X-Sudoku: A Friendly Walkthrough
X-sudoku adds two diagonal constraints to classic. The grid solves faster from the centre out, with the same techniques.
X-sudoku, also called diagonal sudoku, adds one small rule to the classic puzzle and changes the feel of every solve. In addition to the rows, columns and boxes, the two main diagonals of the grid also have to contain the digits 1 to 9 exactly once. Two extra constraints, eighteen new cells worth caring about, and a board that solves itself a little faster from the centre out.
The new rule sounds tiny. It changes the puzzle more than you might guess.
What the diagonals do to your scan
The two diagonals intersect at the centre cell, so the centre is constrained by three units in the classic puzzle and five units in X-sudoku: its row, its column, its box, and both diagonals. That extra constraint usually places the centre cell early.
Cells on a diagonal generally have four constraining units instead of three. They give up placements faster. Cells off both diagonals have the usual three constraints; they behave like regular sudoku.
The diagonal scan
Treat each diagonal like an extra row. Walk through digits 1 to 9. For each digit, ask where it can go on each diagonal. The diagonal has only nine cells; the constraints are tight; hidden singles appear quickly.
After the diagonal scan, fold the new placements into the rest of your scanning. The diagonals usually contribute three or four placements per puzzle that classic scanning would not have found until much later.
The pencil-mark trade
X-sudoku has more constraints per cell, on average, so the pencil-mark candidate sets are smaller. You can usually get through an X-sudoku of equivalent rated difficulty with fewer marks than the classic version of the same puzzle. That makes X-sudoku friendlier for solvers who prefer to play without marks at all.
Where the difficulty hides
Some X-sudoku puzzles are easier than their classic equivalent because the diagonals leak placements. Others are harder because the constructor uses the diagonals to engineer specific contradictions that classic sudoku does not allow. A "medium" X-sudoku from a careful constructor can feel like a hard classic. Read the difficulty label sceptically the first few times you play.
The naked-pair behaviour
Naked pairs and triples work the same on diagonals as they do on rows. A pair on the main diagonal eliminates the two digits from the rest of the main diagonal, not from the rest of any row or column. Treat each diagonal as a unit in its own right when applying any technique.
Pointing pairs and box-line reduction also work, with the diagonals taking the role of rows or columns. The mechanics are unchanged; only the unit changes.
Why try it
If classic sudoku is starting to feel like muscle memory, X-sudoku is a small refresher that does not require learning a whole new rulebook. The diagonals re-introduce a bit of friction without changing what makes the puzzle a puzzle. Most solvers who switch to X-sudoku for a week come back to classic with sharper eyes for the standard units.
The variants catalogue includes X-sudoku and several other small-twist puzzles. Browse them at the variants page, or try the diagonal sudoku variant for a board that is X-sudoku by another name.
Keep reading
- Naked Triples: A Deep DiveNaked triples extend naked pairs to three cells. The pattern hides in plain sight because the three cells do not need matching candidate sets.
- Flow State and SudokuSudoku ticks every box that flow-state research lists for absorbed attention. What that means, and what it does not mean.
- Samurai Sudoku: A Friendly WalkthroughFive overlapping 9x9 grids in a single shape. Samurai is easier than its size suggests, once you know the rhythm.