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The Harvard-MIT Mathematics Tournament (HMMT) is an annual high school math competition that started in 1998. The location of the tournament is in Cambridge, Massachusetts, and it alternates between Harvard University (November tournament) and MIT (February tournament).The contest is written and staffed entirely by Harvard and MIT students.
HMMT February is attended by teams of eight students each. Teams can represent a single school, or a regional math team as large as a state. In recent years, teams have represented over 20 states, as well as Africa, Asia, Europe, and South America.
The Individual Round consists of exams in Algebra/NT, Combinatorics, and Geometry. Each of the three exams is 50 minutes in length and contains 10 questions. The exams are open-answer; that is, the answers can take just about any format it wants.
For the Team Round, the eight-person teams compete together on a 60-minute-long test. The Team Round is a collaborative event with proof-style combinatorics problems, sometimes arranged into groups of several problems on the same theme. Thorough justifications are required for full credit. The Team Round is worth a total of 400 points, and problems are weighted according to difficulty. This round is targeted at teams comfortable with rigorous mathematical 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.
HMMT February also features events on the Friday evening prior to the tournament. Some of these events include a dinner and social for students and coaches, and Mini-Events such as math talks about famous problems and math-related games.
The top 50 competitors at HMMT February are also invited to compete in the Harvard MIT Invitational Competition (HMIC) which is a five-question four-hour proof contest started in 2013.
Scoring and AwardsEdit
HMMT February uses a unique scoring algorithm to score the competitors on the Individual Rounds. While the problems on these tests are weighted according to difficulty, they are done so after the testing has completed. This helps create a very fair method for weighting problems according to their actual difficulty (as determined by how often and by whom they were solved) as opposed to their perceived difficulty prior to the tournament. The weights assigned to each problem are calculated using a scoring algorithm that takes into account which problems were solved by which students. The weights of the problems on the Team and Guts Rounds are given on the tests.
Prizes are given to the ten highest-scoring individuals overall, the top ten scorers on each of the subject rounds, the ten highest-scoring teams on the Team Round (A and B), and the ten highest-scoring teams on the Guts Round. The top ten teams overall will be named the Sweepstakes winners. The calculation of Sweepstakes scores is roughly half individual round performance and half collaborative round performance.
This competition, as stated above, is considered to be one of the most prestigious high school math competitions in the world. The contest organizers state that, "HMMT, arguably one of the most difficult math competitions in the United States, is geared toward students who can comfortably and confidently solve 6 to 8 problems correctly on the American Invitational Mathematics Examination (AIME)." As with most high school competitions, knowledge of calculus is not required; however, calculus may be necessary to solve a select few of the more difficult problems on the Individual Rounds.
HMMT November has been held since 2008, alternately at MIT and Harvard, for teams of six students. Students are required to come from the United States to participate in this competition, unlike in the February competition, and no student may compete in both November and February in a given school year, due to spacing issues. The tournament is similar in style to HMMT February, and is organized by the same Harvard and MIT students. Instead of three topic tests, HMMT November has two Individual 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). Additionally, the Team Round is entirely short answer, instead of proof-based. HMMT November is considered to be an easier alternative to HMMT February.