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There is a well-known story (the details vary) of a father who, when he died left his seven camels to his three sons in the following way: The eldest son was to receive one half of the camels, the middle son was to receive one fourth, and the youngest was to receive one eighth. This will disturbed the sons greatly, because it seemed to necessitate cutting some of the camels into pieces. The family's wise neighbor volunteered to solve the problem for them. He added one of his own camels to the herd, bringing the number up to eight. Then the eldest son received four, the middle son received two, and the youngest son received one camel. The wise neighbor then took back his camel, and everyone was happy. Kinda amazing, huh? Was this solution fair?
Answer: The solution is fair, but only because everyone was happy. The above clever solution does not actually fulfill the terms of the will. The terms of the will result in the following division of camels. The eldest son gets 3.5 camels, the middle one gets 1.75 camels, the youngest gets .875 camel, and nobody gets the remaining .875 camel. The neighbor's clever solution is just a way of dividing up the remaining .875 camel between the three brothers so that all of them get whole camels, instead of parts of a camel. The will did not say what to do with the extra .875 camel. Presumably it is fair to divide it among the sons, and not pay it as taxes or whatever.
Addendum:
I received email describing the above puzzle with different fractions. That email was wiped out by a virus. So, I am not sure of the numbers. I think that the sons are asked to divide up the herd of eleven camels into 1/2, 1/4, and 1/6. The rest of the story is the same. One might guess that the puzzle could be told with infinitely many different combinations of numbers. But, if there are three sons, and we insist upon three different unit fractions (a fraction with 1 as the numerator), and the wise neighbor only loans out one camel, then it is fairly well known that there are only seven sets of numbers that will work:
| camels | first son | second son | third son | |
| 1 | 7 | 1/2 | 1/4 | 1/8 |
| 2 | 11 | 1/2 | 1/4 | 1/6 |
| 3 | 11 | 1/2 | 1/3 | 1/12 |
| 4 | 17 | 1/2 | 1/3 | 1/9 |
| 5 | 19 | 1/2 | 1/4 | 1/5 |
| 6 | 23 | 1/2 | 1/3 | 1/8 |
| 7 | 41 | 1/2 | 1/3 | 1/7 |
It is not very difficult to show that the first son must receive half, otherwise we need more sons for the sum to come within a unit fraction of 1. And similar considerations set limits on the other fractions. This puzzle is related to Egyptian Fractions. Sometimes the story is about horses.