Kurotto
Shade some cells. Each circled number equals the total size of the shaded blocks — orthogonally connected groups — sharing an edge with that circle; circles are never shaded. And that is the whole rule book: no connectivity rule, no 2×2 rule, no border rule. Click a cell to cycle shaded → white → empty; right-click erases. Every shaded block of two or more wears its current size in the corner — the number a Kurotto player keeps recounting.
There is no global rule
Strip the circles away and ask what a finished board can look like: anything. All 16 shadings of the 2×2 board are valid, all 512 of the 3×3 — the configuration space is the full hypercube, 2n² boards. This series has spent entries hunting bijections between legal boards and samplable objects; Kurotto is the degenerate end of the hunt, where the bijection is the identity and a uniform sample is n² coin flips. Everything the earlier puzzles got from connectivity theorems, Kurotto must buy with arithmetic alone — and the only global force left in the puzzle is the demand that the answer be unique.
Floors, ceilings, doors
A circle's clue is bracketed by two floods: a floor — the shaded cells already attached to it — and a ceiling — everything still reachable through non-white cells. The brackets never lie: the floor only rises, the ceiling only falls. When the clue touches the ceiling, the whole potential region shades; when it touches the floor, the frontier seals white (a 0-clue is just this with an empty floor). And a circle still below its clue must grow through a door — a free cell adjacent to it or to its attached blocks; one door means a forced shade. Beyond that the ladder assumes a cell and listens for the echo: first in every circle's arithmetic, then through the whole ladder itself.
Where the ambiguity lives
A circle can only ever speak about its potential region — the cells its floods can reach. A free cell outside every region is a free second solution before a single deduction is made: shade it or not, no circle can tell. Measured on the raw stream, that assassin never actually strikes — but two others do: single silent flips, and silent pair flips, two cells whose joint flip reshuffles blocks without any circle noticing. Those pairs are also where a series-long law finally broke: for the first time, a handful of boards are provably unique yet no chain of single-cell assumptions — the probe rule — can finish them. The uniqueness proof lives outside the world a one-cell hypothesis can see.