(idea) by Ziller Sat Jan 11 2003 at 20:12:24

Valtteri Suomalainen's book "Sauna Syyriassa" describes a similar method being used by the Syrians, using e.g. rocks. Say we want to multiply 10 by 6:

  1. Make two piles of rocks (or what ever material is being used) side by side, 10 rocks in one and 6 in the other. Let's name the piles A0 and B0 (the order doesn't matter). In this case, let's call the bigger pile A0. 
       A   B
0 10   6
  2. Make another pile (A1) under pile A0, containing half as many rocks as there is in A0, rounding down; in this case, 5 rocks (floor(10/2) rocks). Then make a new pile (B1) under pile B0, with twice the number of rocks in pile B0; in this case, 12 rocks.
    3.    A   B
0 10   6
1  5  12
  3. Repeat the previous step until you get a pile An with only 1 rock, and a corresponding pile Bn. In this case, Bn will contain 48 rocks.
    4.    A   B
0 10   6
1  5  12
2  2  24
3  1  48
  4. Remove all the lines k where Ak is even. In our example, these are lines A0 (=10) and A2 (=2).
    5.    A   B
0 10   6
1  5  12
2  2  24
3  1  48
  5. Add together all the remaining B's: 
    B1 + B3 == 12 + 48 == 60 == 10 * 6
    QED.

Any information on the origins of this particular method would be most welcome.

I like it!