Exactly one per row
Each horizontal line contains one cat — no more and no fewer. A row holding two cats is invalid even when every other constraint is satisfied. A row holding none means the board is unfinished, not wrong.
Exactly one per column
Each vertical line contains one cat. Together with the row rule this fixes the population of the board: an N×N grid holds exactly N cats, one per row and one per column, with no line ever shared.
Internalize this early, because it turns counting into a tool. If you have placed six cats on an 8×8 board, exactly two remain, and they must live in the two rows and two columns still standing empty. Late-game positions are often finished by counting rather than scanning.
Exactly one per colored region
The board contains exactly N connected regions, and each holds one cat regardless of its shape or area. A region of two cells and a region of eleven cells carry the same single cat, which is why small regions are worth far more attention than large ones.
Connected means orthogonally connected: every cell in a region can be reached from every other by moving up, down, left, or right without leaving the color. Two same-colored blocks that meet only at a corner are two regions, not one — a distinction worth tracing carefully on a crowded board, and the single most common thing to misread in a screenshot.
Cats never touch
Two cats cannot share an edge or a corner. Every placed cat forbids up to eight surrounding cells, and this is the only rule that constrains cells outside the cat’s own row, column, and region.
That makes it the most productive rule on the board. The other three describe lines and colors you were already reading. The no-touch rule reaches diagonally into regions you were not.
Every valid puzzle has exactly one solution
A board admitting two different arrangements is not a harder puzzle — it is a broken one. Every puzzle generated here is verified to have a unique solution before it is served, and that solution is always reachable through certain moves alone. You should never need to guess and check.
Board sizes
The solver accepts boards from 4×4 through 12×12. The generator makes boards from 5×5 through 12×12, because a 4×4 grid rarely leaves room for an interesting region layout. Difficulty is not a function of size alone: a well-shaped 7×7 can be harder than a loose 10×10.
Starter cats
Some boards arrive with cats already placed. They obey the same rules and are simply deductions the puzzle grants you for free. If starter cats conflict with one another — sharing a row, a column, a region, or a corner — the board is invalid, and nothing after that point is worth solving.
Imported boards
A screenshot or hand-drawn board must have N connected regions and non-conflicting starter cats. If it is invalid, the solver reports no solution or multiple solutions instead of inventing an answer.
Both answers are useful diagnostics. No solution usually means a region boundary was misread and one region got split in two. Multiple solutions usually means a boundary was missed and two regions were merged into one. In either case, correcting the region outline in the editor is faster than re-taking the screenshot.