XY Wing Tutorial



XY Wing (aka Y Wing)

XY Wing (sometimes called Y Wing) is another advanced technique for eliminating candidates.

It starts by finding a cell with only two candidates (a bi-value cell) called the pivot.

These 2 candidates are called X and Y.

In our sample - R5C5 is the pivot, X=6 and Y=9.
Sudoku XY Wing

Next, we look for two more bi-valued cells that are buddy cells with the pivot.

They are called pincers, one should have X and Z as candidates and the other one - Y and Z.

Z is any digit different than X and Y.

In our example Z=7 and the pincers are R5C2 (same row as pivot) and R8C5 (same column).

R5C2 candidates are 6 and 7 (X=6, Z=7).

R8C5 candidates are 9 and 7 (Y=9, Z=7).
Sudoku XY Wing

In XY Wing we are interested in Z and the other cells it's affecting.

There are only two options for the pivot (6 or 9) and it's pincers to resolve:

if pivot=6 (X) then:

R8C5=9 (Y) and R5C2=7 (Z).
Sudoku XY Wing

or the second option, if pivot=9 (Y) then:

R8C5=6 (X) and R5C2=7 (Z).
Sudoku XY Wing

Either way, one of the pincers R5C2 or R8C5 has to be a 7 (Z) marked in blue:
Sudoku XY Wing

Therefore, any cell that is a buddy with both pincers R5C2 or R8C5 cannot be a 7 (Z).
Sudoku XY Wing Example

Take R8C2 - we can definitely remove 7 (Z) from its candidate list:
Sudoku XY Wing Example

The previous example had a shape of an X but it isn't necessarily has to be so.

Let's have a look at another example where R7C1 is the pivot:
Sudoku XY Wing Example

R2C1 is one pincer (it's on the same column as the pivot).

R9C3 is the second pincer (it's in the same box as the pivot).

X=7, Y=9 and Z=3 (marled in blue)
Sudoku XY Wing Example

Any cell that is buddy with both pincers R2C1 and R9C3 cannot be 3 (Z).

If we can find such cells that have 3 as a candidate we can remove 3 from their candidates.

The buddy cells of both pincers are marked in blue.

Can you find which cells cannot be a 3?
Sudoku Y Wing Tutorial

The answer is both R2C3 and R3C3.

They are in the same box as the first pincer - R2C1 and in the same column as the second pincer R9C3.
Sudoku Y Wing Tutorial

They cannot be a 3 so we can remove it from their candidates list.

This time we eliminated Z from two cells, XY is not limited for affecting only one cells but all cells that fits its rules.
Sudoku Y Wing Tutorial

How to find them

XY wings must involve 3 buddy cells that are bi-value (have only 2 candidates each) so start by searching for 3 bi-value buddy such.

Those 3 cells must then have XY, XZ and YZ as candidates.

One you find this scenario, look for the buddy cells of both XZ and YZ cells and eliminate Z from those.
Sudoku Y Wing Tutorial

End of Tutorials

Time to play Sudoku.

Previous Lesson:
Advanced Solving Techniques - X Wing
LiveSudoku.com

Back to the list of tutorials | Back to the Homepage