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? (3/3)

...

There are a good many equally correct answers to this question. Here is one of them:

A 6 × 12 = 72

B 12 × 3 = 36

C 17 × 1 = 17

D 120 × ½ = 60

E 45 × 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.

(2/3)

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?

(1/3)

was lost by Mr. Potts, and had the effect of doubling the money then held by his wife and the professor. It was then found that each person had exactly the same money, but the professor had lost five shillings in the course of play. Now, the professor asks, what was the sum of money with which he sat down at the table? Can you tell him? (2/2)

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Puzzles from Henry Ernest Dudeney's "Amusements in Mathematics"

Source: https://www.gutenberg.org/ebooks/16713

Joined Sep 2017