Abdul and 10 Thieves

Outline Mathematics
Word Problems

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. Move the mouse over the underline. 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 six,four,five,six pearls left over, and the junior,junior,senior members have already received their portion, so the remaining six,four,five,six pearls must go to the senior,junior,senior 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 four,four,five,six short of the total finger count, the junior thieves were prevailed upon to remove a single finger,a single finger,two fingers,four fingers each. Thus four,five,six,four fellows had to receive five,four,five,six pearls. Which says that the number of those who received five,four,five,six pearls was four. The number of senior members was therefore six,four,five,six.

References

  1. R. Smullyan, The Riddle of Scheherazade, Alfred A. Knopf, 1997

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Copyright © 1996-2018 Alexander Bogomolny

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