MIT runs a summer program called RSI where high school students come in and work on research with MIT professors and postdocs. There are research projects in all sorts of scientific fields, including many in mathematics.
This year, the RSI math students have decided to start a blog. About half their posts seem to be background to their research, like this post on classifying the representations of . The other half seem to be puzzles and Olympiad problems; for example, this post starts out by talking about the first US Olympiad problem ever, and moves to discussion of lattices and mobius functions.
Give them a visit at deltaepsilons.wordpress.com/!