Techniques › XYZ-Wing
XYZ-Wing
An XY-Wing whose pivot holds all three digits, so targets must see all three cells.
A pivot with three candidates {X,Y,Z}, and two bivalue pincers {X,Z} and {Y,Z} that it can see.
Now the Z could be in any of the three cells rather than just the two pincers — so the conclusion is weaker. A cell can only be cleared of Z if it sees all three, pivot included. In practice that usually means the whole pattern sits in one box.
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.
| 5 | 3 | 4 | 79 | 27 | 29 | 8 | 1 | 6 |
| 7 | 2 | 8 | 6 | 3 | 1 | 5 | 9 | 4 |
| 6 | 1 | 9 | 8 | 5 | 4 | 7 | 2 | 3 |
| 8 | 6 | 7 | 1 | 4 | 5 | 2 | 3 | 9 |
| 3 | 5 | 1 | 2 | 9 | 7 | 4 | 6 | 8 |
| 4 | 9 | 2 | 3 | 8 | 6 | 1 | 5 | 7 |
| 2 | 7 | 6 | 49 | 1 | 89 | 3 | 48 | 5 |
| 1 | 4 | 35 | 57 | 6 | 38 | 9 | 78 | 2 |
| 9 | 8 | 35 | 457 | 27 | 23 | 6 | 47 | 1 |
- NudgeThree cells pincer digit 7: whichever way the pivot falls, one pincer takes it.
- WhereXYZ-Wing: r9c4, r8c4, r9c8
- Do itRemove r9c5 ≠ 7
How to spot it
Look for a trivalue cell with two bivalue neighbours whose candidates are both subsets of it, overlapping in exactly one digit. Then find cells seeing all three.
Where you will meet it
XYZ-Wing sits at tier 4 of our ladder, which means it first becomes necessary at Expert. Puzzles below that band never require it, though it may still appear as a shortcut.
Read next
- XY-Wing A pivot and two pincers. Whichever way the pivot falls, one pincer takes the digit.
- Simple Colouring Follow one digit's forced chain through the grid in two alternating colours.