Eight queens: Let the user give the initial position of m (m <= 8) Queens, you first check if these m Queens violate the eight Queens' rule (meaning among these m Queens, there is at least one pair of Queens that they can "eat" each other). If the input violates the rule, tell user the input is illegal. If the input does not violate the rule, fixing these m Queens, computing the positions of the rest 8-m Queens. Note there could be no solution or multiple solutions.