HMMT Rules

General | Registration | Testing | Awards | Calculators | Grading

General Information

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 be composed almost exclusively of 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.

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Registration Policy

How do I register?

Teams can register at hmmt.mit.edu/welcome.

The HMMT has received an increasing number of student registrations over the past several years. Our capacity is approximately 600 students, and last year we had to turn away even some teams that registered on time. If we again have too many registered teams, we will give priority to the first few teams registered per school. You should register on time to maximize your chances of being able to attend.

The regular registration deadline is December 1. Organizations that register by December 1 will be sent email by December 15, confirming if we have space for them to attend. All teams registered by December 1 will have priority over all teams registering after that date. No new reservations will be accepted after February 1.

Schools should not pay for teams until we have confirmed by e-mail that we will have space for them. In case of cancellations, we will inform schools on our wait list that they can bring (additional) teams.

If I already registered last year, am I all set?

No. Whether or not you registered last year is irrelevant. You need to reregister every year that you compete.

Am I really supposed to determine how many students I'm bringing, which students to put on which teams, and what subject tests each student is taking all by December 1st?

Before December 1, all parts of registrations may be changed freely. From December 2 through February 1, the names of students, the tests they are taking, and their teams may be changed freely. Any extra students added will be treated as late registrations. After February 1, no changes will be allowed. Until February 1, we will give refunds if a student is not able to come. After February 1, there will be no refunds.

What if I don't have a team? Can I register as an individual?

Yes! Any student without a team is welcome to register their own team with only one student on it. The student will be considered equally for individual awards and be placed on a composite team for the team rounds.

How much does it cost to attend the competition?

The participation fee for teams registered before December 1 and paid for by February 1 is $10/student. (Note that this means you should mail payment before then.) The fee for any teams registered after December 1 is $15/student. Regardless of when registration occured, if the registration fee has not been paid by February 1 it rises to $15/student, and then to $25/student on the day of the contest.

How do I pay?

Schools should not pay for teams until we have confirmed by e-mail whether and how many of their students we have room for.

Make checks payable to Harvard-MIT Math Tournament. Send them to
HMMT c/o Maria Monks
290 Mass Ave
Cambridge, MA 02139

Are there any other policies that I should be aware of?

We require each school to provide one adult per team to help proctor on the day of the contest. This proctor must be available between 10:00 and 12:30. If you can't manage to bring one proctor per team, please contact us at hmmt-request@mit.edu for an exception.

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Testing Information

Individual Tests | Guts Round | Team Round | Mini-Events

Individual Tests

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 out of 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 100-minute test with 20 short-answer questions, split into two 50-minute halves. 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.

Starting in the 2007 tournament, the overall individual rankings will be determined according to the following scheme. The average of the top 10 scores will be calculated for every test. Students' scores on each test will then be divided by the appropriate averages. Students taking two subject tests will have their two resultant numbers added, and students taking the general test will have their single resultant number multiplied by 1.6. The individual winner will be the student having the highest aggregated score, etc. We hope that this scheme helps balance tests with different difficulties.

Also new in 2007, the individual component of the team sweepstakes score will be calculated from aggregated scores. Details below.

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 roughly 80% of two Subject Tests.

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Guts Round

Content:

Historically, the Guts Round has been an 80-minute team event with 45 short-answer questions on an assortment of subjects, of varying difficulty and point values. Starting with the 2007 HMMT, the round will be shortened to 36 questions, (but will be otherwise unchanged). 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 approximately 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.

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Team 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.

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Mini-Events

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; informal lectures; a game of Buzz; campus tours; etc. The mini-events available vary with each year.

Participation:

Individuals may choose which mini-event they wish to attend, if any.

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Awards

Individual and Team Awards

Prizes will be given to the ten highest-scoring individuals (as explained above), 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 may also be given out for mini-event winners.

The Sweepstakes Award

Prizes will be awarded to the five highest-scoring teams. Each team's sweepstakes score is determined by summing the corresponding adjusted individual, team, and guts round scores. Adjusted scores will be computed as follows. The aggregated individual scores (computed as described in the "Individual Tests" section of this page) obtained by the members of each team will be added, and these totals assigned to each team. These sums will then be scaled so that the largest adjusted score obtained by any team is 800. The team round and guts round scores will also be scaled, but by constants chosen to set 400 as the highest adjusted score on each. For each team, the three numbers so obtained will be added, and the winning team will be the team having the highest total, etc. We hope that this system ensures that the winning teams gain approximately half of their point totals from the individual tests and half from the cooperative rounds.

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Calculators and Other Computational Aids

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. However, even during the Guts Round, communication devices such as but not limited to laptops, PDAs, and cell phones are prohibited.

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Grading Requirements

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 in writing. The deadline to do so will be announced on the day of the contest.

Tiebreakers

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. Last correct answer occuring latest.
  2. Iterate with the previous correct answer, etc.
  3. First wrong (not blank) answer occuring latest.
  4. Iterate with the next wrong answer, etc.
  5. 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 trophy later.

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

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This page is maintained by Beth Schaffer <hmmt-webmaster@mit.edu>.