This year's informatics olympiad is this week. There are (I think) four questions each day on Monday, Tuesday and Wednesday. While the contestants take part in Bulgaria, you can follow along at home and submit your answers on the web. Generally you have a problem to solve and must write a program (in C, C++ or Pascal) to solve it within certain time and memory constraints. You can then upload your program to their server and it will be run on secret test data. When the contest is over your grade will be determined by how many test cases it passed. Generally an inefficient program can still gain some marks, but you'll need something with good computational complexity to get maximum marks.
There are training questions already up to get you familiar with the system. The first is deliberately trivial, but the remaining two are rather interesting. Go have a look. I'm going to follow up with a post on each of them to discuss my attempts at solutions.
EDIT - Here's my post on Hill, and my post on Museum.