What makes a Shikaku hard
Not the size of the grid. Not the size of the rectangles. The number of times the direct deductions run out and you have to look ahead.
By Gonzalo Fuentes, who built Kaku Updated
Most puzzle apps grade difficulty by the size of the board, or by how many numbers they hand you. Both are proxies, and both lie: a 12×12 whose every number is forced is a pleasant twenty minutes, and a 7×7 can hide a knot that stops you cold.
The honest measure is how far you have to reason without a foothold. Kaku's generator measures it directly: before a puzzle reaches you, the app tries to solve it the way a person would, using only the two techniques from Shikaku techniques. Whatever the human solver cannot deduce, it must search: assume a placement, follow the consequences, and back out on a contradiction. It counts those searches. That count is the difficulty.
The ladder
Because deduction depth and board size climb together in a well-made set of puzzles, each tier is bound to a size. Choosing a difficulty is choosing a board, which is why you will never find a "hard 7×7" here. Every board below is a real, uniquely solvable puzzle of its tier.
Beginner, 7×7
Forced singles alone are enough. (no lookahead)
Every number, at some point in the solve, has exactly one legal rectangle. You never have to reverse the question. This is the tier to learn on, and it is the only one where you can finish without ever thinking about an empty cell.
Easy, 8×8
Cell ownership becomes necessary. (no lookahead)
The cascade of forced singles stalls at least once, and to restart it you must find a cell that only one number can reach. Still no guessing, still no lookahead, but you now need both eyes.
Medium, 9×9
One assumption, followed to a contradiction. (one lookahead)
Once, somewhere, both deductions run dry. You take the number with two options, assume one, and follow it until the board either completes or breaks. This is where Shikaku starts to feel like a puzzle rather than a procedure. The daily is Medium or Hard, never harder.
Hard, 10×10
Two separate assumptions. (two lookaheads)
The board makes you do it twice, in different corners, and the second one usually depends on having resolved the first. Ten by ten, so there is room for the arguments to be genuinely independent.
Expert, 12×12
Three or more, sometimes nested. (three or more lookaheads)
The full 12×12. Not because a big grid is hard, but because a grid this size can hold three independent knots and still be a single puzzle with one answer.
Why size still matters
If difficulty is search depth, why bind it to a grid size at all? Because a small grid cannot hold a deep puzzle without becoming ugly. To force three independent lookaheads onto a 7×7 you would need enormous rectangles and very few numbers, and the board stops looking like a Shikaku and starts looking like a trick. The size gives the difficulty room to be natural.
The same reasoning caps the rectangles. Kaku holds them to a modest maximum area, growing from 4 on Beginner to 12 on Expert, so that the challenge comes from deduction rather than from a single 20-cell slab sitting across the board.
Where the daily sits
Everybody in the world gets the same Shikaku each day, and it is always Medium or Hard, never Beginner and never Expert. That is deliberate. A shared daily puzzle has to be finishable by someone who plays once a day on the bus, and interesting enough for someone who plays every day. One lookahead, sometimes two.
Reading a board's difficulty before you start
You can often feel the tier in the first ten seconds, without counting anything.
- Lots of numbers near walls and corners means lots of forced singles, which means an easy opening whatever the size.
- Numbers clustered in the middle, far from any edge, have the most legal rectangles each and the fewest forced singles. That is where the searches hide.
- Many primes (5, 7, 11) make a board easier than it looks: those rectangles can only be single rows or columns.
- Many highly composite numbers (8, 12) make it harder: an 8 can be 1×8, 2×4, 4×2 or 8×1, and each of those can sit in several places.
Start where you are
If you have never played, start at Beginner and let the cascade teach you. If you solve Sudoku, you will be at Medium within a day, and this comparison will tell you what to unlearn. The rule itself takes one sentence, and it is in how to play Shikaku.