When the diagonal helps

The most useful habit you can build in Sudoku X — or Diagonal Sudoku, depending on which name you prefer — is glancing at the diagonals as a fourth unit during scanning. It's not a complicated technique. It's the realisation that there are two more rows on the board that you haven't been checking.

The pattern most beginners miss

A solver new to Sudoku X usually plays the first few puzzles exactly like classic. They scan row 1, column 4, box 7. They place digits the same way. Some easy puzzles solve cleanly that way; some don't. The ones that don't stall in the same place a classic puzzle would have stalled — the digit could go in either of two cells, no row-column-box logic separates them — and the solver looks for a more complex technique to break it.

But often the puzzle isn't stuck. The diagonal is just another unit. If one of the two candidate cells sits on a diagonal and that diagonal already contains the digit in question, the cell is eliminated and the digit lands.

The fix is almost embarrassingly simple: when you find yourself reaching for a technique heavier than scanning, glance at the X first. The diagonals are marked on the board with a dotted ring for exactly this reason.

A worked example

Suppose you're working on a medium Sudoku X. You're trying to place 7 in box 5 (the centre box). Scanning the rows and columns of box 5, you see 7 could go in either (5, 4) or (5, 6). Neither row nor column rules either out.

Both of those cells sit on neither diagonal, so the diagonal rule doesn't help here. But — and this is the useful generalisation — the diagonal might still be carrying a 7 somewhere on the X, and that placement might constrain a different cell in box 5 via the row or column, and that constraint might break the symmetry between (5, 4) and (5, 6).

In practice, you don't have to do the chained reasoning consciously. You just keep the diagonals in your mental list of units to scan, and the deductions surface when they're there. The diagonal is most useful not as a direct constraint on the cell you're working on, but as an indirect constraint on cells that affect the cell you're working on.

Where the diagonal is most directly useful

Three patterns recur often enough to be worth naming:

The first is when a digit is already placed at one or two cells on a diagonal, and you're trying to place the same digit elsewhere on the board. The diagonal eliminations cascade through any cell that intersects the diagonal at a row, column, or box level.

The second is when the diagonal contains a diagonal pair — two cells on the diagonal where two specific digits are the only candidates. Like a regular naked pair, this eliminates those two digits from every other cell on the diagonal.

The third is the forced cell on the diagonal: a cell where the row, column, box, and diagonal constraints together leave exactly one candidate, even though no single constraint would have managed it alone. This is the deduction that most directly justifies the variant's existence.

A habit to build

Spend the first three or four Sudoku X puzzles deliberately glancing at the diagonals before reaching for any technique heavier than scanning. By puzzle five, the scan is automatic, and the diagonals stop being a thing you remember to check and start being a thing your eye looks at on the way to the next placement. That's the moment the variant clicks.

If you'd like a refresher on the basic constraint, the rules of Sudoku X lay out the four-unit picture in a few sentences. Or jump straight in at the easy tier — the diagonal-scan habit forms faster on real puzzles than on diagrams.