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
If the executor divided the 17 camels according to the will, then
There is of a camel left over.
However, if the executor divided 18 camels, then
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.