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.

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 away the candidates the technique removes - 4 of them - then press Check. Nothing is saved, and your own game is untouched.

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 next technique is X-Wing. You get the name, but no digit and no cells.
  2. Hint 2 Two lines point at the same two lines, which locks one candidate into the corners. Sudokuno highlights the lines, still without naming the digit.
  3. Hint 3 The corners lock one candidate; remove it only from the highlighted target cells. Both the pattern and the targets are now marked.

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 finds X-Wings with exactly two candidate cells in each base line, both row-based and column-based. Finned and sashimi variants are not implemented.

Where to go next

  • Swordfish A Swordfish is the same idea as an X-Wing with three lines instead of two. One candidate has only two or three possible cells in each of three rows, and together those cells touch exactly three columns. The candidate is then confined to those three columns and can be removed from every other cell in them.
  • Simple Colouring Simple Colouring looks at one digit at a time. When a row, column or box has exactly two places left for that digit, the two cells are strongly linked: exactly one of them holds it. Join such pairs together and you get a network that can be coloured alternately in two colours, and then exactly one of the colours is the true one. That is enough to remove candidates, even though you do not know which colour is which.
  • Y-Wing A Y-Wing is three cells that each have exactly two candidates. The pivot sees both wing cells. It shares one candidate with each wing, and the two wings have a third candidate in common. That third candidate has to land in one of the wings, so it can be removed from any cell that sees both of them.

All Sudoku techniques