HMMT Rules

Events

Five individual tests (a General Test and four Subject Tests: Algebra, Geometry, Calculus, and Combinatorics) and two team events (the Team Round and the Guts Round) will comprise the major events of the Tournament. A portion of the day will also be devoted to numerous mini-events, as described below.

This year, we will have two divisions for the Team Round. The A Division will have difficult proof problems comparable to those from previous years. The B Division will have simpler proofs and/or short answer questions, designed so that teams with less experience with proof questions can have an enjoyable problem solving experience. Teams entered in the B division will not be eligible for Sweepstakes awards. The division designation only affects the Team Round and Sweepstakes awards.

Participation

Each school may attempt to register as many teams as it wishes; a team comprises up to eight individuals. We may not be able to allow all teams to attend; see our registration policy for details. The event is intended for high school students, but any student not yet in high school who wishes to compete is welcome to come. A coach may bring teams that include students from multiple schools or homeschooled students.

Content:

The Subject Tests (Algebra, Geometry, Calculus, and Combinatorics) are 50-minute tests each with 10 short-answer questions of increasing difficulty. Each test is worth a total of 50 points, with problems weighted according to difficulty. Individuals may take any two of the four tests. The problems are generally comparable to those of the Mandelbrot or ARML.

The General Test is a 110-minute test with 20 short-answer questions. It is designed to be more accessible than the Subject Tests to students with less math background and is held concurrently with the Subject Tests. The General Test is worth a maximum of 80 points (the problems are again unequally weighted). The difficulty is somewhat comparable to a Mu Alpha Theta test or tests given in many Southeastern math tournaments.

Participation:

Each individual may choose any two Subject Tests or the General Test, but the choices must be submitted in advance. Note that the General Test counts as 80% of two Subject Tests. However, to lessen the pressure on students who feel more comfortable taking the General Test, only the top six scores from a team will be considered in sweepstakes scoring.

Content:

The Guts Round is an 80-minute team event with 45 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 three. At the starting signal, each team sends a runner to an assigned problem station to pick up copies of the first triplet of 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 triplet. It is not expected that students will finish all the problems. Grading is immediate and scores are posted in real time. The Guts round is worth a total of 400 points. This event originated at the Greenhill High School Math Tournament in Texas, and it is similar to team ciphering at a Florida math tournament, only with a lot more people and excitement.

Participation:

All teams may participate in the Guts Round.

Content:

The A Division Team Round is a 60-minute collaborative event with 15 to 20 proof-style problems, arranged into groups of several problems on the same theme, which may come from any area of elementary mathematics. Thorough justifications are required for full credit. The Team Round is worth a total of 400 points; problems are weighted according to difficulty. The event is similar to an ARML Power Round, but the problems are easier and more numerous. This round is targeted at teams comfortable with rigorous mathematical proofs.

The B Division Team Round is a 60-minute collaborative event (at the same time as the A Division round) with a mixture of 15 to 20 proof-style and short answer questions, which may come from any area of elementary mathematics. Thorough justifications are required for full credit on the proof questions. No Sweepstakes value is assigned to this round.

Participation:

All teams take part in the Team Round.

Content:

For an hour of the competition, a variety of smaller events will be available: ARML-style relays, in which each problem depends upon the answer from a teammate's problem; several informal lectures; combinatorial games tournaments in hex, phutball, and chomp; a game of Buzz; and Rigor Mortis, an event in which teams compete to find the flaws in false proofs as quickly as possible.

Participation:

Individuals may choose which mini-event they wish to attend, if any. Lectures, combinatorial games, and Buzz are open to any individuals, and relays and Rigor Mortis are open to teams of four.

Individual and Team Awards

Prizes will be given to the ten highest-scoring individuals (regardless of choice of tests), the top three scorers on each individual event separately, the five highest-scoring teams on the Team Round, and the five highest-scoring teams on the Guts Round. Several honorable mentions may also be named in each category. Small prizes will also be given out for mini-event winners: the top three teams in relays and Rigor Mortis, the top three individuals in Buzz, and the top four individuals in the combinatorial games tournament.

The School Sweepstakes Award

Prizes will be awarded to the five highest-scoring schools. Each school's sweepstakes score is its top team score, which in turn is determined by summing the six highest individual scores, the Team Round score, and the Guts score (for a maximum of 1400).

You may not use books, notes, calculators, pocket organizers, slide-rules, abaci, or any other computational aids. Similarly you may not use graph paper, rulers, protractors, compasses, architectural tools, or any other drawing aids. These restrictions do not apply to the Guts Round.

Answers

Answers must be simplified and exact unless otherwise specified. For example, 22/7 and 3.14 are not acceptable substitutes for pi.

Rational numbers should be given in lowest terms.

Radicals must be simplified if possible, so that the radicand contains no fractions and is not divisible by the square of any positive integer other than one. Also, denominators should be rationalized.

Correct mathematical notation must be used.

No partial credit will be given unless otherwise specified.

Protests

If a student believes that an answer given on the answer key is incorrect, he must go to the designated Appeals Room and submit an appeal before 12:30 if the protest concerns a morning event and before 3:45 if the protest concerns an afternoon Event.

Tiebreakers

HMMT reserves the right to change the following policy until the day of the contest.

If two papers have the same score, an item analysis will be performed. The paper which has correct answers on harder problems, as determined by the item analysis, will be declared the winner. If a tie remains after item analysis, the tie will not be broken.

Tie breaking / item analysis algorithm:

1. Most questions correctly answered.
2. Last correct answer occuring latest.
3. Iterate step two with the next correct answer, etc. If the tie is not for the top three places, let it stand.
4. First wrong (not blank) answer occuring latest.
5. Iterate step four with the next wrong answer, etc.
6. If two contestants answered the same questions with the same ones correct, the tie stands and the less psychic contestant (think of a number...) will be mailed a will be mailed a trophy later.

Decisions of the coordinators of the Harvard-MIT Math Tournament are final.