The rules of Sudoku X

Sudoku X is classic Sudoku with one extra rule. The same 9×9 grid, the same digits 1 through 9, the same row-column-and-box constraints — and then, on top of all of that, both diagonals must also contain each digit exactly once. The two diagonals trace an X across the board, which is where the name comes from. It also goes by Diagonal Sudoku, which is the more descriptive label and the one you'll see more often outside English-language puzzle communities.

The constraint set

If you already know how to play classic Sudoku, you already know most of Sudoku X. The full rule set is four lines instead of three.

1. Every row contains the digits 1 through 9, each exactly once.
2. Every column contains the digits 1 through 9, each exactly once.
3. Every 3×3 box contains the digits 1 through 9, each exactly once.
4. Each diagonal — top-left to bottom-right, and top-right to bottom-left — contains the digits 1 through 9, each exactly once.

That's the whole puzzle. Rules one through three are inherited verbatim from classic Sudoku. Rule four is the addition that makes a Diagonal Sudoku what it is.

The geometry of the X

The two diagonals cross at the centre cell of the board, the one at row 5, column 5. That cell is the only one that belongs to both diagonals, which gives it a slightly tighter constraint than the other diagonal cells — it has to satisfy two diagonal-uniqueness rules in addition to the row, column, and box.

Each diagonal contains nine cells, one from each row and column. One diagonal runs through (1, 1), (2, 2), (3, 3), and so on down to (9, 9). The other runs through (1, 9), (2, 8), (3, 7), and so on down to (9, 1). The two diagonals share only the centre cell, so the total number of cells participating in the extra constraint is seventeen — nine plus nine minus the shared centre.

On Sudoku Mountain's board, the diagonal cells are marked with a soft dotted ring so you can see them at a glance. You don't have to do the geometry in your head; the visual cue handles it.

What changes mechanically

In classic Sudoku, every cell belongs to three units: a row, a column, and a 3×3 box. In Sudoku X, the seventeen cells on the diagonals belong to four units instead. That's it. There's no new technique vocabulary to learn — every constraint-propagation move you already know (scanning, naked singles, hidden singles, pencil marks, pairs, locked candidates) works the same way; the diagonal just gives those moves more places to fire.

The other 64 cells — the ones not on the X — play exactly as they would in a classic Sudoku. Their constraints are unchanged. This is what makes Sudoku X feel like a small, friendly extension rather than a different puzzle entirely.

Where the rule pays off

The diagonals are most useful when row, column, and box scanning has run out. If you've scanned every unit for a digit and the placement still isn't forced, glance at the diagonals — there's a reasonable chance the digit appears on one of them and narrows the candidate set further. This pattern is common enough that it has its own name: a forced cell on the diagonal, where the row, column, box, and diagonal constraints together leave exactly one candidate even though no single one of them would have done it alone.

If you'd like to see it in practice, our easy Sudoku X puzzles are the right starting point. The rules click after one puzzle; the tactics take two or three more.