Say I wanted to be able to carry enough coins in my pocket such that at any time, I could count out exact change totaling any of the prime numbers less than 100. How would I determine the minimum set of coins I would need to carry? I don't care about being able to count out multiple primes - meaning the set does not have to remain useful after one number has been counted out.
So, given the standard US coins: penny, nickel, dime, and quarter - what would be the minimum number of each coin that I would need to be able to count out exactly $3, 5, 7, 11$ up to $97$ cents.