XYZ-Wing

This is a variation of an XY-wing. In the partial puzzle below, consider the cells that have only the candidates shown. Any cells that share a unit with all three cells XYZ, XY and YZ, can have Z eliminated from their candidates.

  YZ  
XYZ * *
     
     
  XZ  
     


It can be easily seen that which ever value is in XYZ, the cells marked with the asterisk cannot be Z.

if XYZ = X, then XZ = Z, so * cannot be Z
if XYZ = Y, then YZ = Z, so * cannot be Z
if XYZ = Z, then * cannot be Z

This allows Z to be eliminated from the candidates for the marked cells.

 

In the Sudoku puzzle below, the XYZ-wing in the green cells allows 1 to be eliminated from the blue cell.

Sudoku XYZ-Wing example

These Sudoku puzzles can be solved using XZY-wings: (What are .sdk files?)