XYZ-Wing in Sudoku: The Complete Guide

What is an XYZ-Wing?

An XYZ-Wing is an advanced Sudoku technique involving three cells in a specific pattern. It's closely related to the XY-Wing but with one key difference: the pivot cell has three candidates instead of two.

The pattern consists of:

• Pivot cell: Contains exactly three candidates {X, Y, Z}
• Wing cell 1: Contains {X, Z} and can see the pivot
• Wing cell 2: Contains {Y, Z} and can see the pivot

The Elimination Rule:

If any cell can see all three cells (pivot + both wings), you can eliminate candidate Z from that cell. Why? Because Z must be placed in one of these three cells, so it cannot be anywhere else that sees all three.

Example:

Pivot at Row 5, Col 5 with {2, 4, 7}. Wing 1 at Row 5, Col 2 with {2, 7}. Wing 2 at Row 2, Col 5 with {4, 7}. Any cell that sees all three cells cannot contain 7, because 7 must go in one of these three cells.

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Why XYZ-Wing Matters

• It extends XY-Wing logic to three-candidate pivots.
• It appears more frequently than XY-Wing in some advanced puzzles.
• It provides eliminations when simpler techniques fail.
• It's essential for advanced puzzle solving.
• It demonstrates sophisticated pattern recognition skills.

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How to Spot an XYZ-Wing

1. Find a pivot cell with three candidates.
   Look for cells with exactly three candidates like {1,3,5} or {2,6,8}. Call these candidates X, Y, and Z.
2. Look for wing cells with two candidates.
   Find two cells that each have two candidates: one contains {X,Z} and the other contains {Y,Z}. Notice both share Z with the pivot.
3. Verify visibility.
   The pivot must be able to "see" both wing cells (same row, column, or box).
4. Find elimination targets.
   Look for cells that see all three cells (pivot and both wings).
5. Eliminate Z.
   Remove candidate Z from any cell that sees all three cells in the pattern.

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XYZ-Wing vs XY-Wing

These related techniques differ in one key aspect:

• XY-Wing:
  • Pivot: {X, Y} (two candidates)
  • Wing 1: {X, Z}
  • Wing 2: {Y, Z}
  • Elimination: Z from cells seeing both wings (pivot doesn't need to be seen)
• XYZ-Wing:
  • Pivot: {X, Y, Z} (three candidates, includes Z)
  • Wing 1: {X, Z}
  • Wing 2: {Y, Z}
  • Elimination: Z from cells seeing all three cells (including pivot)

Think of XYZ-Wing as "XY-Wing plus one" - the pivot gains candidate Z, and elimination targets must see the pivot too.

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Step-by-Step Example

Let's identify an XYZ-Wing in a puzzle:

Pattern cells:

• Pivot: Row 4, Col 5 contains {3, 6, 8}
• Wing 1: Row 4, Col 2 contains {3, 8} (shares row with pivot)
• Wing 2: Row 1, Col 5 contains {6, 8} (shares column with pivot)

Verification:

• ✓ Pivot has three candidates: {3, 6, 8}
• ✓ Wing 1 has {3, 8} - shares 3 and 8 with pivot
• ✓ Wing 2 has {6, 8} - shares 6 and 8 with pivot
• ✓ Common candidate across all three: 8
• ✓ Pivot sees both wings (same row/column)

The Logic:

Candidate 8 must go in one of these three cells:

• If 8 goes in the pivot → wings must be 3 and 6
• If 8 goes in Wing 1 → pivot must have 6, Wing 2 must have 6 (contradiction if both need 6)
• Actually, if 8 is in Wing 1, pivot uses 3 or 6, Wing 2 uses 6
• If 8 is in Wing 2 → pivot uses 3 or 6, Wing 1 uses 3

Elimination:

Any cell that can see Row 4/Col 5 (pivot), Row 4/Col 2 (Wing 1), AND Row 1/Col 5 (Wing 2) cannot contain 8.

For example, Row 1, Col 2 (intersection of Wing 1's column and Wing 2's row) sees all three cells. If it contains candidate 8, eliminate it.

