The Online Math Open is an online math competition for teams of up to four people. This competition is renowned for having some of the most interesting, elegant, and high-quality problems written by the best high school students in the nation. For more information, see here.
To quote an official announcement
We are pleased to announce that the Fall OMO 2014 will be taking place from October 17 to October 28, 2014. You can register a team by following the instructions on our info page. OMO is a team-based contest, and we allow for teams to be up to four people. (Teams of size less than four are welcome too. In fact, every year some brave individuals solo the OMO!)
We've created a set of thirty short-answer problems ranging in difficulty from easy to very challenging. Hopefully, you will find these problems to be instructive, elegant, but most importantly, fun to work on.
Cheers, The OMO Team