Outline Mathematics
Word Problems

Abdul and 10 Thieves

Here's a problem to tackle:

"Another time," Said Scheherazade, "ten thieves stole into Abdul's shop. Some of them were armed and some were unarmed. The armed ones were those of senior rank. Anyway, they stole a bag of fifty six pearls. When it came to dividing them up, each senior robber took six pearls, and each junior robber got five. How many of the robbers were senior?

Solution

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Copyright © 1996-2018 Alexander Bogomolny

Solution

"Another time," Said Scheherazade, "ten thieves stole into Abdul's shop. Some of them were armed and some were unarmed. The armed ones were those of senior rank. Anyway, they stole a bag of fifty six pearls. When it came to dividing them up, each senior robber took six pearls, and each junior robber got five. How many of the robbers were senior?

(In the text below, some words are omitted. These have been underlined. Click just above the line. See what happens.)

This can be solved in many ways: by trial and error, using algebra, or common sense as below.

First let each take five pearls. There are then pearls left over, and the members have already received their portion, so the remaining pearls must go to the men, so there are six senior thieves.

Now, relying on common sense is a risky enterprise. For, somebody's common sense may not be the same as somebody else's. For example, I see a different way to handle what's happening. To maintain silence, the robbers agreed to show on fingers the number of pearls each of them would like to receive. It so happened that all of them showed six fingers. Since the real number of pearls was short of the total finger count, the junior thieves were prevailed upon to remove each. Thus fellows had to receive pearls. Which says that the number of those who received pearls was four. The number of senior members was therefore .

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Copyright © 1996-2018 Alexander Bogomolny