Unavoidable Set

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An unavoidable set is a deadly pattern from the point of view of a puzzle maker, or somebody who is investigating solution grids.

Take the following example:

  1  
    2
     
  2  
  1  
     
   
     
     
  2 1
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     

If there were no givens in any of these 6 cells, the solver would eventually reach a point were a choice must be made how to place digits 1 and 2 in them. The conclusion would be that the puzzle has 2 possible solutions. It is unavoidable for the puzzle maker to place at least one given in one of these cells.

The fact that this pattern cannot appear in a valid Sudoku gives rise to a whole new range of solving techniques in the category uniqueness.