The Camel Principle
A neat mathematical trick told through a timeless folk tale
Do you know the Camel Principle?
It is a nifty trick we often use in derivations in mathematics and physics. The trick is to add and subtract a term in an expression, usually resulting in a simplification that leads to the solution of the problem at hand.
The Camel Principle got its name from a tale in ancient Arabian folklore. Long ago, there lived a rich merchant in Arabia whose property consisted of an oasis and 17 camels. He had three sons. Unfortunately, he died while his sons were still young, leaving behind a will to be executed. The will was a bit strange.
It stated that the oasis would remain in the common possession of the sons, while the eldest son was to receive half of the 17 camels, the second son one third, and the youngest one ninth. When the sons tried to divide the camels, a great dilemma arose. The camels could not be perfectly divided into a half, a third, and a ninth. The elders they consulted could not resolve the problem either. A greedy relative even suggested killing all the camels for a feast and selling the meat, then dividing the money among the sons, but the brothers loathed the idea.
Finally, a wise man from India came along — and he turned out to be a mathematician as well. When the sons asked him how to solve their dilemma, he thought for a moment and replied, “Seventeen is a prime number, so it can’t be done in the normal way. Let me add and subtract.” Then he brought one of his own camels and added it to the herd. “Dear young chaps,” he said, “behold — we now have 18 camels. The first son gets half of these, which is 9 camels.” He led 9 camels to stand beside the eldest son. Then he called the second son and said, “Now you get one third of the camels.” He gave him 6 camels. Finally, he granted the youngest son 2 camels, which is one ninth of 18. After that, the wise man took back his own camel — the one remaining after the sons had received 9 + 6 + 2 = 17 camels in total.
If you think the wise man cheated by adding his own camel, remember that he only increased the count temporarily—something the boys themselves would readily agree to!
Mathematical takeaway: Sometimes a problem becomes simple if we temporarily add something convenient, solve in that setting, and then subtract it away — changing the form, not the value.
