XYZ-Wing
XYZ-Wing focuses on finding three cells that form a connection, where two have two possible numbers and the third (pivot) shares a number with each of the other two.
When to use it
Use when a three-candidate pivot cell is flanked by two pincers that each share candidates with it.
Worked example
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A pivot {1,5,9} sees two pincers {1,9} and {5,9}; all three share the digit 9.
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A cell seeing the pivot and both pincers cannot be 9, so the 9 is eliminated there.
In practice
In practice, if you find this configuration in a sudoku game, an opportunity opens up to significantly reduce the possibilities. By applying the XYZ-Wing technique, you can eliminate options strategically, facilitating the resolution of the most complex parts of the puzzle.
Common mistakes
- Picking pincers the pivot cannot actually see (not in the same row, column or box).
- Eliminating from a cell that does not see all three of the wing's cells.
Frequently asked questions
How is XYZ-Wing different from an XY-Wing?
In an XY-Wing the pivot has two candidates; in an XYZ-Wing it has three, so the eliminated cell must also see the pivot itself.