## How Many Camels

A Camel merchant willed his 17 camels to his three sons. In the merchant’s will, the camels were to be divided among them as follows:

The eldest son was to receive half of the camels;
The middle son was to receive a third of the camels;
The youngest son was to receive a ninth of the camels.

The executor of the merchant’s estate was perplexed. Finally, he devised a method for dividing the camels without having to slaughter any of the animals. How many camels did each son receive and explain his solution?
Source: mathcontest.olemiss.edu 5/4/2009

SOLUTION
If the executor divided the 17 camels according to the will, then
$\frac{17}{2}+\frac{17}{3}+\frac{17}{9}=8\frac{1}{2}+5\frac{2}{3}+1\frac{8}{9}$
$=14+\left (\frac{1}{2}+\frac{2}{3}+\frac{8}{9}\right )$
$=14+\left (2\frac{1}{18}\right )$
$=16\frac{1}{18}$

There is $\frac{17}{18}$ of a camel left over.

However, if the executor divided 18 camels, then
$\frac{18}{2}+\frac{18}{3}+\frac{18}{9}=9+6+2$
$=17$

There is exactly 1 camel left over.

So the executor added 1 camel to the lot of 17 making it 18 camels. He then divided the 18 camels according to the will. Then, he takes back 1 camel that is left over.

Answer: Oldest son received 9 camels; middle son 6 camels; youngest son 2 camels. His solution = add 1 camel to the lot of 17; divide the 18 camels according to the will; take back 1 camel that is left over.