Guess what's cool? The Internet Problem Solving Contest is cool. Like the ACM International Collegiate Programming Contest and TopCoder, it is a competition focusing on the ability to design and implement non-trivial algorithms quickly. Below are some sample problems to give you an idea of what is involved in this.

• A Tiling Problem from IPSC
• The Problem Set of the 2003 ICPC World Finals

The problems normally take the form of little combinatorial or geometric math puzzles suited to solution techniques such as divide-and-conquer, greedy techniques, or dynamic programming. Such problems are not really representative of real, everyday programming tasks, but they are a fascinating diversion and an excellent mental workout. Developing the ability to solve them quickly is very useful for your mathematical skills.

I was on UW's ICPC team for one year, but I no longer have time to spent on these activities. It's really fun to try solving some of the problems, though; both the IPSC and ICPC have large archives of past problems available on their websites.