Two brothers, both princes, had an argument.

Two beautiful maidens had been presented to their father, the Sultan, by the ruler of a neighbouring land (a custom which is, naturally, abhorrent to us now, but was certainly acceptable to the princes, and, as it happened, to the maidens in question). The argument, then, was over to which prince (or princes), the maidens should be wed.

“As I am the elder,” began the elder brother, “my claim to the throne is twice as great as yours, and thus I am twice as worthy of this honour. It is only fitting that I marry both maidens.”

“Ah,” replied the younger, “but that leaves me with no maidens. And if your claim is indeed twice as great as mine, with which I have not the slightest quarrel, then twice nothing is still nothing.”

This puzzled the elder brother, but he hid it well. Clearly, he would make an excellent Sultan.

“What do you propose, brother?” he asked.

“I propose,” replied the other, “that each of us have a share of the maidens, according to our rightful position. I, as the lesser, shall have one share, and you, twice as worthy as I, shall have two shares.”

“But that makes three shares, and there are only two maidens,” countered the elder brother, after only a moment’s consideration.

“Well, naturally, some calculations must be performed,” said the younger brother. “There are now a total of three shares, of which you, honoured brother, claim two, and I claim one. The maidens, then, must be apportioned equally: two thirds to you, and the remaining third to me.”

Here, his brother started to object, but he raised a hand and continued: “I see you have spotted a potential problem with the division of the maidens. After all, of what use to a man is one third of a maiden (for any third, without the others, is clearly without worth)? But the answer is simple. Here, let each maiden be represented by three stones in each of two piles, thusly:”

“Put together, we have six stones, of which you take two thirds — that is, four stones — and I take the remainder.”

“Now, the question is: how can we move the fewest stones so that each pile has either three stones (one maiden), six stones (two maidens), or no stones (no maidens)?”

The elder brother contemplated this at length. He scratched his head and rubbed his beard. His brow furrowed, his nose twitched, and his eyes flashed. Finally, with a triumphant flourish, he moved a single stone from the larger pile into the smaller, sat back, and awaited his brother’s response.

The younger brother applauded vigourously.

“A wise choice, Highness,” he said. “Now your pile has three stones — one maiden — and mine has three also. And no blood need be shed this day.”

The elder brother rose to his feet and, drawing his curved scimitar, neatly sliced off his brother’s head. Then, placing all the stones neatly in a single pile, he left the palace and went riding.