The seventeen camels

Question

A man dies leaving 17 camels to his three sons: half to the eldest, one third to the middle son and one ninth to the youngest. Half of 17 is 8 and a half, and camels cannot be shared, so the sons are stuck. A stranger rides up on his own camel, adds it to the herd to make 18, gives the eldest 9, the middle son 6 and the youngest 2, takes his own camel back, and rides off. Everyone is happy. Explain how this can work. Did the sons get more or less than their shares? Where is the trick?

Accepted Answer

The will does not add up to a whole: one half plus one third plus one ninth is 17/18, not 1. The stranger's camel fills the missing eighteenth, and each son actually receives slightly more than his stated share. The fractions. 1/2 + 1/3 + 1/9 = 9/18 + 6/18 + 2/18 = 17/18. The father's will only allocates seventeen eighteenths of the estate, which is why 17 camels split into 17/18 parts so awkwardly: each "share" of a 17-camel herd is a fraction of a camel. What the stranger does. With 18 camels, half is 9, a third is 6, a ninth is 2. These are whole numbers and they add to 17, leaving exactly…

The seventeen camels

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