A father leaves 17 camels to his three sons with these conditions: the oldest gets $\frac{1}{2}$, the second gets $\frac{1}{3}$ and the youngest gets $\frac{1}{9}$. Splitting camels is not allowed. How can the distribution be made by exactly complying with the will?
Classic recreational arithmetic puzzle in the Middle East
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The inheritance of the 17 camels (Arab tradition)
Hints
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- There is no magic: it is a trick of least common multiple and addition of fractions. The extra camel only allows you to execute an entire distribution compatible with the will.
- That is why it is convenient to take 17 to 18: it makes all partitions whole.
- A camel is temporarily added to work on 18 and then removed.
Solution
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Answer: A camel is temporarily added to work on 18 and then removed.
1) Arithmetic idea
The fractions of the will are
$$ \frac12,\ \frac13,\ \frac19, $$
and its sum is
$$ \frac12+\frac13+\frac19=\frac{17}{18}. $$
That is why it is convenient to take 17 to 18: it makes all partitions whole.
2) Distribution over 18
- to the greatest: $18/2=9$,
- to the second: $18/3=6$,
- to the minor: $18/9=2$.
Total delivered:
$$ 9+6+2=17. $$
Exactly 1 camel left: the one temporarily added.
3) Methodological conclusion
There is no magic: it is a trick of least common multiple and addition of fractions. The extra camel only allows you to execute an entire distribution compatible with the will.
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