The following problem was invented by an unknown arabic mathematician many thousand years ago. The problem is very beautiful and that’s the reason why it survived all these thousand years.
3000 years ago there were no cars, no refrigerators, no electricity, no money. People did not go to work, and there were no schools. Life was really different from what we are used to today. In an arabic country, since there was no money, wealth was measured in real assets, like camels.
At that time, there was a wealthy men who had 3 sons. Among his most prized possessions were 17 camels. He was also known to be very shrewd. In his will, he determined that his oldest son should get 1/2 of his estate ( = whatever he owned at the time of death), while his second born son should inherit 1/3 of his estate. His youngest son, being the youngest should inherit 1/9 of his estate. (In case you wonder, at that time people did not believe in fairness. The first born son was always prefered).
After the father died, the three brothers were quite happy to inherit that wealth. After all, owning 17 camels is like owning 17 big trucks today except that trucks do not produce milk while camels do. They loved and respected their father very much so they were quite eager to satisfy the will of their father exactly. However, they did not like the idea of killing some of the camels in order to honor the last will of their father:
1/2 of 17 camels makes 8 and 1/2 of a camel figured the oldest brother,
1/3 of 17 camels makes 5 and 2/3 of a camel calculated the second brother,
1/9 of 17 camels makes only 1 and 8/9 camels thought the youngest brother.
A dead camel was not worth much, so it made perfect sense that they hesitated to proceed with the execution of the will. How could have our father made such a mistake in his will, they thought. He must have been very bad in arithmetic they thought. They asked their friends for advice, but nobody really knew what to do in this case. Finally, somebody recommended that they travel to the next large city where a well known old philosopher was living. He was known to have solved many difficult problems. Eager to solve their problem, they followed that advice and travelled to the big city (taking their camels with them – you could not leave anything behind since there was no police at that time) and found the wise men after some effort.
The philosopher offered them some tea and then listened to their story. “I agree, this is a difficult problem and I do not know what to do. But please come back tomorrow morning, perhaps I have an idea over night”.
The next morning they came back and found the old men already expecting them. Says he: “This was indeed a very difficult problem, and I had to think all the night long before I saw how to solve it. Before solving your problem, let me make you a gift. I am very much impressed by your eagerness to honor the will of your father, so I will give you in addition to the 17 camels you already own one more camel out of my own possession.”
The three brothers were now very excited, they got a free camel, great! OK, said the old man. Let’s now try to execute the will of your father. You, the oldest son, how much are you supposed to get? One half of 18 camels, says the oldest son. That makes 9 camels concludes he with satisfaction in his voice. And you, second som, how much are you supposed to get? Well, answers he, one third. OK, how much is one third of 18 asks the philosopher? Sir, that’s 6 camels. OK take the 6 camels. Finally, he turns to the youngest son and asks him: How many camels do you get? Well sir, answers the third brother, I am supposed to get 1/9 of 18 camels which makes precisely 2 camels.
The three brothers take the 9 plus 6 plus 2 camels away and discover to their surprise that there is one camel left. (9+6+2 = 17 but there were 18 camels). “This camel”, says the old man, “happens to be my own camel and, although I gave it to you as a present, I will now take it back as a fee for the service I performed by solving the problem”.
The three brothers were extremely pleased. No camel had to be killed, and yet the will of their father was completely satisfied. Full of admiration for the wisdom of the old men, they thanked him many times and left back home. Going over the miraculous solution on the way home, they started to realize that their father must have known arithmetic much better than they thought originally.
