X-Wing in Sudoku

Specialist S1 Fish

An X-Wing appears when one candidate has exactly two possible cells in each of two different rows, and both pairs sit in the same two columns. The four cells form a rectangle. The candidate must then occupy two opposite corners, one per row, so it can be removed from every other cell in those two columns.

A candidate is a digit that can still go in an empty cell. Cells see each other when they share a row, column or 3×3 box. A strong link means a digit has exactly two possible cells in one such group: exactly one must contain it.

How to spot it

  • Work on one candidate at a time. An X-Wing is always about a single digit.
  • Find rows where that candidate has exactly two possible cells. Sudokuno requires exactly two - if the row has three, it is not an X-Wing.
  • Look for two such rows whose pairs land in precisely the same two columns.
  • The four cells form a rectangle. Those corners are the pattern; the eliminations happen elsewhere in the two columns.
  • The mirror image works just as well: two columns with exactly two spots each, pointing at the same two rows.

Why it works

Each row must contain the candidate exactly once. In the two base rows it survives in only two cells apiece, and both pairs lie in the same two columns.

That leaves only two ways to fill the rectangle: one diagonal or the other. Either way, both columns are used exactly once.

So whichever arrangement is correct, the candidate is already accounted for in both columns. It cannot appear anywhere else in them, which is what you eliminate.

A real example from Sudokuno

The board below is a real Sudokuno puzzle, shown exactly as it stands just before X-Wing applies. Everything up to this point was solved with ordinary techniques.

 5
6 8 1
9 4
1
7
6 5
6
9 5
5
6 7 3 2 4 1
7 1 3 8 4 9 2 6 5
4
1 5 6
7
1
9 2
5
6
6 5
1
9 2
8 2 9 5 6
4

Click a candidate to cross it out; click it again to restore it. Remove the 4 candidates ruled out by this technique, then press Check. This exercise leaves your game unchanged.

Sudoku: SNC-00591 — Sudokuno

  • Candidate 8
  • Houses: row 2, row 4, column 2 and column 9
  • Pattern: R2C2, R2C9, R4C2 and R4C9
  • Removes 8 from R3C2, R3C9, R6C9 and R8C9
  • Step 25 of 56 in the solve

Key: pattern cells target cells

How the hint helps you

Sudokuno's hint reveals the structure in three steps, without giving away the digit straight away.

  1. Hint 1 The hint names X-Wing. No cells or digit are revealed yet.
  2. Hint 2 The two rows and two columns are highlighted. Find the digit whose two places in each row align in the same columns, or the reverse for a column-based pattern.
  3. Hint 3 The four corners and target cells are marked. The targets lose the digit held within the corners.

The hint never names the digit itself. You get the structure and make the elimination yourself. Press once more and Sudokuno performs the step for you - but the round then stops counting towards the leaderboards.

Ready to try it yourself?

You will get a real Sudokuno puzzle at Specialist level S1, where X-Wing is needed to finish it.

Practise X-Wing

What Sudokuno covers

Sudokuno covers plain X-Wing in both orientations: exactly two possible cells per selected row or column, aligned with the same two columns or rows.

Where to go next

  • Swordfish Work on one digit. Find three rows with two or three possible cells each for it, all within the same three columns. Those columns must contain the digit in the selected rows, so remove it from their other cells. The same pattern works with rows and columns reversed.
  • Simple Colouring Simple Colouring follows one digit through a network of strong links. Colour linked cells alternately: either every cell of colour A holds the digit and none of B does, or the reverse. Those two possibilities can rule out candidates.
  • Y-Wing A Y-Wing uses three cells with two candidates each. One cell, the pivot, sees both wings. Whichever digit fills the pivot, one wing must hold the digit shared by the wings, so any cell seeing both wings loses that candidate.

All Sudoku techniques