XYZ-Wing

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An XYZ-Wing is an extension of the XY-Wing in which candidate z also appears in the pivot.

How to spot it

• Find two bivalue cells that cannot see each other and contain candidate pairs {x, z} and {y, z}. Their shared candidate is z; these cells are the pincers.
• Find a trivalue cell that sees both pincers and contains {x, y, z}. This cell is the pivot and must share a box with one of the pincers.
• Once the pincers and pivot are in place, candidate z can be eliminated from any cell that sees all three cells.

How it works

• Focus on candidate z in the pivot. Either the pivot contains z, or it does not.
• If the pivot contains z, candidate z must be eliminated from any cell that sees the pivot.
• If the pivot does not contain z, the pivot and two pincers form a standard XY-Wing, so at least one pincer must contain z. Candidate z must therefore be eliminated from any cell that sees both pincers.

Examples

On the board above, R4C2 is the pivot, while R4C3 and R9C2 are the pincers. They initially resemble an XY-Wing with x and y represented by 2 and 7, and z represented by 3. Because the pivot R4C2 also contains candidate 3, the pattern is an XYZ-Wing. Cell R5C2 sees the pivot and both pincers, so candidate 3 can be eliminated from it.

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The board above shows a case where the XYZ-Wing eliminates candidate z from two cells.