how to share the herd of horses?

If it is a question of sharing 18 horses in three equal parts, nothing more simple, it is enough to give six horses to each heir. The last wishes of a deceased person can singularly complicate the work of the notary. Here is a story of paradoxical heritage.

A man had three sons and a herd of horses. When he died, he had decided that his flock should be divided in half for the oldest, a third for the youngest and the ninth for the last. When he died, he had 17 horses.

Since the calculations were not correct, the notary decided to borrow a horse from a neighbor, which made 18 horses in all. He therefore gave 18/2 = 9 horses to the eldest, 18/3 = 6 horses to the youngest and 18/9 = 2 horses to the last. He had thus distributed 9 + 6 + 2 = 17 horses, so there remained one, which he returned to the neighbor. In addition, each had more horses than expected. The first, 1/2 more horse, the second, 1/3 and the last 1/9.

Question:

Where do these surpluses come from?

Reply :

It is a simple miscalculation. The sharing of the father left a part of an eighteenth of horse not allocated because 1/2 + 1/3 + 1/9 = (9 + 6 + 2) / 18 = 17/18.