Diagonal pair
A naked pair where both cells lie on the same diagonal of a Sudoku X. Eliminates the two pair digits from every other cell on that diagonal.
A diagonal pair is the Sudoku X analogue of a classic naked pair: two cells lying on the same diagonal whose candidate set is reduced to exactly two specific digits, the same two digits in both cells. Because the diagonal is a unit obeying the uniqueness rule, those two digits must occupy those two cells in some order — and they cannot appear anywhere else on the diagonal.
How it works
Suppose two cells on the same diagonal — say (3, 3) and (5, 5) — both have candidate set {4, 7} after row, column, and box reductions. The diagonal rule says each digit appears once on the diagonal. The 4 and the 7 must fill (3, 3) and (5, 5) between them. That means no other cell on that diagonal can hold 4 or 7. Eliminate 4 and 7 from the candidate lists of (1, 1), (2, 2), (4, 4), (6, 6), (7, 7), (8, 8), and (9, 9).
The deduction is identical in shape to a row-based naked pair; the only difference is the unit being scanned. The diagonal carries the same uniqueness rule as a row, so every technique that depends on row uniqueness — pairs, triples, locked candidates, X-wings whose lines include a diagonal cell — fires on the diagonal in the same way.
When it fires
Diagonal pairs become common at the medium tier and above. At easy, the diagonal is usually unconstrained enough that pairs don't form. At hard and expert, the construction often deliberately produces diagonal pairs because they're a natural way to make the diagonal pay its keep in the solve.
Hidden pairs work the same way — see hidden pair for the equivalent on a diagonal.
For the practical scan-pattern habit and the wider list of diagonal-aware moves, see when the diagonal helps.
See also
- Sudoku X— A Sudoku variant where both diagonals must also contain each digit 1-9 exactly once. Also known as Diagonal Sudoku. Classic Sudoku plus two new units.
- Diagonal constraint— The extra rule that defines Sudoku X (Diagonal Sudoku): each of the two diagonals must contain every digit 1-9 exactly once, just like a row or column.
- Forced cell on the diagonal— A Sudoku X (Diagonal Sudoku) deduction: a cell on the diagonal whose digit is forced by row, column, box, and diagonal together — no three of them suffice.
- Naked pair— Two cells in the same unit whose candidate sets are identical and contain exactly two digits. Together they claim those digits across that unit and rule them out elsewhere.
- Hidden pair— Two digits whose only possible cells inside a unit are the same two cells — even if those cells still show other candidates. The digit-first sibling of the naked pair.
Read more
- When the diagonal helps
A practical tactic for Sudoku X (Diagonal Sudoku): scan the diagonal when a row-column-box pass stalls. Worked examples of where the extra unit pays off.
- Forced diagonal cells
The signature technique of Sudoku X / Diagonal Sudoku — a cell on the X where row, column, box, and diagonal together force the digit, even when no single constraint does.