Cat puzzle deduction patterns: singles, locks and pairs

Useful cat-puzzle deductions include a single remaining cell, a region confined to one row or column, and multiple required cats reserving the same set of lines. Apply only the exclusions guaranteed by every remaining possibility.

Start with a complete candidate map

A candidate is a cell not yet ruled out by the row, column, colour-region or non-touching rules. Patterns are valid only when the relevant candidate sets are complete. An overlooked cell in an irregular region can invalidate an otherwise convincing deduction.

For the examples below, assume that every omitted candidate has already been excluded for a sound reason. These are local reasoning examples, not complete boards. Read each pattern as a statement about all remaining options in the named units.

Single remaining position

If an unfilled row has only one candidate, that cell must contain its cat. The same applies to a column or region. Place the cat and update all related exclusions before looking for a more complicated pattern.

For instance, a region may cover many cells but lose candidates through occupied rows, occupied columns and diagonal contact. When only one cell survives those tests, its location is forced. Region size itself tells you little about how constrained it has become.

Region locked to a row or column

Suppose every remaining candidate in region A lies in row B. A's cat must occupy row B, so every cell in row B outside A is excluded. You cannot yet choose among A's candidates, but you have reserved the row for that region.

Reverse the perspective as well. If every candidate for row B lies inside region A, that row's cat also supplies A's cat. All cells of A outside row B can be excluded. In one direction the region reserves a row; in the other the row reserves a region.

Candidate restriction	Safe exclusion
Region entirely confined to one row	That row outside the region
Row entirely confined to one region	That region outside the row
Region entirely confined to one column	That column outside the region
Column entirely confined to one region	That region outside the column

Two regions reserving two columns

Suppose region A can place its cat only in columns B or D, and region C can also place its cat only in those columns. The regions each require a cat, and the cats cannot share a column. Together they therefore occupy both B and D in some order.

Exclude candidates in columns B and D that belong to any other region. Do not decide which region takes which column yet. The conclusion concerns the columns reserved by the pair, not a specific placement within either region.

The restriction must cover every candidate in both regions. If A also has a candidate in another column, the reservation is no longer established. A similar argument works with rows, provided the required cats come from distinct regions.

Shared touching-neighbour exclusions

Imagine a required cat with only two candidates: row B column B, or row B column C. A cell at row C column B touches either possible placement, vertically in one case and diagonally in the other. It cannot contain a different cat, regardless of which candidate is correct.

The safe set to exclude is the intersection of the forbidden cells produced by the alternatives. Do not exclude the union: a cell forbidden by only one alternative may remain legal under the other. This distinction makes the difference between a deduction and an unsupported guess.

Apply a pattern without overclaiming

1. Name the unit or units that still require cats.
2. List their complete remaining candidate cells.
3. State what every allowed arrangement has in common.
4. Remove only cells excluded by that common result.
5. Recheck affected units for simple placements.

A pair reservation does not imply a particular diagonal arrangement, and a locked region does not identify its exact cat. Preserve the unresolved possibilities. Their uncertainty is part of the logical state, not something you need to erase immediately.

Where to play

哈基米数独 (Hachimi) offers coloured-region cat puzzles on HarmonyOS with explanatory hints. When a hint supplies an exclusion, compare it with these patterns and identify the complete candidate restriction that makes the step valid.