Naked Pair

Summary

Naked Pair is the third technique to reach for once Row/Column Lock can no longer make progress. The key insight is about the union of two regions' candidate sets: if the union of all candidate rows from region A and region B together spans exactly two rows, then those two regions together monopolize those two rows. Because Nyangjari places exactly one cat per row, no other region can place a cat in either of those rows. Every empty cell in those two rows belonging to a third region can therefore be marked X. The term "Naked" reflects the fact that the two regions have no other possibility — they are fully constrained to those two rows.

Importantly, each individual region need not span both rows. Region A might have candidates only in row 1, and region B might have candidates only in row 3. The union {row 1, row 3} still equals exactly two rows, so the pair is valid. After eliminations, Basic Elimination often triggers a cascade of new cat confirmations.

When to use

• Apply Naked Pair only after Basic Elimination and Row/Column Lock have both run to completion with no further progress.
• A pair qualifies when the union of candidate rows (or candidate columns) from exactly two regions equals exactly two rows (or two columns).
• After marking new X cells, always re-run Basic Elimination before searching for another pair — a single Naked Pair can cascade into several cat placements.
• Check both axes: a board may have no row-based pairs but still have a column-based pair, or vice versa.
• The technique is symmetric: row-based and column-based Naked Pairs follow the same logic, just applied across the other axis.

Why it works

Nyangjari's rules state that each row contains exactly one cat. Suppose region A has candidates only at row 1, and region B has candidates only in rows 1 and 3. The union of their row sets is {row 1, row 3} — exactly two rows. Between them, regions A and B must each place one cat, and both cats must land in rows 1 or 3. Since each row can hold only one cat, rows 1 and 3 are fully claimed by A and B together. Any other region's candidate cell in row 1 or row 3 is therefore impossible and receives an X mark.

The critical requirement is that the union spans exactly two rows — neither more nor fewer. If the union is one row, the situation reduces to Row/Column Lock (a single region locked to one row). If the union is three or more rows, the pair constraint does not hold, and you would need Naked Triple or a stronger technique.

The same reasoning applies column-wise: if the union of candidate columns from two regions equals exactly two columns, those two regions monopolize those columns, and every other region's cells in those columns receive X marks.

Example

▲ Region a's only candidate sits on row 1. Region d's candidates sit on row 3. Union {row 1, row 3} = exactly 2 rows → Naked Pair. All other regions' (b, c) empty cells in rows 1 and 3 are marked ×.

1. Starting state: After Basic Elimination and Row/Column Lock, region a has candidates only on row 1 and region d has candidates only on row 3. All other regions still have candidates on multiple rows.
2. Union check: {row 1} ∪ {row 3} = {row 1, row 3} — exactly 2 rows. Naked Pair confirmed.
3. Eliminate other regions from rows 1 and 3: Every empty cell in rows 1 and 3 belonging to regions b or c is marked ×. The highlighted candidates in regions a and d are left unchanged.
4. Re-apply Basic Elimination: With new X marks in place, check whether any region, row, or column has been reduced to a single candidate. Confirm any such cat placements and propagate further eliminations.
5. Continue scanning: Search for additional Naked Pairs (row-based and column-based) in the updated board before moving to Naked Triple.

Watch out for

• Union must equal exactly two — no more: If the union of candidate rows from two regions spans three or more rows, Naked Pair does not apply. Three rows calls for Naked Triple.
• Individual regions need not span both rows: Region A covering only row 1 and region B covering only row 3 still form a valid pair — the union {row 1, row 3} = 2 rows is all that matters. This is where Naked Pair differs from Row/Column Lock, which requires a single region locked to a single row.
• Check both axes: After scanning for row-based pairs, always scan for column-based pairs. A board may have no row-based pairs yet have a valid column-based pair.
• Elimination targets other regions only: Never mark the paired regions' own candidates as X. Those candidates are the only remaining positions for those regions' cats.
• Re-run Basic Elimination after every pair: New X marks may create single-candidate situations. Skipping Basic Elimination after a Naked Pair means missing easy confirmations.
• Technique order matters: Naked Pair is the third technique. Always exhaust Basic Elimination and Row/Column Lock first. If Naked Pair also stalls, move to Naked Triple.