Advanced Sudoku Strategy
XYZ-Wing Sudoku: How to Find and Use XYZ-Wings
Learn how a three-candidate pivot and two bivalue pincers create a safe candidate elimination.
One Pivot, Two Pincers
Pivot X/Y/Z; pincers X/Z and Y/Z. At least one of the three pattern cells must contain Z.
What Is an XYZ-Wing in Sudoku?
An XYZ-Wing is an advanced three-cell candidate pattern. The pivot contains exactly X, Y and Z. Two pincers contain exactly X/Z and Y/Z. Both pincers must see the pivot by sharing a row, column or 3×3 box. The pincers do not need to see each other. At least one of the three pattern cells must contain Z, so any different cell that sees all three cannot contain Z.
XYZ-Wing Example: Candidates 2, 5 and 8
Suppose pivot R2C2 contains {2,5,8}, pincer R2C3 contains {2,8}, and pincer R3C2 contains {5,8}. All three cells are in the top-left box. If R1C1 also has candidate 8, remove 8 from R1C1: it sees all three pattern cells in the same box.
Why Does XYZ-Wing Work?
If the pivot is 2, the {2,8} pincer must be 8. If the pivot is 5, the {5,8} pincer must be 8. If the pivot is 8, the pivot itself is 8. Thus at least one of the three pattern cells must contain 8, so another cell seeing all three cannot be 8.
How to Find an XYZ-Wing: Step by Step
Step 1: Find a pivot with exactly three candidates. Step 2: Find a bivalue pincer X/Z that sees the pivot. Step 3: Find a bivalue pincer Y/Z that sees the pivot. Step 4: Confirm the common candidate Z. Step 5: Find another cell seeing all three pattern cells. Step 6: Remove Z from that target. Step 7: Rescan for singles or pairs.
XYZ-Wing vs. XY-Wing
XY-Wing uses a two-candidate pivot and two bivalue pincers; its elimination target sees both pincers. XYZ-Wing uses a three-candidate pivot and two bivalue pincers; its elimination target must see the pivot AND both pincers.
When to Look for XYZ-Wing
Look for XYZ-Wings in hard or expert puzzles when simpler singles, pairs and locked candidates are exhausted. Candidate notes make the three-candidate pivot and nearby bivalue pincers easier to spot.
Common XYZ-Wing Mistakes
Do not use a two-candidate pivot. Do not use pincers with extra candidates. Do not eliminate from a cell seeing only the pincers but not the pivot. Do not eliminate Z from any of the three pattern cells themselves.
XYZ-Wing Practice Checklist
Confirm the three-candidate pivot, two complementary bivalue pincers, both pincers seeing the pivot, and a target cell seeing all three pattern cells. Only then remove the shared candidate.
Related Sudoku Learning Pages
Frequently Asked Questions
What is an XYZ-Wing?
A three-cell pattern with pivot X/Y/Z and pincers X/Z and Y/Z.
Where can I eliminate Z?
From another cell that sees all three pattern cells.
Do pincers need to see each other?
No, but both must see the pivot.
How is XYZ-Wing different from XY-Wing?
XYZ-Wing has a three-candidate pivot and requires the elimination target to see the pivot as well as both pincers.
Practise XYZ-Wing Sudoku
Open a Hard or Expert Sudoku puzzle, turn on Notes, and look for a three-candidate pivot connected to two bivalue pincers.