Y-wing (XY-wing)
Three bivalue cells where the pivot shares one candidate with each wing — eliminating the third candidate from any cell that sees both wings.
The Y-wing — also called the XY-wing — is a three-cell deduction built from bivalue cells. A bivalue cell is a cell with exactly two candidates. The pattern needs one pivot cell and two wing cells, each with exactly two candidates, arranged so that the pivot shares one candidate with each wing and the two wings share the third candidate between them.
The shape
Three cells, each with exactly two candidates, in this configuration:
- Pivot: candidates {A, B}
- Wing 1: candidates {A, C}, in a unit shared with the pivot
- Wing 2: candidates {B, C}, in a different unit shared with the pivot
The pivot will end up as either A or B — we don't know which. If the pivot is A, wing 1 must be C. If the pivot is B, wing 2 must be C. Either way, one of the two wings ends up as C. So any cell that "sees" both wings — that is, shares a unit with both wing 1 and wing 2 — cannot be C.
Worked example: pivot at (5, 5) with candidates {2, 7}. Wing 1 at (5, 1) with candidates {2, 9} (shares row 5 with the pivot). Wing 2 at (8, 5) with candidates {7, 9} (shares column 5 with the pivot). The shared candidate between the wings is 9. Any cell that sees both (5, 1) and (8, 5) — for instance (8, 1) — cannot be a 9.
Why "Y-wing" or "XY-wing"
The shape resembles a Y when you draw the pivot with its two wings extending out. The XY-wing name comes from labelling the pivot as XY, the wings as XZ and YZ — the alphabet versions of A, B, and C. The two names are interchangeable.
When you'll see it
Y-wings appear on hard and expert puzzles after the X-wing layer has been exhausted. They're more pattern-recognition-heavy than the X-wing because the three cells are non-rectangular and the candidate sets have to align across three different units. Once you can scan for bivalue cells and check for the {A, B} / {A, C} / {B, C} pattern, the technique becomes recognisable; until then it's nearly invisible.
For a survey of which technique to reach for in different stuck states, see Which technique is this puzzle asking for. The natural next-step extension — same logic, three candidates per cell — is the XYZ-wing.
See also
- X-wing— When a digit's only two cells across two rows form a rectangle in two columns — eliminating that digit from the rest of those columns. Or the same shape rotated 90°.
- XYZ-wing— A three-cell wing pattern where the pivot has three candidates and each wing has two — eliminating the shared candidate from any cell that sees all three.
- Candidate— A digit (1–9) a cell could still legally hold — one not yet ruled out by anything in its row, column, or 3×3 box. Every empty cell has between one and nine.
Read more
- Which technique is this puzzle asking for
How to read a fresh hard Sudoku and predict which intermediate technique will break it open before you've placed a single digit.