Techniques › XY-Wing
XY-Wing
A pivot and two pincers. Whichever way the pivot falls, one pincer takes the digit.
Three cells, each with exactly two candidates. A pivot holding {X,Y}, and two pincers it can see, holding {X,Z} and {Y,Z}.
The pivot is either X or Y. If it is X, the first pincer must be Z. If it is Y, the second pincer must be Z. Either way one of the pincers is Z — so any cell that can see both of them cannot be Z.
The XY-Wing is the most common technique at its level by a wide margin, and the first that uses a genuine either-or argument rather than a counting one. Learning to trust that argument is the main hurdle.
A worked example
Taken from a real puzzle in our bank, at the point where this was the cheapest move available. Pattern candidates are marked in amber; anything the step eliminates is struck through in red.
| 9 | 2 | 4 | 18 | 7 | 6 | 3 | 5 | 18 |
| 8 | 1 | 7 | 3 | 5 | 9 | 6 | 2 | 4 |
| 3 | 6 | 5 | 4 | 2 | 18 | 78 | 17 | 9 |
| 2 | 5 | 1 | 6 | 8 | 3 | 4 | 9 | 7 |
| 7 | 4 | 3 | 9 | 1 | 2 | 5 | 8 | 6 |
| 6 | 8 | 9 | 7 | 4 | 5 | 1 | 3 | 2 |
| 5 | 9 | 2 | 18 | 6 | 178 | 78 | 4 | 3 |
| 1 | 7 | 8 | 2 | 3 | 4 | 9 | 6 | 5 |
| 4 | 3 | 6 | 5 | 9 | 78 | 2 | 17 | 18 |
- NudgeThree cells pincer digit 7: whichever way the pivot falls, one pincer takes it.
- WhereXY-Wing: r3c6, r3c8, r9c6
- Do itRemove r9c8 ≠ 7
How to spot it
Find bivalue cells — usually few enough to list. For each, check the bivalue cells it can see for the {X,Z} / {Y,Z} shape. Then look at what those two pincers jointly see.
Where you will meet it
XY-Wing sits at tier 3 of our ladder, which means it first becomes necessary at Hard. Puzzles below that band never require it, though it may still appear as a shortcut.