A few weeks ago a farmer died. And the will he left behind... fortunately his three sons had had a good education. His will was as follows:

• The first son would get 1/2 of the cows,
• The second son would get 1/3 of the cows and
• The third son would get 1/9 of the cows.

At first, everything seems fine. But unfortunately, the farmer had 17 cows. And pieces of cows weren't any good to the sons.

But, since the sons had a good education, they came up with a solution. They lent a cow from the neighbour. Why? Then they had 18:

• 18 * 1/2 = 9 for the 1st son,
• 18 * 1/3 = 6 for the second son and
• 18 * 1/9 = 2 for the third son.

'But what about the neighbour,' you may say. Well, since 9 + 6 + 2 is 17, the cow that was left over went back to the neighbour.

What do you think about the sons' education?

Each son got more than he deserved: The first son deserved 9/18 of the herd, but he got 9/17 of the herd. The second son deserved 6/18, but he got 6/17. The third son deserved 2/18, but he got 2/17.

In effect, the remaining 1/18 share (unaccounted for in the problem statement) was divided among the sons, proportionally to the size of each bequest.

Which is all fine and well, until the owner of the remaining 1/18 share shows up to claim his inheritance.

Posted by Jim Lyon on 2002-09-14 18:55:02