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A common method for solving a Sudoku puzzle is the use of elimination techniques. At each step one tries to find a specific pattern and eliminates a value in the candidate list. We describe the solution of a Sudoku puzzle as a disparate selection of a set-valued mapping and define critical sets and elimination points for this model. Some of the known techniques can be understood as the search for critical sets and elimination points. Our approach unifies these solution techniques and provides a general elimination process. 

sudoku, solution technique, candidate list, critical set, elimination point, marriage theorem, mathematical programming.