Y-Wing in Sudoku

Specialist S2 Wings

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.

How to spot it

  • Look for cells with exactly two candidates. All three cells in the pattern need two.
  • Pick one as the pivot and check the other two-candidate cells it sees - same row, column or box.
  • Each wing should share exactly one candidate with the pivot, and the two wings should share different candidates with it.
  • The leftover candidate must be the same in both wings. Between them the three cells use exactly three distinct digits.
  • Note that the pivot itself does not hold that leftover candidate. This is what separates a Y-Wing from an XYZ-Wing.

Why it works

The pivot has two candidates and one of them must be correct, which leaves only two cases to check.

If the pivot takes the candidate it shares with the first wing, the second wing must give up its shared candidate and is left with the third one. If the pivot takes the other candidate, the same thing happens to the first wing.

Either way the third candidate ends up in one of the two wings. We do not know which, but we know it is there - so no cell that sees both wings can hold that digit.

A real example from Sudokuno

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

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

Click away the candidates the technique removes - 2 of them - then press Check. Nothing is saved, and your own game is untouched.

Sudoku: SNC-00437 — Sudokuno

  • Houses: row 9, column 3 and box 7
  • Pivot: R9C3
  • Wings: R7C1 and R9C9
  • Its three candidates: 1 and 6
  • Removes 8 from R9C1 and R9C2
  • Step 33 of 54 in the solve

Key: pivot wing 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 Find the pivot and the two wing cells. Nothing is highlighted yet.
  2. Hint 2 Notice how each wing shares one candidate with the pivot. The three cells and the houses connecting them are now marked.
  3. Hint 3 Whichever candidate the pivot takes, the third candidate is forced into one of the wings - so it can be removed from the highlighted cells that see both.

The targets are always cells that see both wings. The pivot is not part of that test, because it does not contain the eliminated digit at all.

Ready to try it yourself?

You will get a real Sudokuno puzzle at Specialist level S2, where Y-Wing is needed to finish it.

Practise Y-Wing

What Sudokuno covers

Sudokuno finds the standard Y-Wing, also called XY-Wing, where all three cells have exactly two candidates. Longer chains of the same kind are not implemented.

Where to go next

  • XYZ-Wing An XYZ-Wing is a Y-Wing whose pivot has three candidates instead of two. The two wings have two candidates each, both drawn from the pivot's three, and they share exactly one candidate with each other. That shared candidate must occupy one of the three cells - the pivot included - so it can be removed from any cell seeing all three.
  • X-Wing 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.

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