Sudoku You’ve learned the XY-Wing — three bi-value cells forming a logical fork that eliminates candidates across the grid. But what happens when the pivot cell has three candidates instead of two? That’s where the XYZ-Wing comes in.
The XYZ-Wing is a natural extension of the XY-Wing that handles situations where the pivot isn’t bi-value. It’s slightly trickier because the elimination zone is more restricted, but the underlying logic is just as elegant.
In this guide we’ll explain exactly what an XYZ-Wing is, show why it works, walk through a real example with before-and-after diagrams, and compare it to the XY-Wing so you know when to use each.
✅ What Is an XYZ-Wing in Sudoku?
The XYZ-Wing is an advanced candidate-elimination technique that uses exactly three cells. Unlike the XY-Wing where all three cells are bi-value, the XYZ-Wing has a pivot with three candidates and two wings that are each bi-value.
An XYZ-Wing consists of a pivot cell with candidates {X, Y, Z} and two wing cells: one with {X, Z} and one with {Y, Z}. The pivot must see both wings. Any cell that can see all three cells — the pivot and both wings — can have candidate Z eliminated.
The name comes from the three candidates in the pivot. X, Y, and Z each play a role: X and Y connect the pivot to its wings, while Z is the digit that gets eliminated. Every candidate in the pivot is “used” — nothing is wasted.
🧠 How the XYZ-Wing Works (The Logic)
The reasoning follows three branches instead of two. Consider three cells on a real grid:
- Pivot R1C3 has candidates {1, 5, 6}.
- Wing R2C3 has candidates {5, 6} — shares digit 5 with the pivot.
- Wing R3C3 has candidates {1, 6} — shares digit 1 with the pivot.
The pivot can be 1, 5, or 6. Let’s trace all three possibilities:
- If the pivot is 1: Wing R2C3 still has {5, 6}. Wing R3C3 loses its 1 (same column), so it must be 6.
- If the pivot is 5: Wing R3C3 still has {1, 6}. Wing R2C3 loses its 5 (same column), so it must be 6.
- If the pivot is 6: The pivot itself is 6.
In every case, at least one of the three cells is 6. That means any cell that can see all three cells can never be 6 — it would conflict with whichever cell holds the 6.
The XYZ-Wing is a three-way fork: no matter which value the pivot takes, the elimination digit Z ends up in at least one of the three cells. The third branch (pivot = Z) is what makes this different from the XY-Wing and why elimination cells must see all three cells, not just the two wings.
🔎 Step-by-Step Example
Let’s walk through a real XYZ-Wing. The pivot sits at R1C3 in Box 1, and both wings are at R2C3 and R3C3 (connected by Column 3 and Box 1). The elimination digit is Z = 6.
Step 1: Identify the three cells
- Pivot R1C3: candidates {1, 5, 6} — the three-candidate cell.
- Wing R2C3: candidates {5, 6} — shares 5 with pivot (same column and box).
- Wing R3C3: candidates {1, 6} — shares 1 with pivot (same column and box).
Step 2: Confirm the pattern
Check the requirements: the pivot has exactly three candidates ✔, each wing is bi-value ✔, the pivot sees both wings ✔, each wing shares one non-Z digit with the pivot ✔, and the common digit Z = 6 appears in all three cells ✔.
Step 3: Find the elimination targets
Which cells can see all three XYZ-Wing cells (R1C3, R2C3, and R3C3) and contain candidate 6?
- R1C2 — {6, 8}: sees all three via Box 1 and Row 1. Remove 6 → {8} — a naked single!
- R2C2 — {2, 3, 6, 9}: sees all three via Box 1 and Row 2. Remove 6 → {2, 3, 9}.
- R3C2 — {2, 3, 6, 8, 9}: sees all three via Box 1 and Row 3. Remove 6 → {2, 3, 8, 9}.
That’s 3 eliminations from a single XYZ-Wing, and R1C2 is instantly resolved as 8!
Step 4: Continue solving
Resolving R1C2 as 8 removes 8 from the other cells in Row 1 and Box 1, causing a cascade of further simplifications. One well-spotted XYZ-Wing can break open an entire puzzle.
Find: A pivot {X, Y, Z} that sees two wings — one with {X, Z} and one with {Y, Z}.
Eliminate: Candidate Z from any cell that sees all three cells.
Result: Fewer candidates, potential naked singles, and a simpler grid.
🕵️ How to Find an XYZ-Wing
1. Scan the grid for cells with exactly three candidates — these are potential pivots.
2. For each triple-candidate cell {X, Y, Z}, look at bi-value cells it can see.
3. Can you find one wing with {X, Z} and another with {Y, Z}?
4. If yes, find cells that see all three and contain Z.
5. Eliminate Z from those cells.
Focus on boxes. Because elimination cells must see all three XYZ-Wing cells, the most common XYZ-Wing pattern has all three cells in the same box or at least the pivot and one wing sharing a box. Look for three-candidate cells in boxes with several bi-value neighbours.
