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Expand Up @@ -12,12 +12,12 @@ experience as well.
<!-- more -->

The online tournament will consist of an asynchronous Power Round on **November
30–December 1, 2024**, as well as the live event, including the Guts and
30–December 1, 2024**, as well as the live event, including the Guts and
Focus/General rounds on **December 7, 2024**.

BMT is intended for high school students, but is open to all students **12th grade
BMT is intended for high school students, but is open to all students **12th grade
and below**, including advanced students at younger grade levels. You may register
**up to 6 students per team**. There are no restrictions on how many teams/students
**up to 6 students per team**. There are no restrictions on how many teams/students
can participate.

{% button_link(href="https://contestdojo.com/") %}
Expand All @@ -27,7 +27,7 @@ Registration Portal {% end %}

## Registration, Waivers, and Pricing

You may register for BMT 2024 Online on ContestDojo any time until November 27,
You may register for BMT 2024 Online on ContestDojo any time until November 28,
2024 at 11:59 PM US Pacific Time.

Registration is performed on ContestDojo. Coaches may register up to 6 people
Expand Down Expand Up @@ -56,12 +56,12 @@ late registration.
including the California version or any of our satellites.
- Coaches may register as few or as many teams as they wish.

## Team Finder
## Teammate Finder

Students may register as a team of 1, however, it is beneficial to compete on a
Students may register as a team of 1. However, it is beneficial to compete on a
team of at least 4 due to our scoring guidelines. For students who do not have a
full team, we organized a [Team-Finder] document. Follow all outlined steps in
the document.
full team, we have organized a [Teammate Finder] spreadsheet. Follow all
outlined steps in the spreadsheet.

# Online Tournament Logistics

Expand All @@ -70,14 +70,14 @@ BMT 2024 Online will take place in two parts:
- **Asynchronous Power Round**: November 30–December 1, 2024
- **Live Event**: December 7, 2024

The asynchronous Power Round will take place on November 30–December 1, 2024.
Tests will be released on November 30, 2024 at 9:00 AM US Pacific Time, and
submissions will be due on December 1, 2024 at 8:59 PM US Pacific Time. The
The asynchronous Power Round will take place on November 30–December 1, 2024.
Tests will be released on November 30, 2024 at 9:00 AM US Pacific Time, and
submissions will be due on December 1, 2024 at 8:59 PM US Pacific Time. The
Power Round will be a proof-based team round, and will be graded by our staff.

| Time (US Pacific Time) | Event |
| ---------------------- | --------------------- |
| November 30, 9:00 AM | Power Round Released |
| November 30, 9:00 AM | Power Round Released |
| December 1, 8:59 PM | Power Submissions Due |

The live event will take place on December 7, 2024. A **preliminary** schedule is
Expand All @@ -86,143 +86,190 @@ provided below:
| Time (US Pacific Time) | Event |
| ---------------------- | ------------------------ |
| 10:00 – 10:30 AM | Opening Ceremony |
| 10:30 AM – 12:45 PM | General and Focus Rounds |
| 10:30 AM – 12:45 PM | General and Focus Rounds |
| 12:45 – 1:45 PM | Lunch |
| 1:45 – 3:30 PM | Guts Round |
| 3:30 – 4:30 PM | Speaker Event |
| 3:30 – 4:30 PM | Activities |
| 4:30 – 5:00 PM | Closing Ceremony |

# BMT Rounds
## Contest Format

### Power Round (90 mins)

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), you will need to
provide a rigorous mathematical justification for your 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.
chosen topic. For all questions (unless stated otherwise), teams will need to
provide a rigorous mathematical justification for their assertions in full
sentences.

### General Round (90 mins)
The topic for the Power Round will likely be at an undergraduate level, but no
substantial previous mathematical background is expected.

The general round is an **individual round** consisting of questions across the
various subjects that comprise the focus rounds. This round is **highly
recommended** for students with less prior contest experience.\*
### Individual Round

### Focus Rounds (60 mins)
For the Individual Round, students may choose to take either the General Test or
two Focus Tests.

There are four focus rounds of 10 questions across four subjects --- Algebra,
Geometry, Discrete Math, and Calculus. Each student can participate in **two
rounds** of focus exams.\*
#### General Test (90 mins)

### 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

\*Students may choose to **either** take the General Round **or** two Focus
Rounds.

## Tiebreakers

The tiebreakers will be held for the top scoring students in the individual
round. Tiebreaker qualifiers will be announced at the end of lunch and the
beginning of activities, and will be a 15-minute test. The test will consist of
three questions, and be scored primarily on correctness and secondarily on
submission time; that is, 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.

## Summary

<table style = "text-align: center">
<thead>
<tr>
<th></th>
<th>Power</th>
<th>General</th>
<th>Focus</th>
<th>Guts</th>
</tr>
</thead>
<tbody>
<tr>
<th>Important Details</td>
<td>Proof Based</td>
<td colspan="2">
Students may choose to participate in <strong>either</strong> the General Round or <strong>two</strong> separate Focus Rounds, but not both
</td>
<td>Submitted and scored live in sets of 3</td>
</tr>
<tr style="text-align: center">
<th># of Questions</td>
<td>TBA</td>
<td>25</td>
<td>10</td>
<td>27</td>
</tr>
<tr>
<th>Duration</td>
<td>90 mins</td>
<td>90 mins</td>
<td>60 mins</td>
<td>75 mins</td>
</tr>
<tr>
<th>% of Score</td>
<td>Separate Ranking</td>
<td colspan="2">60%</td>
<td>40%</td>
</tr>
<tr>
<th>Important Scoring Notes</td>
<td>N/A</td>
<td colspan="2">
If teams have less than 4 members, the remaining scores will be counted as 0. The General Round will only count for half as many points as the Focus combinations
</td>
<td>Teams are live scored, and there will be a displayed scoreboard</td>
</tr>
<tr>
<th>Collaboration?</td>
<td>Yes</td>
<td>No, students will work individually</td>
<td>No, students will work individually</td>
<td>Yes</td>
</tr>
</tbody>
</table>
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.

