Harvard-MIT Mathematics Tournament
The Harvard-MIT Mathematics Tournament, usually abbreviated HMMT, is a math competition for high school students organized by students at Harvard University and the Massachusetts Institute of Technology (MIT) each winter. It has been running since 1998. The contest takes place alternatively at Harvard or MIT each year. It is composed of two tournaments, the February Tournament and the November Tournament.
The February Tournament
The February Tournament is the more difficult of the two tournaments, with its problems ranging from mid-AIME to National and International Olympiad level questions.
The Individual Round consists of three subject tests in Algebra, Geometry, and Combinatorics. Each subject test consists of 10 questions and is 50 minutes in length.
In the Team Round, 6-8 person teams compete together on a 60 minute test. The problems are weighted according to difficulty, adding up together to 400 points. The round is targeted at teams comfortable writing rigorous proofs.
The Guts Round is an 80 minute team event with 36 short answer questions on an assortment of subjects, of varying difficulty and point values. Each team is seated in a predetermined spot, and the questions are divided into groups of four. At the starting signal, each team sends a runner to an assigned problem station to pick up copies of the first set of four problems for each team member. As soon as a team has answers for one problem set, the runner may bring the answers to the problem station and pick up the next set. It is not expected that students will finish all the problems. Grading is immediate and scores are posted in real time, resulting in an exciting atmosphere for the competitors. The Guts round is worth a total of approximately 400 points.
Harvard MIT Invitational Competition (HMIC)
The top 50 scorers at the February are invited to compete in the (HMIC), which is a five question proof contest with a length of 4 hours. The problems both years have been quite difficult, with competitors fully solving three problems being extremely highly ranked.
The November Tournament is the less difficult of the two tournaments, with its problems ranging from mid-AMC to upper-AIME questions.
The Individual Round consists of two rounds: a General Test (ten questions from Algebra, Geometry, and Combinatorics) and a Theme Test (ten questions, many of which are tied together by a common theme).
The Team Round consists of short answer questions instead of proof-based questions. Like the February Tournament, the round is 60 minutes long, but teams are 4-6 person teams.
The Guts Round still contains 36 problems, and follows the same format, but the problems the runner picks up come in sets of 3 instead of sets of 4.