There's always the classic "making change" problem:

What is the least number of coins required to total $x.xx?

Variations on that problem could include:

• Allow the user to input the value of each coin (instead of relying on the assumed values of a penny, nickel, etc)
• Add restrictions on the maximum (or minimum) number of coins available (e.g., you can use no more than one nickel)
• Find a solution that uses some exact number of coins
• Count how many different ways are possible (using any number of coins)