2025 Berkeley Math Tournament

The Berkeley Math Tournament (BMT) 2025 will take place in two parts:

• Asynchronous Power Round: November 29–30, 2025

• Live Event: December 6, 2025

Contest Format

Power Round (Async)

The Power Round is a proof-based team round. Contestants will answer a series of questions centered around a single topic not typically seen in competitive mathematics, culminating in incredible results in the field of that chosen topic. For all questions (unless stated otherwise), teams will need to provide a rigorous mathematical justification for their assertions in full sentences.

The topic for the Power Round will likely be at an undergraduate level, but no substantial previous mathematical background is expected.

Individual Round

For the Individual Round, students may choose to take either the General Test or two Focus Tests.

General Test (90 mins)

The General Test is an individual test consisting of questions across the various subjects that comprise the Focus Tests. This test is intended to be easier than the Focus Tests and is highly recommended for students with less prior contest experience.

Focus Tests (60 mins)

There are four Focus Tests of 10 questions across four subjects — Algebra, Geometry, Discrete (Combinatorics and Number Theory), and Calculus. Each student can participate in two Focus Tests.

Guts Round (75 mins)

The Guts Round consists of 9 sets of 3 problems across various subjects in math. The key feature of this round is that each set must be turned in before the next set is given. All teams can see a live scoreboard with their standings.

Scoring

Individuals are only ranked within the tests they choose to take. Individual Round scores are determined by the number of correct answers. Each correct answer is worth 1 point, i.e. there is no weighting among the problems.

Team scores are determined based on a combination of teams' scores on the Guts Round and the Individual Round scores of their team members. The weights are displayed in the table in summary table below.

When weighting team scores, scores for a given test will be normalized by either the average of the top 10 scores or the top 10% of scores, whichever represents more students/teams. Additionally, if a student takes the General Test instead of the two Focus Tests, their score will only count for half as many points as the Focus Test combinations would.

The asynchronous Power Round will not be counted towards the overall team score; we will have a separate ranking category for the Power Round.

Tiebreakers

A tiebreaking procedure is employed for top awards for each test. Ties are not broken for honorable mentions or calculating overall team scores.

To streamline the event, we have a new automatic tiebreaker policy this year, which works as follows:

1. First, problems are ordered from hardest to easiest, based on the number of correct submissions.

2. The n-th hardest problem is assigned a tiebreaking value of 2⁻ⁿ. For example, the hardest problem will have a tiebreaking value of ½, the second hardest problem will have a tiebreaking value of ¼, et cetera.

3. Each student's tiebreaking index is calculated as the sum of their original score and the tiebreaker values of the problems that they correctly answered.

4. Students are ordered by their tiebreaking index, determining their tiebroken rank.

In simpler terms, among those tied for the same score, whoever solved the hardest problem is placed the highest, followed by the one who solved the next hardest, and so on.

Additional Tiebreaker Procedure

If a tie remains on the Individual Round after the preceding automatic tiebreaking procedure -- i.e., if two students correctly answered precisely the same set of problems, then those students will participate in an additional Tiebreaker Round. Ties that remain on the Guts Round or Power Round will not be tiebroken.

This 15-minute test will consist of either three (for the Focus Tests) or five (for the General Test) questions, and be scored primarily on correctness and secondarily on submission time; i.e. an earlier submission will be worth more than a later one with the same number of correct answers, but less than a later one with more correct answers.

Students may submit multiple times within the duration of the test, but only the last submission will be considered.

Check the BMT website for more details.

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