XYZ-Wing in Sudoku: prove the three-cell pattern
Do not trust the shape alone. Check the pivot and both wings, follow every possible value in the pivot, then test whether the target sees all three possible places for the shared candidate.
One visible proof
Whichever value the pivot takes, candidate 3 must appear in the pivot or one wing.
- 1. Check the three linked cellsR1C1 is the pivot with candidates 1, 2, and 3. Its wings are R1C2 with 1 and 3, and R2C1 with 2 and 3.
- 2. Follow every pivot valueIf the pivot is 1, the second wing becomes 3. If it is 2, the first wing becomes 3. If it is 3, the pivot itself contains 3.
- 3. Test the target against all threeR2C2 sees the pivot and both wings because all four cells share the same 3×3 box. It cannot contain candidate 3.
Candidate 3 must occupy R1C1, R1C2, or R2C1. R2C2 sees all three possible sources, so candidate 3 can be removed from R2C2. No solved grid or later move is revealed.
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