Y-Wing in Sudoku

Specialist S2 Wings

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.

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

  • 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

For example, let the pivot have candidates 1/2 and the wings 1/3 and 2/3. The pivot sees both wings, meaning it shares a row, column or box with each.

If the pivot is 1, the 1/3 wing must be 3. If the pivot is 2, the 2/3 wing must be 3. Either way, at least one wing is 3.

Any other cell that sees both wings cannot be 3. The pivot does not contain 3, so the target does not need to see the pivot.

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 a candidate to cross it out; click it again to restore it. Remove the 2 candidates ruled out by this technique, then press Check. This exercise leaves your game unchanged.

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 Look for a two-candidate pivot and two two-candidate wings. Nothing is highlighted yet.
  2. Hint 2 The pivot and wings are marked. Each wing shares a different digit with the pivot; the wings share one other digit.
  3. Hint 3 The target cells are marked. They see both wings, so they lose the wings' shared candidate.

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 covers standard Y-Wing, also called XY-Wing: a two-candidate pivot, two two-candidate wings and eliminations from cells seeing both wings.

Where to go next

  • XYZ-Wing An XYZ-Wing has a pivot with three candidates and two wings with two each. The pivot sees both wings, whose pairs come from its three candidates. The digit shared by the wings must fill one of the three cells, so any other cell seeing all three loses it.
  • 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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