http://www.charlesleifer.com/photos/project-euler/
I just learned of a very cool site called Project Euler, named after the mathemetician Leonhard Euler. The site hosts a list of increasingly challenging mathematical puzzles that require some analytical thinking and usually a computer program to solve.
You begin by registering with the site, and then you can access the problems, input your answer and track your progress through the problem sets. A running tally of the number of solvers serves as a decent indicator of how difficult the problem is. When you've got your solution, you enter it in the box and (hopefully) receive a congratulations message!
http://www.charlesleifer.com/photos/problem-solved/
I've had a great time working on these problems, and then reading through the message boards that become accessible to solvers and looking at other people's solutions.
More posts to come as I get some more of these solved!
Edit (10/10/09): Euler solutions are now on GitHub
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