Arithmetics of Camels

G. L. Filkovsky,
Nomura Securities International,
New York, USA

It doesn't look like Roni Horowitz has submitted anything to the TRIZ Journal this month. It rather looks like Elen Domb made an article [1] herself, by simply posting Roni's newsletter. To be able to say in editorial, This is our biggest issue ever? What is it good for? Does she unconditionally believe in the bigger, the better?

Anyway, let's look into this charming story and what we can learn from it. Three sons need to split 17 camels in such a way that one of them gets half, the other - third and the other - one ninth of the camels. Roni asks, What should the sons do? And, with no explanation, he suggests that they should use ASIT Multiplication idea.

I have a better idea: why wouldn't they use a good ol' simple arithmetics? If they just add up the parts the way we learn at school, they can see that:

1/2 + 1/3 + 1/9 = 9/18 + 6/18 + 2/18 = 17/18

They don't add up to a whole 1. They can think than that either the father was senile or he just ment them to split 17/18, i.e. 17 out of 18, camels. The later means that one gets 9, the other - 6, and yet the other - 2 camels. It's all right here and requires only usual additions and multiplications, rather than an artificially interpreted ASIT Multiplication.

Unlike Roni's conclusion, this is what I suggest to learn from this story: Simple math can be used very effectively in "real life" too!

Moreover, a more generic structure becomes clear, which can't be achieved by the "ASIT Multiplication". Let's say, there are 59 camels and the will says to get one half, one fifth and one seventh. What would ASIT do? Trial and error? Arithmetics answer is clear:

1/2 + 1/5 + 1/7 = 35/70 + 14/70 + 10/70 = 59/70.

They get 35, 14 and 10 camels, respectively.

Roni could say, that at least this is still "ASIT Multiplication" (they should "borrow" 11 camels rather than 1). Then, how about this: there are 26 camels, which should be split one half, one third and one forth? Arithmetics:

1/2 + 1/3 +1/4 = 12/24 + 8/24 + 6/24 = 26/24.

They get 12, 8 and 6 camels.

Now, in the style of Roni's interpretation, here instead of "ASIT Multiplication" the sons should come up with "ASIT Separation": put two camels aside, to get 24; then give one son a half of them, i.e. 12; give other son a third of them, i.e. 8; then, while trying to give the last son a forth, i.e. 6 camels, discover that there are two camels missing - aha! here are these two camels waiting on a side... Clearly, arithmetics is better!

Remarks by the editor:

The problem can be also solved as follows:

17/2 = 8 + 1/2;
17/3 = 5 + 2/3;
17/9 = 1 + 8/9;

The simple rounding of these numbers gives rise to 9, 6, and 2 respectively. No artificial "ASIT multiplication" is needed.

The riddle was probably composed in the times when rounding was not known. Otherwise, there would be no riddle. But why one should be puzzled by it nowadays, remains unclear.

R E F E R E N C E S:

  1. ASIT Technique For A Week, Issue 136, By: Roni Horowitz, The TRIZ-journal, October 2003.