Someone turned me on to Project Euler last night and I have to admit its quite a gem.  From the site:

"Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems."

Each problem should take less than a minute to solve once the solution is implemented; my newer computer gives me a much needed handicap.  This is excellent for me since Math is an area where I've not been very successful at self study.  I didn't register yet but I solved #1 and #2 as fast as I could type and then began over-engineering my solution to #3 by attempting to implement a Sieve of Atkin in C#.