how to share the herd of horses?

Since time immemorial, notaries have had to carry out complicated divisions between heirs. Here's how to split 18 horses into three equal parts.

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.

Find out more about Hervé Lehning

A normalien and an aggregator of mathematics, Hervé Lehning has taught his discipline for some forty years. Crazy about cryptography, a member of the Association of Reservists of the cipher and information security, he in particular broke the secrets of the encryption box of Henri II.

  • His blog MATH'MONDE on ABSMARTHEALTH

  • The Hervé Lehning's latest book :

Also to discover: The universe of secret codes from Antiquity to the Internet published in 2012 by Ixelles.

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