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Visual Example: The Basic Pattern

• Setup: You find three cells forming a small "Y" or "T" shape in the grid.
• Pivot: Cell at Row 6, Col 6 in Box 5 (center) with {1, 5, 9}
• Wing 1: Cell at Row 6, Col 3 with {1, 9} (same row)
• Wing 2: Cell at Row 8, Col 6 with {5, 9} (same column)
• Common candidate: All three cells contain 9
• Elimination target: Row 8, Col 3 sees all three cells
• Action: Remove 9 from Row 8, Col 3 if it exists

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Strategies for Spotting XYZ-Wing Quickly

1. Start with three-candidate cells
   Scan for cells with exactly three candidates. These are your potential pivots.
2. Look for bi-value neighbors
   From each potential pivot, check cells in the same row, column, or box for cells with exactly two candidates.
3. Check for the Z pattern
   Verify that both wing cells share one common candidate with the pivot (the Z value).
4. Geometric awareness
   XYZ-Wings often form L-shapes or T-shapes on the grid. Train your eye to spot these configurations.
5. Use after XY-Wing searches
   When scanning for XY-Wings, also note three-candidate cells. You're already in the right mindset.

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Common Pitfalls

• Wrong pivot: The pivot must have exactly three candidates, not two or four.
• Missing the common Z: All three cells must share one common candidate (Z).
• Incorrect elimination: Only eliminate Z from cells that see ALL THREE cells, not just two.
• Visibility errors: Make sure the pivot truly sees both wing cells (same row, column, or box).
• Confusing with XY-Wing: Remember, XYZ-Wing pivots have three candidates; XY-Wing pivots have two.

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Practice: Find the XYZ-Wing

Try identifying this pattern:

Given cells:

• Row 3, Col 7: {2, 4, 7}
• Row 3, Col 4: {2, 7}
• Row 5, Col 7: {4, 7}
• Row 9, Col 4: {1, 3, 6, 8}
• Row 5, Col 4: {1, 2, 4, 5, 7, 8}

Question: Is there an XYZ-Wing pattern? If so, what can be eliminated?

Solution:

• Pivot: Row 3, Col 7 with {2, 4, 7}
• Wing 1: Row 3, Col 4 with {2, 7} (same row)
• Wing 2: Row 5, Col 7 with {4, 7} (same column)
• Common candidate: 7 appears in all three cells
• XYZ-Wing confirmed!

Elimination: Find cells that see all three:

• Row 5, Col 4 sees Wing 1 (column 4), Wing 2 (row 5), and Pivot? Let's check...
• Row 5, Col 4 is in Row 5 (sees Wing 2), Column 4 (sees Wing 1), but doesn't see Row 3, Col 7 (pivot) directly...
• Actually, we need to check Box relationships too. Row 3, Col 7 is in Box 3. Row 5, Col 4 is in Box 5. They don't see each other.

The elimination would apply to cells in Row 3 that are also in Column 7's box, or in Row 5 that are in Column 4's box, creating a cell that sees all three through row/column/box relationships.

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Why XYZ-Wing Sets the Stage

XYZ-Wing bridges intermediate and expert techniques:

• It extends familiar XY-Wing logic to a new scenario
• It prepares you for WXYZ-Wing (four-cell version)
• It demonstrates how adding one candidate changes elimination rules
• It improves your ability to track complex cell relationships
• It's practical enough to appear regularly in advanced puzzles

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Quick Recap

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Final Thought

When you're stuck on an advanced puzzle, look for three-candidate cells that might be XYZ-Wing pivots. Does a three-candidate cell have two bi-value neighbors sharing a common candidate? You might have found an XYZ-Wing!

Frequently Asked Questions

Browse all techniques in our complete strategy guide.

Next Technique

• WXYZ-Wing — extends the same pivot-and-wings logic to four cells; the natural next challenge once XYZ-Wing feels comfortable.

Related Strategies

• XY-Wing — the two-candidate pivot version this technique builds on; revisit it if the elimination logic feels unclear.
• Remote Pairs — an intermediate technique in the same difficulty range that trains the same "cells that see each other" scanning habit.
• Simple Coloring — the next major category after wing techniques; introduces chain-based elimination logic worth learning once wings feel natural.
• Naked Triples — sharpens candidate-set thinking and is useful for spotting the multi-candidate patterns XYZ-Wing depends on.
• XYZ-Wing Sudoku Technique — a blog post with additional worked examples and elimination walk-throughs

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