Hachimi Sudoku rules: one cat per row, column and region
Learn the coloured-region cat puzzle rules, including diagonal contact, X marks, placement controls and the difference from conventional number Sudoku.
Updated 2026-11-13
Place exactly one cat in every row, every column and every coloured region. Cats cannot touch, including at diagonal corners; the puzzle is about locating cats rather than filling cells with numbers.
Treat the rules as simultaneous constraints
A cat placement has to satisfy the row, column and region conditions together. Finding an empty cell in a region is not enough if its row already contains a cat. Likewise, a row may need a cat, but a particular cell is unavailable if its column or colour region is already occupied.
Colour regions are the coloured groups of cells drawn on the board. They are not the regular square boxes of classic Sudoku. Follow the actual region boundaries, including irregular shapes, rather than mentally dividing the board into equal blocks. Every region needs its own cat regardless of its shape.
What “cannot touch” means
Two cats cannot occupy neighbouring cells that share an edge or a corner. The diagonal part is easy to forget because those cells belong to different rows and columns. A placement may pass the row and column checks and still fail because it touches a cat diagonally.
For a cat at row B, column B, the cells immediately around it are excluded by contact. Its entire row, entire column and entire coloured region are also unavailable for other cats. Those larger exclusions come from separate rules and can extend far beyond its immediate neighbours.
| Rule | What a confirmed cat rules out |
|---|---|
| One per row | Every other cell in its row |
| One per column | Every other cell in its column |
| One per region | Every other cell of its colour region |
| No touching | Adjacent cells, including diagonal ones |
Mark exclusions before placing
A single tap marks an X. A double-tap places a cat. Dragging can mark several Xs. Use an X for a cell you have proved impossible, not for a cell that simply looks inconvenient. A wrong placement costs a life, and an attempt begins with three lives.
This gives the two actions different jobs. Marking records a deduction that a cell cannot contain a cat. Placing records a deduction that a cell must contain one. Neither action needs to be a speculative test of the hidden answer.
A worked local example
Suppose a region has only two unmarked cells, both in row B. Its cat must be in row B, although you do not yet know which of those two cells contains it. Therefore every cell in row B outside that region can be crossed out.
Now suppose a different column is reduced to a single available cell after those exclusions. That cell must contain the column's cat. Place it, then cross out its row, column, region and touching neighbours. This shows how the rules cooperate: a regional restriction can create a column placement elsewhere.
The example assumes that all other cells in the region were excluded for sound reasons. Do not invent a forced placement by forgetting an unmarked corner of an irregular region.
Check completion by counting obligations
A finished board has one cat for each row, one for each column and one for each colour region, with no contact between cats. A board can satisfy some of those conditions while violating another. Do not stop after filling every row if a colour region is empty or duplicated.
When learning, review a placement in the same order each time: row, column, region, touching neighbours. A consistent order helps prevent the diagonal rule from disappearing from your attention once the row and column requirements become familiar.
Use explanations to build a method
If you ask for a hint, read which cells are excluded and why. Then identify the rule that makes the step valid. Repeating the reasoning on the board is more useful than immediately accepting a location and moving on. On the next puzzle, look for the same kind of restriction rather than the same shape of artwork.
Where to play
哈基米数独 (Hachimi) is the HarmonyOS cat-and-colour-region puzzle. Daily challenges open after level 20. Its hints explain logical exclusions or placements, making them useful when learning how the rules combine.