sets and maps fig sudoku puzzle after one pass away all other values that appear in the chosen cell applying this rule to the fifth row in fig results in the fourth column being reduced to containing because does not appear in any other cell in the th row this rule also applies in the last row of the puzzle where is only possible in the second column after removing and from that cell because they appear within other cells in that row note that the puzzle in fig is not fully reduced the reduction process can be applied iteratively until no more reductions are possible the sudoku solver algorithm keeps applying this reduction process until no more changes are made during pass of reductions on all the groups within the puzzle applying these two rules in this manner will fully reduce many sudoku puzzles sets the reduction algorithm for sudoku puzzles manipulates sets of numbers and eliminates possible values from those sets as the reduction progresses set is collection that does not allow duplicate values sets can be composed of any values integersemployee objectscharactersstringsliterally any object in python could be an element of some set set has cardinality the cardinality of set is the number of items in it this copy belongs to 'acha