I like maths problems! You can see some of my competition experience at the International Mathematical Olympiad here. Here are some useful resources and documents if you like them too:
The Art of Problem Solving website has some great links and resources
26 years of Irish Maths Olympiad problems. Some other useful stuff is elsewhere on the IRMO website and those of the training centres.
Past papers of the International Maths Olympiad. Pick your difficulty based on the year, more recent is generally harder.
Some books and PDFs:
Problem Solving Strategies by Arthur Engel. A great book on some useful methods for looking at problems.
Basics of Olympiad Inequalities by Samin Riasat. Does what it says on the tin.
And here are 6 of my favourite problems:
