**From New Scientist #1367, 21st July 1983** [link]

I wonder if you could answer the following question from Hind’s *Algebra*, “designed for the use of students in the University”, published at Cambridge in 1839.

“In how many different ways may £100 be paid in crowns and moidores?”

Before answering you might ask —

*A*. Am I to include ways using only crowns or only moidores?

*B*. How many shillings is a moidore worth?

The answer to *A*, I can tell you, is “no”. The answer to the question is 14.

Now can you answer *B*? You will find you cannot be certain. But, assuming a moidore to be worth an exact number of shillings, what is the smallest and what is the greatest possible number of shillings in a moidore?

(Note to overseas and young readers: £1 = 4 crowns = 20 shillings).

**Note:** I am waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment. The current estimate is that the line will be connected at the end of September 2014.

[enigma221]

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This Python program runs in 106ms.

Solution:The smallest possible value for a moidore is 27 shillings. The largest possible value is 140 shillings.The other possible values are 28 shillings and 135 shillings.

The dictionary on my computer defines a

moidoreas:This is an example of a ‘frobenius problem’ (see http://ccgi.gladman.plus.com/wp/?page_id=563)