(5) In the formation of the sequence of differences, we always obtain as the first result the difference d1 such that
These investigations, especially the proofs, give practice with the algorithms for sub- traction and review of the principles of our number system as desirable secondary effects. Furthermore, in determining the number of three-digit numbers for which the difference ends in zero after n steps(n 1, 6), combinatoric thinking is required. Consider, for example, the fol- lowing 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.