XY-Wing
Three bi-value cells forming a hinge and two wings. Cells seeing both wings cannot hold the shared digit.
What it is
An XY-Wing uses three cells with exactly two candidates each. The hinge holds {X,Y}, one wing {X,Z} and the other {Y,Z}, and the hinge sees both wings. Whatever the hinge turns out to be, one of the wings is forced to Z. So any cell that sees both wings can never hold Z. Unlike fish patterns, this technique works across three different digits.
How to spot it
Look for cells with exactly two candidates. For each, check the cells it sees for two more bi-value cells that share one digit with it and one digit with each other. The shared digit of the two wings is the one you eliminate, in cells seeing both wings.
Worked example
Step through the reasoning below. Each step adds one layer: first the position, then the pattern, then the candidates involved, and finally what can be eliminated.
Step 1 of 4: The starting position
- Pattern cells
- 6/7, 9/7, 7/7
- Digits
- 2, 8, 7
- Eliminations
- 4/7, 7/9, 9/9
Press a marked square to point it out on the board above.
Why it matters
The XY-Wing is the first technique that reasons across several digits at once, and it is where many solvers make the jump from pattern-spotting to genuine logic. It appears regularly on hard puzzles.
Practise now
Solve a puzzle where this technique decides the game
Frequently asked questions
What does bi-value mean?
A cell with exactly two candidates. All three cells of an XY-Wing must be bi-value — that is what makes the forcing argument work.
Which digit gets eliminated?
The digit shared by the two wings but absent from the hinge. In a {X,Y} hinge with {X,Z} and {Y,Z} wings, that digit is Z.
Does the hinge have to see both wings?
Yes, that is essential. The hinge must share a row, column or box with each wing separately; the two wings need not see each other.
Put it to use
Where you will meet it
Hard grids are built around moves like this one. That is where it earns its keep.
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