I have stumbled across this website off and on through my education and the forces which inspire participation have finally converged in time and space to affect my joining up.
Project Euler is a website which simply poses questions of mathematical (primarily number theory) interest which generally require a clever algorithm and expression in some computer language. The questions are well stated and challenging.
You can register and let the site keep track of which problems you have solved. When you solve a problem, you can look at a message board with comments and code snippets from people who have also already arrived at the solution. This has been a good challenge for me as I try to learn and relearn how to program.
The last problem I solved (don't worry, I won't give away the answer) asked for the sum of the prime factors of 20,000,000C15,000,000, which is a rather large number that can be found about a quarter of the way through the twenty-million and first row of Pascal's triangle, but I rarely write that many rows.
Leonhard Euler was a Swiss mathematician who would have enjoyed these problems. Blind and hundreds of years before Java, he still would have knocked the socks off the likes of me.