Hey everybody,

Recently, I've ran into an interesting problem in a good book by Sasha
(rec. math book), and I hope I'm not braking any copyrights by stating
this problem. I'll call it the currency problem. I would like to
compare answers with anybody else who wants to attempt the same
problem.

You are given a task to set up three different coins for a currency
system for a king of a small kingdom. The prices in the kingdom range
from 1 to 99 cents and all are equally likely to occur if you purchase
something in the kingdom. The objective is, is to minimize the number
of coins one should need to use (given that the coins you need for the
purchase are always at your disposal) for any given purchase.
Obviously, one will need a one cent coin, so we should only have to
find the value for the other two. I found that a 1, 4, and 15 cent
coins does the trick with the total number of coins used for purchases
1 through 99 is 198. I did this in Maple 10.0 and my code is on my
webpage here: (under construction, follow to projects page)

http://web.unbc.ca/~minarm/

Extensions of this problem would be to give a solution for four coins,
etc. and to find non-integer solutions (useless, I know, but
interesting) via a non-discrete model. Give it a shot! Post here or
e-mail me at majamin@gmail.com with your attempts. Thanks,

M.M.