I'm not sure what level of math you're at, but doing previous IMO problems would presumably be useful; here's a book containing over 1900, with solutions.
(Btw, the authors' grasp of English is a little shakey at times, and they rewrote some of the problem statements, so be warned.)
Lately I've resolved to try harder at teaching myself math so I have a better shot at the international olympiad (IMO). These basically involve getting, say, three really hard math problems and trying your best to solve them within 5 hours.
My current state:
What does the intrumental-rationality skill of LWers have to say about this? What recommendations do you guys have for improving problem-solving ability, in general and specifically for olympiad-type environments? Specifically,