1. Count possibilities, not squares.
A big region can become easy after other cats block most of its cells. A tiny region can still have several plausible choices. Check the remaining legal positions in every row, column and region.
Only one spot left.
If the other five cells of a row are genuinely ruled out, its cat must go in the fourth cell. The same deduction works for columns and regions.
2. Let every cat do its full job.
After placing a cat, eliminate the rest of its row, its column and its colored region. Then check its immediate diagonal neighbors. One placement often supplies several useful exclusions.
This row is spoken for.
With a cat in the third cell, the other five cells cannot hold cats. You can mark them X before looking elsewhere.
Horizontal and vertical neighbors are already covered by the row and column rules. The extra diagonal restriction only concerns touching corners, not a whole diagonal line.
3. Look for a region squeezed into one line.
Imagine that the sage region has just two legal cells, both in row 4. You may not know which of those cells contains its cat yet, but you do know that row 4’s cat belongs to the sage region. All row 4 cells outside that region can be marked X.
The same idea works for a column. It can also run in the other direction: if every legal spot in a row belongs to one color, the rest of that colored region cannot hold its cat.
4. Scan again after every deduction.
A useful X may turn three choices into two, or two choices into one. Move between rows, columns and colors instead of staring at the same region. When a group has only one legal spot, place its cat and repeat.
5. Treat your notes as claims you can revise.
An X is a claim that a square cannot contain a cat. If you make a mistaken mark, a puzzle can appear impossible. Undo the latest uncertain step, or ask for a hint to check whether your current cats and marks still allow a completion.
Red outlines point out direct conflicts between cats. A lack of red outlines does not prove that a position can be completed; sometimes a mistake only becomes visible several deductions later.
What our hint button does
The hint system uses rule-based exclusions, single remaining positions and groups restricted to rows, columns or colors. Every generated board is checked against these deductions before you see it. A hint describes the reason, and you can choose whether to apply it or make the move yourself.
There is no penalty for taking a nudge. Learning why a move works is a good solve, too.