## Acceptable Answers
#### Focus Tests (60 mins)

Students are responsible for familiarizing themselves with the
[acceptable test formatting document](/assets/answer-formats.pdf) and
[common notions document](/assets/common-notions.pdf) for details on how their
answers should be submitted. Answers not submitted in the listed formats will be
graded as incorrect, even if equivalent.
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.

## Scoring
### Guts Round (75 mins)

To calculate the individual score, we will take the average of every team
member’s score on their individual portion if the team has 4, 5, or 6 members.
If the team has fewer than that many members, we will add 0’s until the team has
reached at least 4 scores, of which we will take the average.
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.

While individuals are allowed to register a 1-person team, we highly encourage
students without a team to use the [Team-Finder] to create a team of at least 4.
## Scoring

Scores for a given round will be normalized by either the top 10 scores or the
top 10% score, whichever is greater.
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
and Power Rounds, as well as 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.

### 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.
1. The _n_-th hardest problem is assigned a **tiebreaking value** of
2<sup>−*n*</sup>. 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.
1. 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.
1. 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 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.

### Round & Scoring Summary

<table>
<colgroup>
<col span="1" style="width: 20%;">
<col span="1" style="width: 12%;">
<col span="1" style="width: 24%;">
<col span="1" style="width: 24%;">
<col span="1" style="width: 20%;">
</colgroup>

<thead>
<tr>
<th></th>
<th>Power</th>
<th>General</th>
<th>Focus</th>
<th>Guts</th>
</tr>
</thead>

<tbody>
<tr>
<th>Important Details</td>
<td>Proof-based</td>
<td colspan="2" class="text-center">
Students may choose to participate in <strong>either</strong> the General Test or <strong>two</strong> separate Focus Tests, but not both.
</td>
<td>Submitted and scored live in sets of 3</td>
</tr>
<tr>
<th>Location</td>
<td colspan="4" class="text-center">
Assigned Classrooms — See Tournament Guide
</td>
</tr>
<tr>
<th># of Questions</td>
<td>TBA</td>
<td>25</td>
<td>10</td>
<td>27</td>
</tr>
<tr>
<th>Duration</td>
<td>90 mins</td>
<td>90 mins</td>
<td>60 mins</td>
<td>75 mins</td>
</tr>
<tr>
<th>% of Score</td>
<td>30%</td>
<td colspan="2">40%</td>
<td>30%</td>
</tr>
<tr>
<th>Important Scoring Notes</td>
<td>N/A</td>
<td colspan="2">
If a team has less than 4 members, scores of 0 will be added until the team has 4 Individual Round scores. The General Test will only count for half as many points as the Focus Test combinations.
</td>
<td>Teams are scored live, and a scoreboard will be displayed.</td>
</tr>
<tr>
<th>Collaboration?</td>
<td>Yes</td>
<td>No</td>
<td>No</td>
<td>Yes</td>
</tr>
</tbody>
</table>

If a student takes the General Round instead of the two Focus rounds, their
score will only count for half as many points as the Focus combination will.
### Acceptable Answers

The asynchronous Power Round will not be counted towards the overall team score;
we will have a separate ranking category for the Power Round.
Students are responsible for familiarizing themselves with the [acceptable
answer formats document](/assets/answer-formats.pdf) and [common notions
document](/assets/common-notions.pdf) for details on how their answers should be
submitted. Answers not submitted in the listed formats will be graded as
incorrect, even if equivalent.

# Frequently Asked Questions
## Frequently Asked Questions

### Are calculators or other reference material allowed?

Expand All @@ -233,21 +280,16 @@ answers will not be graded. Cheating in any form will not be tolerated, and
failure to comply with all rules may result in immediate and irreversible
disqualification.

### Can middle school students compete? What if I don’t have a team?
### Can middle school students compete? What if I don't have a team?

Yes! BMT is open to any student in 8th grade or below, including those who
haven’t entered high school. While students are allowed to compete as
individuals under “LAST_NAME Homeschool” or some other variation, we highly
recommend that students compete on a team of at least 4 due to our scoring
guidelines. To calculate the overall Individual score, we will take the average
of every team member’s score on their individual portion if the team has 4, 5,
or 6 members. If the team has less than that many members, we will add 0’s until
the team has reached at least 4 scores, of which we will take the average.
Yes! BMT is open to any student in 12th grade or below, including those who
haven't entered high school. While students are allowed to compete as
individuals, we highly recommend that students compete on a team of at least 4
due to our scoring guidelines.

### Will there be awards?

Although we will provide an official ranking as well as certificates for
top-scoring teams, there will not be physical awards for the online tournament.

[Team-Finder]:
https://docs.google.com/spreadsheets/d/1mY4kX2pINp2-4qBjuHhf_3gyhyZVl_dsg5D_iBrMNQw/edit?usp=sharing
[Teammate Finder]: https://docs.google.com/spreadsheets/d/1mY4kX2pINp2-4qBjuHhf_3gyhyZVl_dsg5D_iBrMNQw/edit?usp=sharing

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