Making change

A couple of days ago, Chris Yocum asked me to help him out with some OCaml code. He's learning OCaml at the moment, and thought he'd practice it by solving a problem he'd encountered in his research on early Irish law.

In early Irish law, murder was punishable by a fine dependent on the status of the victim. Ten-and-a-half cows per king murdered (no, really!), five for a major nobleman, and so on. At one particular event, we know the total fine levied, but not the number of victims. Chris wanted to find out the range of possibilities. This is an example of the change-making problem: given small change of various denominations, how can you give your customer 73p? I most often encounter this problem with rugby scores: if Wales beat England 67 - 3 (I can dream...), then at seven points for a converted try, five for an unconverted try and three for a penalty, what might have happened?

( Be the change you want to make )

All suggestions for improvement, as ever, gratefully accepted :-)