180 SPECIAL TOPICS IN THEORETICAL ARITHMETIC

MULTIPLYING ON THE FINGERS

463. The lazy man’s rule for multiplication can be trans-
formd into a still simpler rule by using the hands as a com-
puting machine.

Assign the numbers 6, 7, 8, 9 to the fingers of each hand,
starting at the little finger, as shown in the figure below, in
the columns markt a¢ and b on the left and right hands re-
spectivly.

 

Let a be any one of the numbers 6, 7, 8, 9. We will divide
the fingers of the left hand, including the thumbs, into two
groups, the lower group starting at the little finger and ending
with the ¢ finger, and the upper group containing the fingers
above the a finger. For example, if a is 7, the lower group
contains 2 fingers, the upper group 3.

Evidently the number of fingers in the lower group is the
excess of @ over 5, which we have called e, and the number of
fingers in the upper group is ¢, the complement of ¢ with
respect to 10.

If b also is one of the numbers 6, 7, 8, 9, we divide the
fingers of the right hand similarly into groups, the number of
fingers in the lower group, which ends with the b finger, being
f, the excess of b over 5, and the number of fingers in the upper