SudokuGratis Italiano

The X-Wing Technique

What it is

The X-Wing is the first pattern that spans the whole grid. Take a candidate — say, 5 — and two rows where that candidate can sit in only two cells each. If those four cells line up pairwise, occupying the same two columns, they form the corners of a rectangle. And the lock snaps shut: in each of the two rows, the 5 will land in one of its two corners, necessarily in different columns. However it plays out, both columns receive their 5 from those rows. So the 5 can be erased from every other cell of the two columns.

The name comes from the rectangle's diagonals, which trace an X. It also works transposed: two columns doing the locking, two rows getting cleaned. It's the founding member of the fish family — the patterns that pin a candidate across parallel lines.

How to spot it, step by step

  1. Pick a candidate and walk through the rows one by one.
  2. Note the rows where that candidate appears exactly twice in the pencil marks.
  3. Compare those rows in pairs: you're looking for two rows whose two positions fall in the same two columns.
  4. Verify the rectangle: four cells, two rows, two columns, one candidate.
  5. Erase the candidate from every other cell of the two columns — never from the rows forming the pattern, and never from the four corners.

The example in the diagram

5 5 5 5 5 5 5 In the two shaded rows, 5 fits only in the corner columns: the rest of those columns is swept clean.

In the two shaded rows, candidate 5 survives only in the amber cells: two positions per row, in the same two columns. The rectangle is complete. Those columns will get their 5s from the corners, so the other 5s pencilled along them — three here, crossed out — are erased.

Common mistakes

The classic one: eliminating along the rows instead of the columns. The rows with only two positions are the base of the pattern; the cleanup happens on the cover units, the columns. The second: accepting a row where the candidate has three positions. The X-Wing demands exactly two in both base rows — with three, you need a bigger pattern. The third: erasing one of the four corners. They are the engine of the lock, not its target.

Where you'll need it

The X-Wing is the signature pattern of hard sudoku — and the doorway to the tier above: the expert-level Swordfish is the same principle stretched to three rows. Before you get there, it pays to have the basic interactions down, like Pointing Pairs; the full picture is in the techniques index.