Find the least number of coins required that can make any change from 1 to 99 cents

Question

Recently I challenged my co-worker to write an algorithm to solve this problem:

Find the least number of coins required that can make any change from

Answer 1

Assuming you're talking about US currency, you would want a Greedy Algorithm: http://en.wikipedia.org/wiki/Greedy_algorithm

In essence, you try all denominations from highest-to-lowest, taking as many coins as posible from each one until you've got nothing left.

For the general case see http://en.wikipedia.org/wiki/Change-making_problem, because you would want to use dynamic programming or linear programming to find the answer for arbitrary denominations where a greedy algorithm wouldn't work.