Here's an easy ad-hoc Prolog program for the first problem:
% Given a set of coin denominations,
% find the minimum number of coins
% required to make change.
% IE for USA coinage and 37 cents,
% the minimum number is four
% (quarter, dime, 2 pennies).
num(0). num(1). num(2).
num(3). num(4). num(5).
?- num(Q), num(D), num(P),
37 is Q * 25 + D * 10 + P
You can just paste it into [1] to execute in the browser. Using 60 as target sum is more interesting as you can enumerate over two solutions.
[1]: https://quantumprolog.sgml.net/browser-demo/browser-demo.htm...
3
2