Three Sons, Eleven Horses

Here’s an old fraction puzzle. I have no idea who invented this, or whether it is decades or centuries old, but it’s always been a favorite conundrum of mine.

It starts with a man who wills his possessions to his three sons. The will specifies that the eldest son should get half his fortune, the second son a quarter, and the youngest son a sixth.

In time, the old man passed away, and the sons discover that the man’s entire fortune consists of a herd of eleven horses. This presents a problem, since they don’t know how to divide eleven horses by two, four or six. The first son wouldn’t accept just five horses, the others wouldn’t let him take six, and five and a half horses is worse than five!

So the three brothers were arguing by the side of the road, when a wise man rode up. He dismounted and asked them what the problem was. They explained about the father’s will, and how they didn’t know a fair way to give the eldest son half, the second son a quarter, and the third son a sixth of the eleven horses.

The wise man said “Well, why don’t you take my horse?”

They thanked him for his generosity, and proceeded to divide the twelve horses.

The first son took half of twelve, that is, six horses.

The second son took a quarter, that is, three horses.

The youngest son took a sixth, that is, two horses. In the end, there was one horse left over.

“We are satisfied that our father’s wishes have been fulfilled. But what shall we do with the extra horse?” the sons asked.

“Give it back to me,” said the wise man, and he took the reins, mounted, and rode away.

The puzzle is this : Why were the sons able to share eleven horses according to the will, by borrowing this extra horse? And if it’s so easy to fulfill the will, why did they have so much trouble at the start?

I’ve given this puzzle to many people over the years, and only one person was able to explain it to my satisfaction. Can you?