Rare Justice: Judgements, Decisions and Answers to Difficult Questions part 19

Mathematical Problems

1. The Equal Division of Seventeen Camels Without Friction Three persons had a dispute about the division of seventeen camels. The ratio of their share was 1/2, 1/3 & 1/9 and they could not divide the figure of seventeen proportionately without friction.

Finding no way out they wanted to cut one camel into pieces for the purpose of the correct division, but before acting upon this last alternative, they took their problem to Hazrat Ali (A), for they were sure it was he who was capable of solving their problem.

Hearing their problem Hazrat Ali (A) asked them if it was agreeable to them to add one of his own camels to their seventeen camels and make the total eighteen. As they agreed to it, he gave half of the total number of the camels i.e., nine to the first man (1/2 of the total), and six to the second man making 1/3 of the total, and two camels to the third man which is 1/9 of the total. Thus all the three men got the camels divided according to respective shares, the total amounting to seventeen only. Thereafter he took back his own camel. Thus he solved the problem of dividing the seventeen camels proportionately according to their respective shares to their satisfaction and displeasing none of them and without cutting one of the camels into pieces. (Nasikhut Tawarikh vol. 3, p. 757).

2. The Problem of Eight Breads

Two persons while travelling on a road sat under the shade of a tree for lunch. One of them took out of his big five breads and the other took out three breads out of his bag and put them near the five breads of his companion making the total number of the breads to eight. They had not yet started eating when a third person happened to pass by them.

Invited by the first two, the third man also sat with them and shared their lunch and while departing after meal, he gave them eight Dirhams against the share of the food he had taken with them.

After he had gone, the first two travellers started quarrelling about their portions in the eight Dirhams. One of them who had five breads claimed to have five Dirhams reasoning