Least wasteful use of stamps to achieve a given postage 
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?

This is a simple variation of the Knapsack problem. Which is a NP-Complete problem.
Let n to be the target value, it can be solve using knapsack's dynamic programming solutions.
If you have a finite amount of stamps, then you can add them all up, subtract the target value. Run 0-1 knapsack on the stamps with the resulting number. The stamps outside the knapsack is the solution.
If you have a infinite amount of stamps. You can either make them finite: $\lceil \frac{n}{t_i}\rceil$ stamps for stamps with value $t_i$ and run the above process, or you can compute the result by running knapsacks O(log n) times similar to a binary search.
It's no better than a naive backtracking solution when n is large. I assume you are not going to pay $100 for stamps. ;)