🔄 XYZ-Wing vs XY-Wing
The XYZ-Wing is a direct extension of the XY-Wing, but they differ in important ways.
| Feature | XY-Wing | XYZ-Wing |
|---|---|---|
| Pivot candidates | 2 (bi-value {X, Y}) | 3 (triple {X, Y, Z}) |
| Wing candidates | 2 each ({X, Z} and {Y, Z}) | 2 each ({X, Z} and {Y, Z}) |
| Pivot contains Z? | No | Yes — the key difference |
| Elimination sees… | Both pincers (not necessarily the pivot) | All three cells (pivot + both wings) |
| Elimination zone | Can span the entire grid | Restricted — usually within the pivot’s box |
| Difficulty | Advanced | Advanced+ |
The crucial difference is that in an XY-Wing, the pivot cannot be Z (it only has X and Y), so elimination cells don’t need to see the pivot. In an XYZ-Wing, the pivot can be Z, so elimination cells must also see the pivot — making the elimination zone smaller but the technique applicable to more grid configurations.
📌 The Elimination Zone Explained
This is the trickiest part of the XYZ-Wing. An elimination cell must see all three cells: the pivot and both wings. In practice, this usually means:
- Same box as all three: If the pivot and both wings are in the same box (as in our example), any other cell in that box with candidate Z is an elimination target.
- Same box as pivot, same row/column as wings: Occasionally, a cell outside the box can see the pivot (via row/column) and both wings (also via row/column). But this is rarer.
In an XY-Wing, the pivot doesn’t contain Z, so it can’t “block” the elimination. But in an XYZ-Wing, the pivot does contain Z. When the pivot is Z, only cells that see the pivot are protected. That extra constraint shrinks the elimination zone but makes the technique valid in situations where the XY-Wing can’t apply.
Despite the smaller elimination zone, XYZ-Wings are valuable because they work with three-candidate pivot cells — which are far more common than bi-value cells as a puzzle progresses.
⚠️ Common Mistakes to Avoid
1. Forgetting that elimination cells must see all three cells
This is the most common mistake. Unlike the XY-Wing, seeing just the two wings is not enough. The elimination cell must also see the pivot because the pivot contains Z.
2. Confusing XYZ-Wing with XY-Wing
If the pivot has exactly two candidates, it’s an XY-Wing, not an XYZ-Wing. The techniques are related but have different elimination rules.
3. Wrong digit assignment
Z is specifically the digit that appears in all three cells. Each wing must share a different non-Z digit with the pivot. If both wings share the same digit with the pivot, the pattern is not an XYZ-Wing.
4. Eliminating from cells that don’t contain Z
Only cells that actually have candidate Z as a pencil mark are affected. Check carefully before removing any candidates.
📅 When to Look for XYZ-Wings
- Basic techniques: Naked Singles, Hidden Singles, Full House.
- Intermediate techniques: Naked Pairs, Hidden Pairs, Naked Triples, Pointing Pairs, Box/Line Reduction.
- Advanced techniques: X-Wing, Swordfish, XY-Wing.
- Expert techniques: XYZ-Wing, Jellyfish, Chains, Almost Locked Sets.
Puzzles requiring XYZ-Wing are typically rated Expert. They appear when standard advanced techniques like XY-Wing and X-Wing aren’t sufficient. Our hard puzzles are a good starting point for practising this technique.
🚀 Beyond XYZ-Wing
| Technique | Pivot Candidates | Wings | Elimination Sees |
|---|---|---|---|
| XY-Wing | 2 (X, Y) | 2 bi-value | Both wings |
| XYZ-Wing | 3 (X, Y, Z) | 2 bi-value | All 3 cells |
| WXYZ-Wing | 4 (W, X, Y, Z) | 3 bi-value | All 4 cells |
The Wing family continues to grow: WXYZ-Wing adds a fourth candidate to the pivot with three wings. Each step up adds more complexity but also more power. Master XYZ-Wing before moving to WXYZ-Wing — the logic is the same, just with more branches.
XY-Wing, XYZ-Wing, and WXYZ-Wing form a family of increasing complexity. Each adds one more candidate to the pivot, and the elimination zone shrinks accordingly because more cells must be “seen.” In practice, XY-Wing and XYZ-Wing are the most commonly useful.
🎯 Practice XYZ-Wings
- Fill in all pencil marks: XYZ-Wing depends on knowing every candidate in every cell.
- Scan for three-candidate cells: These are your potential pivots — more common than bi-value cells in harder puzzles.
- Check the box: Most practical XYZ-Wing eliminations happen within the pivot’s box.
- Verify with the solver: Use our Sudoku solver to confirm your findings.
Sudoku Hard
Hard puzzles where XYZ-Wing and other advanced techniques are regularly needed.
▶ Play Hard SudokuXY-Wing Guide
Master the XY-Wing first — it’s the foundation for understanding XYZ-Wing.
▶ Read XY-Wing GuideFrequently Asked Questions
An XYZ-Wing uses three cells: a pivot with {X, Y, Z} and two wings with {X, Z} and {Y, Z}. The pivot sees both wings, and any cell seeing all three can have candidate Z eliminated.
In an XY-Wing, the pivot has two candidates and elimination cells only need to see both pincers. In an XYZ-Wing, the pivot has three candidates and elimination cells must see all three cells, making the elimination zone smaller but the technique applicable in more situations.
Look for cells with exactly three candidates {X, Y, Z}. Then find two bi-value cells the pivot can see — one with {X, Z} and one with {Y, Z}. Eliminate Z from any cell that sees all three.
The pivot must be X, Y, or Z. In each case, at least one of the three cells ends up being Z. So any cell seeing all three can never be Z — it would conflict with whichever cell holds Z.
Because the pivot contains Z. When the pivot is Z, only cells that see the pivot are blocked. In an XY-Wing the pivot can’t be Z, so you only need to see the wings. The extra constraint is the trade-off for handling triple-candidate pivots.