Furthermore, in determining the number of three-digit numbers for which the difference ends in zero after n steps(n = 0,1,..., 6), combinatoric thinking is required. Consider, for example, the following different cases:
all three digits are different and unequal to zero; exactly two digits are equal and all are unequal to zero; all three digits are equal and unequal to zero; exactly one digit is O and the two others are different; exactly one digit is o and the two remaining digits are equal two digits are 0.