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## THE FIVE BRIGANDS.

(

Money Puzzles)

The five Spanish brigands, Alfonso, Benito, Carlos, Diego, and Esteban,

were counting their spoils after a raid, when it was found that they had

captured altogether exactly 200 doubloons. One of the band pointed out

that if Alfonso had twelve times as much, Benito three times as much,

Carlos the same amount, Diego half as much, and Esteban one-third as

much, they would still have altogether just 200 doubloons. How many

doubloons had each?

There are a good many equally correct answers to this question. Here is

one of them:

A 6 x 12 = 72

B 12 x 3 = 36

C 17 x 1 = 17

D 120 x 1/2 = 60

E 45 x 1/3 = 15

___ ___

200 200

The puzzle is to discover exactly how many different answers there are,

it being understood that every man had something and that there is to be

no fractional money--only doubloons in every case.

This problem, worded somewhat differently, was propounded by Tartaglia

(died 1559), and he flattered himself that he had found one solution;

but a French mathematician of note (M.A. Labosne), in a recent work,

says that his readers will be astonished when he assures them that there

are 6,639 different correct answers to the question. Is this so? How

many answers are there?

Read Answer