1. ## Seventeen Camels

Seventeen Camels

A mathematical conundrum from a thousand years ago

A father dies leaving instructions that his 17 camels are to be split up between his 3 sons as follows -

half the camels are to go to the eldest son
a third of the camels are to go to the middle son
and a ninth of the camels are to go to the youngest son

Failing to think of a way of carrying out their father's wishes, they decided to seek help. So they sent a message across the desert to their uncle, who though poor was considered to be wise.

A month later, up rode their uncle on his grotty old camel. After he'd had a rest and something to eat, they explained their problem to him.

"Tell you what", he said, "I'll lend you my camel, then you'll have 18, and you should be able to divide them up without difficulty."

So the eldest son chose his 9 camels from the flock, the middle son chose his 6 camels, and the youngest son chose his 2 camels. Uncle then got back on his camel (which no-one had chosen because it was old and grotty) and rode back home across the desert (no doubt muttering to himself about the failings of the younger generation).

2. Spoiler:

I don't really get the conundrum..?
$\displaystyle \frac{1}{2} + \frac{1}{3} + \frac{1}{9} = \frac{17}{18}$

Spoiler:

I don't really get the conundrum..?
$\displaystyle \frac{1}{2} + \frac{1}{3} + \frac{1}{9} = \frac{17}{18}$

You know the answer is 17, but how do you set it up so that the arithmetic will work out?

Add the fractions, $\displaystyle \frac{1}{2}+\frac{1}{3}+\frac{1}{9}=\frac{17}{18}$

If the proportions were correct, the sum would have been $\displaystyle \frac{17}{17}$.

The only way to successfully solve this "conundrum" is to add the 18th camel.

The fly in the soup is the fact that with their final apportionment of 9, 6, and 2 camels,
their actual ratios were $\displaystyle \frac{9}{17}\:\frac{6}{17}\:and\:\frac{2}{17}$.

We know this, because the equation would be

$\displaystyle \frac{17}{18}x=17$

$\displaystyle {\color{red}x=18}$.

x has to equal 18 to solve the problem using the initial fractional apportionment. So, the wise uncle throws in his camel to the mix making the total 18, which works great with the assigned proportionality. The three knuckleheads were happy because they thought they received exactly what was bequeathed.

Historical Note:

This problem is present in an ancient Egyptian document, the Ahmes Papyrus -- a.k.a. Rhind Mathematical Papyrus. And Leonardo of Pisa (1175?-1250?) -- a.k.a. Fibonacci -- generalzed it.)

4. ## Comment

The first time I saw this problem, it was with horses. To mention, the uncle gets back his camel after his nephews divide according to the will (a nice problem).