XYZ-Wing

A worked example

This position comes from SudokuByte’s lesson on the XYZ-Wing. Gold cells hold the evidence; green cells are the pattern’s ends.

1. Where to look

   Find a three-candidate pivot with two two-candidate wings.

   The pivot has XYZ and its wings have XZ and YZ. Z is guaranteed in at least one of these three cells.

2. Read the evidence in this position

   The pivot r9c8 contains 4, 5, 9. Its wings are r7c8 with 4, 9 and r9c2 with 4, 5. Each wing sees the pivot.

3. Why the deduction must follow

   Try each pivot candidate. If the pivot is 4, it supplies the 4 itself. If the pivot is 5, r9c2 cannot be 5 and must be 4. If the pivot is 9, r7c8 cannot be 9 and must be 4. Therefore remove 4 only from cells seeing the pivot and both wings.

4. Apply the result

   Erase 4 from r9c7. The pattern may remove candidates without immediately solving a cell.