The third major type of summer math camp focuses on problem solving. The Mathematical Olympiad Summer Program (MOSP or MOP) is the best of these, but it's the US math olympiad training camp; people qualify based on USAMO or USAJMO scores as opposed to applying.
As far as I know, the first non-MOP problem solving camp in the US was AwesomeMath, which started in 2006. Pretty quickly, others began popping up, and many have multiple locations. Students tend to be in middle school or the first couple of years of high school. The camps tend to split students up by level, and students in each level cover two subjects a day, one in the morning and one in the afternoon.
Lots of the camps have day camp as well as residential camps. I'll write only about the residential sites/formats here, but check the websites for day camp details.
Details about the various camps and the locations/dates for 2013 are below the fold.
