Shikaku techniques
Two deductions solve almost every board. Here they are, plus what a puzzle is really asking of you when neither one fires.
By Gonzalo Fuentes, who built Kaku Updated
If you have not met the rule yet, start with how to play Shikaku, which walks one small board from empty to solved. This page assumes you can do that, and goes after the part that actually makes you faster: seeing why a candidate dies, and knowing what to do on the boards where the two deductions stop firing.
Everything below is how Kaku's own solver thinks. Before a puzzle is ever shown to you, the app tries to solve it the way a person would, using exactly the two techniques on this page. Whatever it cannot deduce, it counts as a search, and the number of searches decides the puzzle's difficulty. So these are not tips someone invented. They are the definition.
1. The forced single
For a given number, enumerate every rectangle of that area which contains it and no other number. If exactly one rectangle survives, place it. There is no risk: no other arrangement can ever be legal.
Three things kill a candidate rectangle, and you should learn to see all three at once:
- The wall. It runs off the edge of the grid.
- A rival number. It would cover a second number. One number per rectangle.
- An occupied cell. It overlaps a rectangle you have already placed.
The reason to sweep for forced singles first is that they cascade. Each placement occupies cells, which kills candidates for every neighbouring number, which creates new forced singles. A whole Beginner board is one long cascade.
2. Cell ownership
Sooner or later nothing is forced. Every number has two or three homes and none is certain. The move now is to reverse the question.
Stop asking where a number can go. Point at an empty cell and ask which numbers could still reach it. Every cell must end up inside somebody's rectangle, so if only one number can reach a cell, that number owns it. And a number forced to cover a specific far-away cell usually has only one rectangle that does so, which is how ownership turns into a placement.
Cell ownership is what separates an Easy board from a Beginner one in Kaku. Beginner boards are guaranteed to fall to forced singles alone. Easy boards are guaranteed to need this.
3. What to do when neither fires
On a Medium board or above you will reach a position where no number is forced and no cell has a single owner. This is not a flaw in the puzzle and it is never an invitation to guess.
Pick the number with the fewest options, usually two. Assume the first. Follow the consequences with forced singles until either the board completes or you hit a contradiction: a number with nowhere legal to go, or a cell nobody can reach. A contradiction proves the assumption wrong, so the other option is right. That is not luck, it is proof by exhaustion.
Kaku counts each of those lookaheads. Zero means Beginner or Easy, one means Medium, two means Hard, three or more means Expert. It is measured, not decorated, which is why a small Expert board and a big one feel equally sharp. See the difficulty ladder for the whole mapping.
Five habits worth stealing
Work the corners first
A number in a corner has lost half of its rectangles to the wall before you start. Edges are nearly as good. This is where forced singles hide.
Hunt the primes
A rectangle of five cells is 1×5 or 5×1. Nothing else. Same for 7, 11 and 13. Prime numbers are long thin bars, and a long thin bar has very few places to lie down.
Count what is left
The numbers always sum to the number of cells. If you have placed rectangles covering 18 of 25 cells and the numbers you have left add up to 7, then everything is consistent. If they do not, you have made a mistake somewhere, and you can find it now rather than at the end.
Watch for the orphan cell
A cell that no remaining number can reach means an earlier placement was wrong. In a valid puzzle this can only happen because of something you did. It is the cheapest error check there is: scan for cells nobody wants.
Do not fear the big rectangle
Beginners avoid drawing long rectangles because they look risky. They are not. A 12 has to be 12 cells wide or 6×2 or 4×3, and the wall usually rules out most of that. Large numbers are often the most constrained on the board, not the least.
Common questions
Do you ever have to guess in Shikaku?
No. A well-made Shikaku has exactly one solution, and being solvable without guessing is what puzzle generators check for. If you are stuck, there is a deduction you have not spotted yet. Harder puzzles may need you to hold a chain of consequences in your head, which feels like guessing but is not.
What is the fastest way to start a Shikaku puzzle?
Start with numbers in corners and along edges, because half of their rectangles run off the board. Then take the primes: a 5 or a 7 can only ever be a single row or column, so they are the easiest to pin down.
What makes a Shikaku puzzle hard?
Not the size of the grid, and not the size of the rectangles. Difficulty is how many times you must look ahead, assuming a placement and following its consequences, because no direct deduction is available. A puzzle needing three such lookaheads is hard whatever its dimensions.
Practice
If you arrived here from Sudoku, the habits transfer better than you would think, though what your eyes hunt for does not: Shikaku vs Sudoku covers what to unlearn.
Reading about deduction is a poor substitute for doing it. Kaku gives everyone the same Shikaku each day, sized to its difficulty from a gentle 7×7 up to a 12×12, and every solve is pressed into an album as a stamp. Free, no ads, no subscription.