XYZ-Wing

As a variation of an XY-Wing, XYZ-Wing is a more advanced technique. Any cells that share a unit with all three cells XYZ, XY and YZ, can have Z eliminated from their candidates.

  * YZ
  XYZ  
  *  
     
  XZ  
     
  1. If XYZ=X, then XZ=Z, so * cannot be Z. (Same column)
  2. If XYZ=Y, then YZ=Z, so * cannot be Z. (Same block)
  3. If XYZ=Z, then * cannot be Z. (Same block)

So whichever value is in XYZ, the marked cell can never be Z. Here is an example:

Sudoku Technique: XYZ-Wing 01 In this puzzle, suppose X=9, Y=7, and Z=6. So [D5] is XYZ, [B5] is XZ, and [D6] is YZ. Based on the analysis above, the candidate 6 can be eliminated from the candidates in cell at [F5].

There is another variation for XYZ-Wing pattern.

* XYZ *
     
YZ    
  XZ  
     
     

All cells marked with the asterisk can have Z eliminated from their candidates. For example:

Sudoku Technique: XYZ-Wing 02 In the puzzle to the left, suppose X=2, Y=5, and Z=4. So [B2] is XYZ, [B9] is XZ, and [C3] is YZ. Based on the analysis above, the candidate 4 can be eliminated from the candidates in cell at [B1].

To quickly for you to get familiar with this technique, let's see more examples:

Sudoku Technique: XYZ-Wing Example 1 Sudoku Technique: XYZ-Wing Example 2

See also: ««  Direct Elimination Techniques  »» ««  Candidates Elimination Techniques  »»