XYZ-Wing

Volodymyr Sakhan  ·  May 26, 2026

XYZ-Wing is an advanced sudoku technique and a direct extension of the Y-Wing (XY-Wing). Where Y-Wing uses a pivot with two candidates, XYZ-Wing uses a pivot with three — making it more powerful but also harder to spot.

If you've worked through Y-Wing already, you'll recognize the same three-cell shape here. The key difference is the tighter elimination rule: because the pivot also contains the shared digit Z, only cells that see all three pattern cells at once can have Z removed.

What Is XYZ-Wing?

An XYZ-Wing is a three-cell pattern built around a pivot cell that holds exactly three candidates {X, Y, Z}. The two wing cells each hold two candidates that are subsets of the pivot's set:

• Pivot — three candidates {X, Y, Z}. Must see both wing cells (via shared row, column, or box).
• Wing 1 — candidates {X, Z}, a subset of the pivot's set. Shares a house with the pivot.
• Wing 2 — candidates {Y, Z}, a subset of the pivot's set. Shares a different house with the pivot (and does not need to see Wing 1).

The shared digit Z appears in all three cells. Any cell that sees the pivot and both wings simultaneously cannot be Z, because one of those three cells must hold Z no matter how the puzzle resolves.

When to Use XYZ-Wing

Reach for XYZ-Wing after Y-Wing fails to produce any eliminations. Conditions that make XYZ-Wing applicable:

• You have added pencil marks and the board still has unsolved cells.
• There is at least one cell with exactly three candidates — your candidate pivot.
• Two cells that the pivot can see each hold exactly two candidates that are subsets of the pivot's three-digit set.

Why XYZ-Wing Works

Consider the pivot with candidates {X, Y, Z} and follow the three cases exhaustively:

• Pivot = Z — Z is placed directly in the pivot. Any cell seeing the pivot cannot be Z.
• Pivot = X — Wing 1 {X, Z} loses X, so Wing 1 must be Z. Any cell seeing Wing 1 cannot be Z.
• Pivot = Y — Wing 2 {Y, Z} loses Y, so Wing 2 must be Z. Any cell seeing Wing 2 cannot be Z.

In every case, at least one of the pattern cells holds Z. A cell that sees all three is covered by every case — so it can never be Z.

Step-by-Step Examples

The two examples below show the most common XYZ-Wing shapes: one where the pivot and a wing share a column and the other wing sits in the same row, and one where both wings share the pivot's column and box.

Example 1 — Row and Column Elimination (Two Cells)

The pivot is D7 with candidates {1, 2, 8}. Wing 1 is D8 {1, 8} in the same column; Wing 2 is G7 {2, 8} in the same row.

1. Pivot D7 has three candidates {1, 2, 8} — X=1, Y=2, Z=8.
2. Wing 1 D8 has {1, 8} — shares X=1 and Z=8 with the pivot; same column D. ✓
3. Wing 2 G7 has {2, 8} — shares Y=2 and Z=8 with the pivot; same row 7. ✓
4. The shared digit across all three cells is 8.
5. Look for cells that see D7 (row 7), D8 (column D or same box), and G7 (row 7) simultaneously.
6. E7 and F7 each see D7 and G7 via row 7, and see D8 via their shared box (cols D–F, rows 7–9). Eliminate 8 from both E7 and F7.

E7 and F7 both see all three XYZ-Wing cells, so neither can hold 8 — two eliminations from a single pattern application.

Example 2 — Column and Box Elimination

Here the pivot H7 {6, 7, 8} sits between a column-wing H2 {7, 8} and a row-wing I7 {6, 8}, showing a column/box variant.

1. Pivot H7 has three candidates {6, 7, 8} — X=7, Y=6, Z=8.
2. Wing 1 H2 has {7, 8} — shares X=7 and Z=8 with the pivot; same column H. ✓
3. Wing 2 I7 has {6, 8} — shares Y=6 and Z=8 with the pivot; same row 7. ✓
4. The shared digit across all three cells is 8.
5. Look for a cell that sees H7 (col H), H2 (col H), and I7 (box — cols G–I, rows 7–9) simultaneously.
6. H9 sees H7 and H2 via column H, and sees I7 via their shared box. Eliminate 8 from H9.

H9 sees the pivot and both wings via column and box — the only cell in the board that qualifies, making this a single clean elimination.

XYZ-Wing vs. Y-Wing: Key Differences

Both techniques use a pivot and two wings, but the extra candidate in the XYZ-Wing pivot changes what can be eliminated:

• In Y-Wing the pivot has two candidates; in XYZ-Wing it has three. The pivot itself also contains Z.
• Y-Wing eliminates Z from cells that see both wings (but not necessarily the pivot). XYZ-Wing eliminates Z only from cells that see all three cells including the pivot — a stricter requirement.
• Because the elimination zone for XYZ-Wing is smaller, it often produces just one elimination — but that single removal can unlock a cascade.

Practical tip: after adding pencil marks, scan for 3-candidate cells first. For each pivot candidate, check whether two cells it can see each hold exactly two candidates that are subsets of the pivot's set. Then look for any cell that sees all three.

How to Spot XYZ-Wing

Follow these four steps each time you look for an XYZ-Wing:

1. Scan every unsolved cell for exactly three candidates — these are your pivot candidates.
2. For each pivot, list all cells it can see that have exactly two candidates. Check whether any two of those cells each hold a 2-subset of the pivot's three digits.
3. Identify the shared digit Z — the one present in the pivot and both wings.
4. Find any unsolved cell (other than the pivot and wings) that lies in the same row, column, or box as each of the three pattern cells. That cell cannot be Z.

XYZ-Wings are relatively rare because three conditions must align: a 3-candidate pivot, two 2-candidate wings with matching subsets, and a cell that sees all three at once. When you find one, it's a reliable, logic-only deduction.

XYZ-Wing and Related Techniques

XYZ-Wing belongs to the wing family alongside Y-Wing (XY-Wing) and X-Wing. Y-Wing is the most common starting point: its pivot holds two candidates and its eliminations reach any cell that sees both wings. XYZ-Wing extends this by allowing the pivot to hold three candidates, but in exchange the elimination zone shrinks to cells that see all three pattern cells at once — including the pivot. WXYZ-Wing pushes the same idea further with four candidates in the pivot set, though it is rarely needed in standard puzzles. If an XYZ-Wing produces no eliminations on a given board, look instead at Y-Wing on neighbouring cells, or consider colouring techniques for the shared digit.

Practice XYZ-Wing Online

XYZ-Wing appears in hard and expert puzzles. Play hard sudoku on OnSudoku and switch on pencil marks to hunt for 3-candidate pivot cells — each one is a potential XYZ-Wing.

Create a free account to save your progress and track which advanced techniques you've used. Return to our full solving guide for the complete list of techniques.

Frequently Asked Questions