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

that it was his due, but his companion who had three breads did not agree to such a division also reasoning that the stranger who had shared their food had not given them the eight Dirhams to them to share proportionately according to the number of breads they had. Moreover, he argued that the share of the stranger was equal to each of their own. Therefore, he claimed that what the stranger had given them had to be divided equally. Finally they decided to approach Hazrat Ali (A) for a decision between the two. Having heard the case Hazrat Ali (A) first advised them for a compromise and when they did not agree, particularly the one who had three breads, he solved the problem as under:

He said to the one who had three breads and had taken the case to him with the claim that half of the eight Dirhams, i.e., Four Dirhams was his due share:”If you want a righteous decision in the case you should have only one Dirham which is your due actually. When requested to explain he enlightened him as follows:

He asked him; “Had you not had only three breads and your companion five of them?” When he replied in the affirmative he said; “The total of the breads you both had i.e., eight divided into three bits comes to twenty four. And as you say the stranger shared your food equally he should have eaten eight bits, i.e., only one of the nine bits of your breads, seven of them eaten from other’s, that is why you should have only one Dirham for only one bit of the eight bits of breads which the stranger ate.

Feeling uneasy at the above decision of Hazrat Ali (A) the claimant who had taken the case to him agreed to the compromise he had advised for and to the offer of three Dirhams made by his companion. (Zakhaerul Uqba, p. 84, also Kafi)


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