You have sheets of $42$-cent stamps and $29$-cent stamps, but you need at least $\$3.20$ to mail a package. What is the least amount you can make with the $42$- and $29$-cent stamps that is sufficient to mail the package?
A contest problem such as this is probably most easily solved by tabulating the possible combinations, using $0$ through ceiling(total/greater value) of the greater-value stamp and computing the necessary number of the smaller stamp and the total postage involved. The particular example above would be solved with a $9$-row table, showing the minimum to be $\$3.23$, made with seven $42$-cent stamps and one $29$-cent stamp.
Is there a better algorithm for solving this kind of problem? What if you have more than two values of stamps?