XY-Wing
A pivot cell holding {X, Y} with two pincer cells holding {X, Z} and {Y, Z}. Any cell that sees both pincers loses Z.
Advanced sudoku technique
What it is
XY-Wing is the simplest chain technique in sudoku. It needs three cells, each with EXACTLY two candidates, arranged as: - A 'pivot' cell holding {X, Y} - A 'pincer A' cell holding {X, Z}, sharing a unit (row, column, or box) with the pivot - A 'pincer B' cell holding {Y, Z}, sharing a unit with the pivot (the unit can be different from pincer A's) Whatever the pivot ends up holding, one of the pincers is forced to Z. If the pivot is X, pincer A becomes Z. If the pivot is Y, pincer B becomes Z. Either way, ONE of the pincers will end up as Z. Therefore Z can be eliminated from every cell that sees BOTH pincers. Despite the name, no diagonal X shape is required — the technique is named after the {X, Y} pivot and the {X, Z}/{Y, Z} pincers.
When to use it
On expert and master puzzles when X-Wing and Swordfish don't yield a move. Hunt for any bivalue pivot cell that has two bivalue neighbours whose candidate sets complete the {X, Y, Z} triangle.
Worked example
Pivot R2C2 = {1, 7}. Pincer A R2C8 = {1, 4} shares row 2 with the pivot. Pincer B R5C2 = {7, 4} shares column 2 with the pivot. The shared third digit is 4. The pivot ends up as 1 or 7. If 1, pincer A is forced to 4. If 7, pincer B is forced to 4. Either way, one of the pincers holds 4. Therefore 4 can be eliminated from any cell that sees both pincers. R5C8 sees pincer A via column 8 and pincer B via row 5 — drop 4 from its candidate set.
Try it
The Sudoku247Online solver walks you through every move of any puzzle one logical step at a time, naming the technique that justifies each placement. Paste a puzzle to see this technique applied in real time.