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Teknik XYZ-Wing: Kombinasi Sel Tiga dan Dua Kandidat

2025-06-12 · 8 menit baca

XYZ-Wing is an extension of the XY-Wing technique. Unlike XY-Wing which uses three double-candidate cells, XYZ-Wing uses one triple-candidate cell (pivot) and two double-candidate cells (wings) for logical elimination.

         Core Principle:

        XYZ-Wing consists of three cells: a Pivot containing candidates {X,Y,Z}, and two Wings containing {X,Z} and {Y,Z} respectively. The pivot must "see" both wing cells. Regardless of whether the pivot is X, Y, or Z, Z must be in the pivot or one of the wing cells. Therefore, any cell that can see all three cells can have candidate Z eliminated.

XYZ-Wing diagram: The relationship between pivot {X,Y,Z} and wings {X,Z}, {Y,Z}. Z must be in pivot, wing1, or wing2.

Before reading this article, it\'s recommended to understand the XY-Wing concept first, as XYZ-Wing is its natural extension.

Difference between XYZ-Wing and XY-Wing

The main differences between XYZ-Wing and XY-Wing:

Feature	XY-Wing	XYZ-Wing
Pivot Candidates	{X,Y} - 2 candidates	{X,Y,Z} - 3 candidates
Elimination Range	Cells that see both wing cells	Cells that see pivot and both wing cells
Elimination Scope	Larger	Smaller (must see 3 cells)

Structure of XYZ-Wing

XYZ-Wing consists of three key elements:

Pivot: The central cell with candidates {X,Y,Z}, must see both wing cells
Wing 1: Candidates {X,Z}, shares row, column, or box with pivot
Wing 2: Candidates {Y,Z}, shares row, column, or box with pivot

Key feature: The pivot contains three candidates X, Y, Z, and each wing contains Z plus one other candidate from the pivot.

Why Does XYZ-Wing Work?

1 Pivot can only be X, Y, or Z: The pivot cell {X,Y,Z} can only contain one of X, Y, or Z.

2 If pivot is X: Wing 1 {X,Z} cannot be X (no duplicates in same unit), so Wing 1 must be Z.

3 If pivot is Y: Wing 2 {Y,Z} cannot be Y (no duplicates in same unit), so Wing 2 must be Z.

4 If pivot is Z: The pivot itself is Z.

5 Conclusion: Regardless of whether pivot is X, Y, or Z, Z must be in the pivot, Wing 1, or Wing 2. Therefore, cells that can see all three cannot contain Z.

Example 1: XYZ-Wing with R5C6 as Pivot

Let\'s look at the first example showing a typical XYZ-Wing structure.

Figure 1: Pivot R5C6{3,5,7}, Wings R5C1{3,7} and R4C6{5,7}, eliminate candidate 7 from R5C4

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Analysis Process

1 Identify Pivot: R5C6 is a triple-candidate cell with candidates {3, 5, 7}.

2 Find Wing Cells:

R5C1 (Wing 1): candidates {3, 7}, same row as pivot (Row 5)
R4C6 (Wing 2): candidates {5, 7}, same column as pivot (Column 6)

3 Verify XYZ-Wing Structure:

Pivot {3,5,7} contains all three digits
Wing 1 {3,7} contains Z=7 and another pivot digit 3
Wing 2 {5,7} contains Z=7 and another pivot digit 5
Pivot sees both wing cells (Row 5 and Column 6)
Common digit Z = 7

4 Reasoning Process:

If R5C6=3 → R5C1 cannot be 3 → R5C1=7
If R5C6=5 → R4C6 cannot be 5 → R4C6=7
If R5C6=7 → Pivot itself is 7
In all cases, one of R5C6, R5C1, or R4C6 must be 7

5 Find Elimination Target: R5C4 can see the pivot and both wing cells (same row as R5C6 and R5C1, same box as R4C6).

Conclusion:
XYZ-Wing: Pivot R5C6({3,5,7}), Wings R5C1({3,7}) and R4C6({5,7}).
Eliminate candidate 7 from R5C4.

Example 2: XYZ-Wing with R3C7 as Pivot

Now let\'s look at another example showing XYZ-Wing with different positional relationships.

Figure 2: Pivot R3C7{1,4,6}, Wings R3C6{1,4} and R2C7{4,6}, eliminate candidate 4 from R3C9

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Analysis Process

1 Identify Pivot: R3C7 is a triple-candidate cell with candidates {1, 4, 6}.

2 Find Wing Cells:

R3C6 (Wing 1): candidates {1, 4}, same row as pivot (Row 3)
R2C7 (Wing 2): candidates {4, 6}, same column as pivot (Column 7)

3 Verify XYZ-Wing Structure:

Pivot {1,4,6} contains all three digits
Wing 1 {1,4} contains Z=4 and another pivot digit 1
Wing 2 {4,6} contains Z=4 and another pivot digit 6
Pivot sees both wing cells (Row 3 and Column 7)
Common digit Z = 4

4 Reasoning Process:

If R3C7=1 → R3C6 cannot be 1 → R3C6=4
If R3C7=6 → R2C7 cannot be 6 → R2C7=4
If R3C7=4 → Pivot itself is 4
In all cases, one of R3C7, R3C6, or R2C7 must be 4

5 Find Elimination Target: R3C9 can see the pivot and both wing cells (same row as R3C7 and R3C6, same box as R2C7).

Conclusion:
XYZ-Wing: Pivot R3C7({1,4,6}), Wings R3C6({1,4}) and R2C7({4,6}).
Eliminate candidate 4 from R3C9.

How to Find XYZ-Wing?

Finding XYZ-Wing requires a systematic approach:

1 Find all triple-candidate cells: First identify all cells with exactly three candidates as potential pivots.

2 For each triple-candidate cell {X,Y,Z}: Check the double-candidate cells it can see.

3 Look for matching wings: Find two double-candidate cells, one containing {X,Z} and another containing {Y,Z}.

4 Verify structure: Confirm the pivot can see both wing cells.

5 Find elimination targets: Find cells that can see the pivot and both wings, and contain candidate Z.

Important Notes:

Pivot must be a triple-candidate cell (3 candidates)
Both wings must be double-candidate cells (2 candidates)
Pivot must see both wing cells
Elimination target must see pivot and both wings (this limits the elimination range)
Since it must see 3 cells, elimination targets are usually within the pivot\'s box

Technique Summary

Key points for applying XYZ-Wing:

Identification: One triple-candidate cell {X,Y,Z} and two double-candidate cells {X,Z}, {Y,Z}
Structure requirement: Pivot {X,Y,Z} sees both wings
Elimination target: Common digit Z
Elimination range: All cells that can see pivot and both wings

Related Techniques:
XYZ-Wing is an extension of XY-Wing. If you\'ve mastered XY-Wing, XYZ-Wing only requires considering the additional case where the pivot itself is Z.
You can also learn WXYZ-Wing (four-candidate extension) and other advanced Wing techniques.

Practice Now:
Start a Sudoku game and try using XYZ-Wing! When you find triple-candidate cells and nearby double-candidate cells, check if they can form an XYZ-Wing structure.

XY-Wing Naked Pairs Techniques Index