Sudoku Solver

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XYZ-Wing

A more advanced version of the Y-Wing that involves three cells and an extra candidate in the pivot.

The XYZ-Wing is a close cousin of the Y-Wing.

While the Y-Wing uses a pivot with two candidates (XY), the XYZ-Wing uses a pivot with three candidates (XYZ).

It is slightly harder to spot because the "pincers" look less like a clean pair, but the logic is just an extension of the same principle.

Interactive Example

5
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
9
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
5
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
7
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
6
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
4
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
8
1 2 3 4 5 6 7 8 9
3
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
2
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9

Click "Apply Logic" to see the strategy in action.

Real Example Explanation

In the example above, look at the Pivot cell R3C5 (Box 2):

  1. The Pivot:
    • R3C5 contains candidates {1, 6, 7} (let's call them X, Y, Z).
  2. The Wings:
    • Wing A: R5C5 contains {1, 7} (XZ). It sees the Pivot via Column 5.
    • Wing B: R1C6 contains {6, 7} (YZ). It sees the Pivot via Box 2.
    • Notice that both Wings share the "Z" value (7) with the Pivot.
  3. The Logic:
    • The Pivot (R3C5) must be 1, 6, or 7.
    • If Pivot is 1: Then Wing A (R5C5) forces 7.
    • If Pivot is 6: Then Wing B (R1C6) forces 7.
    • If Pivot is 7: Then the Pivot itself is 7.
    • Conclusion: No matter what the Pivot is, one of these three cells must be a 7.
  4. The Elimination:
    • Any cell that sees ALL THREE parts of the formation (Pivot, Wing A, and Wing B) cannot be a 7.
    • R1C5 sees the Pivot (same box), Wing A (same column), and Wing B (same row).
    • Therefore, we can eliminate 7 from R1C5.

How to Spot It

  1. Find a Pivot: Look for a cell with three candidates (XYZ).
  2. Find the Wings: Look for two bivalue cells that:
    • Share a unit with the Pivot.
    • Contain only candidates from the Pivot (one XZ, one YZ).
  3. Check Visibility: The key difference from a Y-Wing is the elimination zone.
  4. Eliminate: Identify the cell(s) that see the Pivot AND both Wings. Remove the common digit (Z).

Comparison: Y-Wing vs XYZ-Wing

  • Y-Wing: Pivot has 2 candidates. Eliminations are found where the Wings intersect.
  • XYZ-Wing: Pivot has 3 candidates. Eliminations are found where Pivot + Wings all intersect (usually just 1 or 2 cells).

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