Dear BMT competitors,
We are very excited to see you this weekend at BMT 2025! We’d like to provide some suggestions on how to approach the Power Round at BMT.
The Power Round is a 90-minute team-based test with questions exploring a single topic not typically covered in competitive mathematics, culminating in new and interesting results. Probably unlike most tests you have taken before, in the Power Round you are not expected to have any prior knowledge of the topic of the test–in fact, we hope that it will be a completely new experience for you! The power round booklet will guide you through the material, providing definitions, theorems, formulas, and guidance alongside the problems.
Since you likely haven’t seen the content before, it’s especially important to carefully read and understand the definitions and ideas provided in the test. Usually, there are questions throughout the Power Round that directly check your understanding of a definition or theorem, and having a good foundation will result in gaining more points and better intuition for more complex problems later in the round. It’s better to spend a few extra minutes working through an example with a teammate or trying something out than to race through and risk misunderstanding a fundamental idea of the chapter.
Because the Power Round is a team-based test, we strongly encourage you to meet with your team before BMT to devise a strategy for working through the test. Sometimes, it is useful to work through the booklet at different paces. For example, at some points of the round, one or two team members could write up solutions to the first couple of problems, while other team members continue reading further into the material. Other times, it is helpful to discuss the content in small groups to fully understand the material. Unlike other rounds at BMT, the questions in the Power Round are not ordered by difficulty; rather, they are sorted by content and provide a roughly progressive exploration of the subject, so it is in your team’s interest to read and attempt as many problems as you can. Even if you don’t solve a problem, you can use the result it states later on, so don’t worry if you aren’t able to figure out everything! It is often better to move on and tackle later problems instead of staying stuck on an earlier one.
Proof-writing may be unfamiliar to you, so we’d like to provide some general thoughts on writing effective proofs. A proof is a step-by-step logical argument that uses known statements to demonstrate new results. There are many proof techniques; some common ones are direct proofs, proofs by contradiction, proofs by induction, and proofs by cases. Sometimes, proofs are very careful (recent efforts in formal verification like Lean push this to the extreme!), and sometimes they are more casual; the level of rigor we expect in solutions to Power Round questions is somewhere in between. When grading, we are generally looking for convincing, cohesive explanations about why the statements are true or false. Although we want you to be thorough, we usually prefer concise, straightforward proofs to lengthy, complicated explanations. Remember that you don’t get points based on how long your proof is–reading lots of long, incorrect proofs tends to make our grading team sad!
We encourage you to look at previous Power Rounds from BMT to familiarize yourself with the layout and expectations of the test. There are also solutions posted adjacent to the power round problems. We invite you to peruse them as they provide good examples of complete and thorough proofs and explanations in addition to solving techniques.
Feel free to email us at team@berkeley.mt if you have concerns about the Power Round or any other aspect of the competition. See you soon!
Best,
BMT Team
