Diagonal Sudoku
Diagonal Sudoku adds one elegant constraint on top of classic Sudoku: both main diagonals (top-left→bottom-right and top-right→bottom-left) must each contain the digits 1–9 exactly once.
What is Diagonal Sudoku?
Diagonal Sudoku (also called Sudoku X or X Sudoku) is standard 9×9 Sudoku with one additional rule: both main diagonals are treated as extra regions. Every digit from 1–9 must appear exactly once along each diagonal.
The two constrained diagonals are highlighted in blue on the board. They create powerful cross-grid constraints that often allow you to solve more cells than classic Sudoku logic alone would permit.
Standard vs Diagonal Sudoku
| Classic Sudoku | Diagonal Sudoku | |
|---|---|---|
| Rows | 1–9 each | 1–9 each |
| Columns | 1–9 each | 1–9 each |
| 3×3 Boxes | 1–9 each | 1–9 each |
| Main diagonal (↘) | No constraint | Must contain 1–9 |
| Anti-diagonal (↙) | No constraint | Must contain 1–9 |
| Given digits needed | More | Fewer (diagonals do extra work) |
Solving tips
- The center cell (row 5, col 5) sits on both diagonals - It's the most constrained cell on the board.
- The four corner cells and the center are on a diagonal. Use diagonal candidates early.
- When you place a digit on a diagonal, eliminate it from all other diagonal cells - Just like a row or column.
- Diagonal constraints often break symmetry, resolving ambiguous positions that classic Sudoku leaves open.
- Treat each diagonal exactly like an extra row or column when scanning for singles and pairs.
Key fact: Both diagonals sum to 45 - The same as any row, column, or box. This means you can apply all the same arithmetic shortcuts used in Killer Sudoku to diagonal regions.