fig annotated sudoku puzzle in the third row in the puzzle because those numbers already appear in other cells applying rules like these reduces the number of possible values for each cell in the puzzle figure shows the puzzle after applying some of these rules if we spend some time thinking about sudoku and how to solve it we can derive two rules that can be used to solve many sudoku puzzles these two rules can be applied to any group within the puzzle group is collection of nine cells that appear in rowcolumnor square within the puzzle within each cell is set of numbers representing the possible values for the cell at some point in the process of reducing the puzzle here are the two rules rule the first rule is generalization of the process that we used above to remove some values from cells within group look for cells that contain the same set of possible values if the cardinality of the set ( the number of items in the setmatches the number of duplicate sets foundthen the items of the duplicate sets may safely be removed from all non-duplicate sets in the group this rule applies even in the degenerative case where the number of duplicate sets is and the size of that set is the degenerative case is what we used above to remove single items from other sets this rule can be applied to fig to remove the from all cells in the th row of the puzzle except the th column where appears by itself rule the second rule looks at each cell within group and throws away all items that appear in other cells in the group if we are left with only one value in the chosen cellthen it must appear in this cell and the cell may be updated by throwing this copy belongs to 'acha