The Mathcamp Puzzle Hunt is an all-day event in which teams of about eight people collaborate to solve a series of very challenging puzzles. Some teams play to compete, some just to have fun solving. The puzzles are intense: they require finding complex hidden patterns and lots of fiddling and exploration. Sometimes they'll also involve some running around or exploring the campus.
Each year's hunt has a website that archives the problems. You're welcome to take a look and see what progress you can make!