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.
The diagonal constraint is the additional rule that turns a classic Sudoku into a Sudoku X. It states that each of the two diagonals — the one running from the top-left corner to the bottom-right corner, and the one running from the top-right corner to the bottom-left corner — must contain every digit from 1 to 9 exactly once.
Structurally, the diagonal constraint is a uniqueness rule on a unit, exactly like the rules on rows, columns, and 3×3 boxes. The two diagonals are simply two extra units that share the same uniqueness obligation. The two diagonals intersect at the centre cell (row 5, column 5), which therefore lies on both — that cell is the only one in the grid that belongs to two diagonals at once.
What it changes mechanically
For the 17 cells on the two diagonals, the diagonal constraint adds a fourth unit to the cell's unit list. Classic Sudoku gives each cell three units (row, column, box); cells on a diagonal in Sudoku X have four. The classic technique vocabulary — naked singles, hidden singles, naked and hidden pairs and triples, locked candidates, X-wings, Y-wings — all fire identically; the diagonals just give them more places to do so.
The deductions specific to it
Two move types only make sense in the presence of the diagonal constraint:
The first is the forced cell on the diagonal — a cell where row, column, box, and diagonal together force the digit, but no three of them would have.
The second is the diagonal pair, the same idea as a naked pair but where the unit involved is one of the diagonals.
Both moves are about the same difficulty as their classic counterparts; the only adjustment is the habit of including the diagonal in the cell's unit scan.
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 Sudoku— An alternate name for Sudoku X — the 9×9 Sudoku variant where both diagonals carry the same digit-uniqueness rule as rows, columns, and boxes.
- 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.
- 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.
- Unit— Collective name for a row, column, or 3×3 box — the three groupings Sudoku's no-repeats rule applies to. Every cell sits in exactly three: its row, column, and box.
Read more
- The rules of Sudoku X
Sudoku X — also called Diagonal Sudoku — is classic Sudoku with one extra rule: both diagonals must also contain each digit 1–9 exactly once.
- 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.