Testing Information

Both tournaments feature individual tests, a team round, and our signature guts round. The testing formats differ slightly between the two tournaments: see this page for a summary of the differences.

You may not use books, notes, calculators, pocket organizers, slide-rules, abaci, or any other computational aids on any HMMT event. Similarly you may not use graph paper, rulers, protractors, compasses, architectural tools, or any other drawing aids. In addition, communication devices such as laptops, PDAs, and cell phones are prohibited.

A full team is considered as 6 students for November's tournament and 8 students for February's tournament. The scoring system for teams aggregates the sum of the individual scores, team round score, and guts score. Thus, it is advantageous to have a full team.

Individual Tests

Each individual test is 10 problems and 50 minutes long, where all answers are single values (i.e. short answers).

The November tournament includes two individual tests

  • General round, drawing from all high school mathematics subjects.
  • Theme round, which is organized into two five-problem themes.
The problems on these exams range from mid-AMC to upper-AIME in difficulty.

The February tournament includes three individual tests:

  • Algebra test, which covers topics from high school algebra and number theory.
  • Geometry test, which covers high school Euclidean geometry.
  • Combinatorics test, which covers high school combinatorics.
The February problems are challenging, ranging from mid-AIME problems to problems which would be suitable for national olympiads such as USAMO.

Scoring

For individual tests, we employ a post-weighting scoring algorithm on our individual tests. Click here for a description of this algorithm. (Other exams are scored traditionally.)

Team Round

The Team Round is a 60-minute, 10-problem test where all members of a team work together. The point weights for each problem are indicated on the exam.

The November tournament’s team round is short-answer based. The problems are often organized into themes. The difficulty is similar to that of the General and Theme round.

The February tournament’s team round is proof based. As a result, students attending the February tournament should feel comfortable crafting and writing rigorous proofs. This is the only round in which teams earn partial marks (unless otherwise specified on the exam). The February Team round is quite difficult; some of the problems are comparable to the hardest problems on national olympiads such as USAMO.

Guts Round

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. The problems are divided into sets of 3 (November) or 4 (February). The point weights for each problem are indicated on the exam.

All teams gather in one of two large lecture halls. At the starting signal, each team sends a runner to an assigned problem station to pick up copies of the first set 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 set. It is not expected that students will finish all the problems. Grading is immediate and scores are posted in real time.

Sweepstakes

Sweepstakes refers to the aggregate scores of each team, used to determine the overall team winners of the contest. The sweepstakes score is defined as the sum of three components:

  1. Individual Total, worth 800 points.
  2. Guts Round, worth 400 points.
  3. Team Round, worth 400 points.
The scores for each component are calculated as follows. The raw score for the Guts and Team Round is the sum of the specified problem weights. The raw score for the Individual Total is the sum of the individual alpha values of students on that team. Then, each component is weighted by a constant factor in such a way that the top score for that component is the number of points it is worth (800 for Individual Total, or 400 each for Guts/Team).

In particular, the maximum possible sweepstakes scores is 1600, which is achieved if and only if the first place team had the highest raw score in all three components across all teams.

HMMT Invitational Competition

Starting in 2013, the top 50 students from the February tournament are invited to compete in the HMMT Invitational Competition, which is a 4-hour, 5-problem olympiad-style exam. See here for the rules of the 2016 HMIC.