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XY-Wing: the Sudoku technique explained

  • Master
  • Needed from Fiendish puzzles
  • 8 points in Duel

Also called a Y-Wing.

An XY-Wing uses three cells with two candidates each: a pivot and two pincers. Whichever value the pivot takes, one of the pincers becomes the same digit, so that digit leaves any cell that sees both pincers.

How it works

Call the three digits X, Y and Z. The pivot can be X or Y. One pincer shares a unit with the pivot and can be X or Z. The other pincer also shares a unit with the pivot and can be Y or Z.

  • If the pivot is X, the first pincer cannot be X, so it is Z.
  • If the pivot is Y, the second pincer cannot be Y, so it is Z.

So one of the two pincers is Z, whatever happens. Any cell that shares a unit with both pincers can never be Z, and you remove it there.

  1. Find a cell with exactly two candidates. This is your pivot, XY.
  2. In its row, column or box, find a two-candidate cell that shares one digit with it: XZ.
  3. Find another one that shares the pivot's other digit and the same third digit: YZ.
  4. Remove Z from every cell that sees both pincers.

A real example

1122334455667788997292693265841234234246781952681546924236237924782485346478138261648234957385278368178269434348948912424876524248795634138651487324289
XY-Wing. R1C5 is either 2 or 6. Either way, R3C4 or R7C5 must be 4, so any cell that sees both cannot be 4. That leaves a simple move: in row 9, 4 fits in only one cell: row 9, column 7.Blue: the pattern. Red: candidates that are removed. R3C7 means row 3, column 7.

The three blue cells are the pivot and its two pincers. The red candidate sits in a cell that shares a unit with both pincers, so it is removed.

How to spot them

XY-Wings are built only from cells with two notes, so start there. Boards in the late middle of a solve, with many two-note cells, are full of near misses. Pick a two-note cell, look along its row, column and box for others that share exactly one digit with it, and check whether two of them agree on a third digit. The pincers do not need to see each other. They only need to see the pivot.

Common mistakes

  • Removing Z from a cell that sees only one pincer. It has to see both.
  • Using a pincer with three candidates. All three cells need exactly two.
  • Picking pincers that share the same digit with the pivot. One must share X, the other Y.

Questions

What is an XY-Wing in Sudoku?

A pattern of three cells with two candidates each: a pivot XY and two pincers XZ and YZ that each share a unit with the pivot. One pincer must be Z, so Z is removed from every cell that sees both pincers.

Is a Y-Wing the same as an XY-Wing?

Yes. They are two names for the same technique.

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