X-Sudoku (Diagonal Sudoku): Rules & How to Solve

The diagonal sudoku rule explained: both main diagonals must also hold 1–9. How X-sudoku differs from classic sudoku, plus the techniques that crack it.

The rule

Does normal sudoku work diagonally?

No — and this is the single most common misunderstanding about sudoku. In classic sudoku the diagonals mean nothing: a digit may repeat along a diagonal, and a correct solution will very often do so. The only regions that must hold 1–9 are the nine rows, nine columns and nine boxes.

Diagonal sudoku — also called X-sudoku — is a variant that bolts one extra rule on top: the two main diagonals each become a tenth and eleventh region that must also hold 1–9 exactly once. If a grid does not say it is a diagonal or X-sudoku, assume the diagonals are unconstrained.

Only the two main (corner-to-corner) diagonals are constrained. Shorter, broken diagonals elsewhere in the grid carry no rule.

How to solve diagonal sudoku

Treat each diagonal as an extra region

The two diagonals behave exactly like rows and columns: nine cells, digits 1–9, no repeats. Every scanning technique you already use — hidden singles, naked pairs, pointing candidates — works on a diagonal unchanged. The habit to build is simply remembering to look: most X-sudoku mistakes are ordinary deductions that were never attempted because the solver only scanned rows, columns and boxes.

The centre cell does double duty

Both diagonals cross at r5c5, so that one cell belongs to a row, a column, a box and two diagonals — five regions at once, more than any other cell in the grid. Whatever you place there eliminates a candidate from sixteen other diagonal cells immediately, which is why solving the centre early tends to cascade.

Only five boxes touch a diagonal

Each diagonal passes through exactly three boxes, three cells at a time: the two corner boxes and the centre. Taken together the diagonals touch only boxes 1, 3, 5, 7 and 9 — the four edge boxes contain no diagonal cells at all. That asymmetry is useful in both directions: deductions propagate fastest through the corner and centre boxes, and when you are stuck there, the edge boxes are pure classic sudoku.

The centre box is half diagonal

Five of the centre box's nine cells sit on a diagonal — the three on each diagonal, sharing r5c5. Only r4c5, r5c4, r5c6 and r6c5 are free of diagonal constraints. When the centre box is heavily clued, those four cells are usually where the remaining freedom lives.

Apply the 45 rule to a diagonal

A diagonal holds 1–9, so it sums to 45. If you know eight of its nine cells, the ninth is forced by subtraction — and more usefully, if a diagonal's three cells inside one box are known to total T, the remaining six cells must total 45 − T. This pairs well with killer-style arithmetic when a puzzle combines both constraints.

Frequently asked questions

What is X-sudoku?

A sudoku where the two main diagonals must also each contain 1–9, named for the X the diagonals form.

Is diagonal sudoku harder than classic?

Slightly — the extra constraints usually make it faster once you remember to scan the diagonals.

Do both diagonals have the rule?

Yes, both the top-left-to-bottom-right and top-right-to-bottom-left diagonals.

Does normal sudoku work diagonally?

No. In classic sudoku only rows, columns and 3×3 boxes must contain 1–9; digits are free to repeat along a diagonal. The diagonal rule applies only in diagonal sudoku (X-sudoku), and only to the two main corner-to-corner diagonals.

What is the diagonal sudoku rule?

Normal sudoku rules apply, and in addition each of the two main diagonals must contain the digits 1–9 exactly once, with no repeats.

Which boxes do the diagonals pass through?

Only the four corner boxes and the centre box. Each diagonal crosses three boxes, three cells at a time; the four edge boxes contain no diagonal cells.

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