rectangle contains a single number equal to its count of squares. Nothing overlaps and no square is left out.
Does a square count as a rectangle?
Yes. A 4 can be a 2 × 2 square, a 1 × 4 strip or a 4 × 1 strip. A 9 can be a 3 × 3 square. The word rectangle includes the square, as in geometry.
Do you ever have to guess?
No, never, on a correct grid. Every level in this game is checked by a solver that only applies forced deductions: if anything has to be assumed to move forward, the grid is discarded before it is served.
How do I know where to start?
Corners and edges first, then prime numbers. A corner square can be reached by very few rectangles, and a prime has only two possible orientations, one of which an edge often removes.
Does Shikaku go by other names?
Yes: "Rectangles", "Divide by Box", sometimes "Cell Block". Its full Japanese name is 四角に切れ (shikaku ni kire), "cut into rectangles".
How is it different from a nonogram?
Both are solved by pure deduction, but a nonogram has you fill squares from runs of numbers in the margins, and reveals a picture. Shikaku cuts the surface into regions: you are not looking for a drawing, you are looking for a partition.
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