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XYZ-Wing pattern in Sudoku
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XYZ-Wing

When the Pivot Has All Three Candidates

By Minimal Sudoku TeamLast updated:

The XYZ-Wing is an extension of the Y-Wing pattern. The difference? The pivot cell contains all three candidates (X, Y, and Z) instead of just two.

Quick Summary
  • Pivot: Contains candidates X, Y, Z (three candidates)
  • Wing 1: Contains X, Z (sees pivot)
  • Wing 2: Contains Y, Z (sees pivot)
  • Result: Eliminate Z from cells that see all three (pivot + both wings)
  • Difficulty: Advanced

The Concept

An XYZ-Wing uses three cells with a specific candidate arrangement:

🎯
Pivot

Candidates: X, Y, Z

Has all three

🪽
Wing 1

Candidates: X, Z

Sees pivot

🪽
Wing 2

Candidates: Y, Z

Sees pivot

All three cells share candidate Z. The elimination happens in cells that can see all three cells.

XYZ-Wing vs Y-Wing

🦋 Y-Wing

Pivot has 2 candidates (A, B)

Wings don't see each other

Eliminate from cells seeing both wings

🔺 XYZ-Wing

Pivot has 3 candidates (X, Y, Z)

Wings must see pivot (can see each other)

Eliminate from cells seeing all three

Key Difference
In XYZ-Wing, the pivot also contains Z, so elimination requires seeing the pivot too — not just the wings. This typically means eliminations are in the same box as the pivot.

The Golden Rule

🔺 XYZ-Wing Rule
When a pivot with candidates XYZ sees two wings (XZ and YZ), eliminate Z from any cell that sees all three cells (the pivot and both wings).

How to Find XYZ-Wings

1

Find tri-value cells

Look for cells with exactly three candidates. These are potential pivots.
2

Find matching wings

For each tri-value cell (X, Y, Z), look for bi-value cells it sees:
• Wing 1 with candidates X, Z
• Wing 2 with candidates Y, Z
3

Identify the common candidate

Z is the candidate that appears in all three cells.
4

Find elimination targets

Look for cells that can see the pivot AND Wing 1 AND Wing 2. These are typically in the same box as the pivot.
5

Eliminate Z

Remove Z from any cell that sees all three XYZ-Wing cells.

Practical Example

XYZ-Wing on Candidates 4, 7, 8

XYZ-Wing pattern example with pivot containing candidates 4, 7, 8

In this example, we have an XYZ-Wing with:

  • Pivot at R2C9: Candidates 4, 7, 8 (the tri-value cell)
  • Wing 1 at R2C3: Candidates 4, 7 (sees pivot via row 2)
  • Wing 2 at R3C8: Candidates 7, 8 (sees pivot via box 3)

The common candidate shared by all three cells is 7. This is our elimination target.

Logic: The pivot must be 4, 7, or 8. If it's 4, Wing 1 becomes 7. If it's 8, Wing 2 becomes 7. If it's 7, the pivot itself is 7. In all cases, one of these three cells contains 7!

Elimination
Eliminate 7 from any cell that sees all three cells (the pivot and both wings). These cells are typically in the same box as the pivot.

Why It Works

Consider the three possible values for the pivot (which has candidates 4, 7, 8):

In all three cases, at least one of the three cells becomes 7. Any cell seeing all three will always "see" a 7 — so we can eliminate 7 from those cells.

Visual representation:
XYZ-Wing pattern on candidates 4, 7, 8Pivot at R2C9 with candidates 4,7,8 connects to Wing 1 at R2C3 with 4,7 and Wing 2 at R3C8 with 7,8.Wing 14, 7Pivot4, 7, 8Wing 27, 8R2C3R2C9R3C8Common candidate: 7→ Eliminate 7 from cells seeing all three
The pivot (4,7,8) connects Wing 1 (4,7) and Wing 2 (7,8). All share candidate 7.
The Either/Or/Or Logic
We don't need to know which cell contains 7 — we just know one of the three definitely does. This is enough to eliminate 7 from any cell that sees all three.

Detection Tips

Eliminations Are Usually Nearby
Because a cell must see all three XYZ-Wing cells, eliminations typically occur in the same box as the pivot. Look there first.
Start with Tri-Value Cells
Cells with exactly 3 candidates are less common than bi-value cells. Use them as your starting point when hunting for XYZ-Wings.
Check Both Wing Configurations
For a pivot with candidates X, Y, Z, there are three possible "Z" candidates. Check each configuration to maximize your chances of finding the pattern.

Related Techniques

Wing Family

🦋Y-Wing🔷WXYZ-Wing
Y-WingAdvanced

Y-Wing

Master the simpler Y-Wing first — same logic but with a bi-value pivot.

Related Techniques

🎨Simple Coloring🔗XY-Chain✈️X-Wing