# Sunday Times Teaser 3015 – Quid Quo Pro

*by Victor Bryant*

#### Published Sunday July 05 2020 (link)

In Readiland the unit of currency is the quid. Notes are available in two denominations and with these notes it is possible to make any three-figure number of quid. However, you need a mixture of the denominations to make exactly 100 quid. Furthermore, there is only one combination of denominations that will give a total of 230 quid.

What are the two denominations?

3 Comments
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Here is a longer but faster solution:

Brian

You have not explicitly shown that there is no solution with F(a,b)>999 (however obvious that may be).

Tony

Hi Tony, I don’t see the relevance of any F(a, b) value above 99. Since all values above F(a, b) can be made by summing multiples of a and/or b, I have ensured all values with three or more digits can be made.