XY-Wing
A pivot, two pincers, and one forced elimination — the smallest chain in sudoku.
The pattern
Find a cell with exactly two candidates — call them X and Y. That's the pivot. Now find two more bivalue cells the pivot can see: one holding X and Z, one holding Y and Z. Those are the pincers. The three cells form a hinge, and the hinge squeezes Z out of every cell that sees both pincers.
A pivot with candidates 1 and 2 sees a {1,3} pincer in its row and a {2,3} pincer in its column. Either pivot value forces a pincer to 3, so a cell seeing both pincers loses its 3.
Why it works
Run the pivot's two cases. If the pivot is X, the X-Z pincer loses its X and becomes Z. If the pivot is Y, the Y-Z pincer becomes Z. There is no third case — the pivot has only those two candidates. So some pincer ends up as Z in every possible world, and a cell that sees both pincers would collide with that Z no matter which world you're in. It can never hold Z.
How to spot one
- Inventory the bivalue cells. XY-Wings live entirely in cells with two candidates — after your pairs and pointing eliminations, list them.
- Pick a pivot and read its letters. For a {1,2} cell, you're hunting peers of the form {1,z} and {2,z} with the same z.
- Check the pincers share z. {1,3} and {2,3} work; {1,3} and {2,4} don't.
- Hunt victims by the pincers, not the pivot. The cells that lose z are the ones seeing both pincers — scan the intersections of their units.
A puzzle that needs exactly one
Generated and verified by our grader: this puzzle solves with 35 naked singles and 20 hidden singles — plus exactly one XY-Wing, the single advanced move the whole solve turns on. That one move earns it the Diabolical grade.
| 8 | 4 | 5 | 1 | |||||
| 3 | 9 | |||||||
| 1 | 9 | 4 | ||||||
| 1 | 6 | 2 | ||||||
| 6 | 8 | 5 | 1 | 9 | ||||
| 7 | 9 | 6 | ||||||
| 3 | 6 | 4 | ||||||
| 7 | ||||||||
| 1 | 9 |
Copy it into the difficulty grader to see the certificate yourself, or take the scan list above hunting on a fresh board.
Common questions
What is the XY-Wing technique in sudoku?
An XY-Wing is a three-cell pattern: a pivot holding exactly two candidates, X and Y, and two pincers the pivot sees — one holding X and Z, the other Y and Z. Whichever value the pivot takes, one of the pincers is forced to be Z. So any cell that sees both pincers can never be Z, and Z is removed from it.
How hard is XY-Wing?
On Stillgrid's technique ladder the XY-Wing sits in the Diabolical tier — above X-Wing, below full chains. Puzzles that require one are uncommon among generated grids; the sample on this page provably needs exactly one XY-Wing and nothing harder.
Does the eliminated cell need to see the pivot?
No — that's the classic mistake. The elimination applies to any cell that sees both pincers; whether it sees the pivot is irrelevant. In practice victims often sit near the pivot, but the rule to check is only: does this cell share a unit with each pincer?