Perspectives from our Problem Writers + Registration!

BrUMO registration is in full swing and will be open until the 20th of December. Sign up on our website!

In the meantime, our problem writers have been hard at work preparing for the competition. However, we’ve managed to get ahold of a few (Amber, Jake, and Mason) to ask them a few questions about their approaches to problem writing and math at large. No spoilers…

——

How do you create a fair/balanced set of problems as a group?

Amber: Lots and lots of test-solving! Problem writers solve our division A contests, while organizers help us test the Division B versions. This gives us some idea about problem difficulty, but its not the full picture — we use these results as a baseline with the expectation that our team of university students would perform better than the average high schooler. After each test-solve, we send out feedback forms to help us craft a fair contest. As for topic distribution, we try to have an equal number of questions in algebra, number theory, geometric, and combinatorics, and we ask each problem writer to provide us with their two favourite problems to include on the test.

What does the process for collaborating on problems look like?

Mason: I write the majority of my problems by myself, because they often formulate in my head over the span of multiple weeks. However, if I have an idea for a problem that seems close to being complete, but has some details that don’t quite work, I might talk it out with other problem writers and try to refine the idea until a good problem statement pops out. Alternatively, what I have done on multiple occasions is enumerate the answer to some number theory problem with a Python script, notice a coincidental pattern, and ask Joshua Kou (one of my co-PW leads and a walking number theory masterclass) if the answer is achievable by hand. However, both of us very easily succumb to rabbit holes when around each other, so proceed with caution if you’re anything like this too.

What common misconceptions do you think students have about writing or solving problems?

Jake: One misconception I know I had about competition math was that it was primarily about memorizing formulas, theorems, and problem solving techniques. This certainly can be true at times, but through BrUMO I've encountered so many problems written by my peers that require ingenuity and creativity to solve, which is really special.

Mason: I would say the biggest misconception about writing problems is the level of competition math “skill” or “performance” you need to have to write good problems—people often think you have to make USAMO multiple times to write quality problems. This just isn’t true and even discourages some people who I think would make great problem writers otherwise. I don’t think there’s too much of a correlation between the best problem writers I’ve met and the people who scored the highest on AIME or whatever contests are relevant. I doubt that at my high school math competition “peak”, I would get more than 8 or 9 out of 15 on BrUMO 2025, and some of my problems I probably wouldn’t be able to solve if they were given to me on the BrUMO exam. To write a problem, all you really need is a creative idea, a willingness to look relevant formulas up, and a lot of persistence. Even if it takes multiple weeks for your idea to become coherent, and even if the details change many times, I think you will eventually create something pretty cool.

What was your favorite problem from BrUMO 2025 and why?

Amber: I really like problem 6 from the team round last year. It's a simple problem that doesn't require much mathematical insight or complicated tricks and instead functions more as a fun logic puzzle. This is also the first time we used the names Aruno, Bruno, Cruno, and Druno, which seem to have stuck around for this year! :)

What's your favorite math problem from a competition?

Mason: I think the most memorable is 2011 IMO Q2, the famous “windmill” question which I only know from watching the 3Blue1Brown video years ago. I don’t really remember particularly “good” math problems on tests I’ve taken, since it’s been a while since I’ve fully grinded competition math, and I usually couldn’t fully appreciate good problems on timed math contests anyways. I do, however, remember a select few AMC problems that made me very tilted, which I will not elaborate on here :)

Did you participate in math competitions as a student and how does that influence your problem writing?

Amber: I competed in almost all of the major Canadian math competitions since middle school. Attending workshop with University of Waterloo's CEMC has definitely had a big influence on how I write problems — we learned about all kinds of solution techniques like pigeonhole principle, tilings, and invariants, which are concepts I sometimes like to integrate into my problems.

Jake: I think my competition math prime was actually in middle school. In high school I still took the AMC10/12 and AIME as well as a few other competitions, but back from 5-8th grade I was actively practicing and preparing for comp math. I think having a competition math background helps me write problems more intentionally. I try to come up with questions that the younger me would enjoy solving.

Mason: I did the typical AMC and AIME, but not much more than that. I don’t really think they influence my problem writing that much—maybe subconsciously I use the same ideas, but I’d say that what I write has a much different flavor than the MAA competitions. (Certain people have told me that my problems are even more ragebait than AMC problems, which I will happily take as a compliment.)

How do you come up with problem ideas? Do you have a go-to starting point?

Jake: Normally I try to take inspiration from some interesting math concept I've come across. For example, the first ever problem I wrote from BrUMO used the idea of representing the probability of an inequality geometrically. Once I have the concept, it's a matter of fine tuning the problem to make sure it's at my intended difficulty level, not too computationally intensive and also has a clean answer.

Mason: Not really. They come to me at random in the shower (yes, problem writers do in fact do this), or sometimes when I don’t understand anything in my real analysis lecture and promptly start daydreaming instead. I will say that, above all, my problems are usually grounded in real life experience. Many talented individuals on the problem writing team are routinely able to come up with seemingly random complex equations that can be solved with a few cool tricks—I cannot do that for the life of me. What I have done, however, is take an idea from my probability class, generalize it, and add an interesting constraint in the problem statement (It just so happened that a specific case of the problem I wrote ended up as the first problem of midterm, which was quite satisfying, and even more embarrassing when I nearly got it wrong.)

For some actual advice, I will say that most of the time, it might be helpful to restrict yourself to some aspect of the problem you want to write. This aspect might be mathematical (e.g. “I want to write a problem that involves rewriting an expression via Vieta’s formulas”) or contextual (i.e. “I want to write a totally, definitely 100% fictional problem about some number of friends and enemies forming groups at a party”). Doing this will hopefully ensure that at the very least, you’ll know where to start, and the refined problem might follow shortly.

If you could only write one type of problem, what would it be?

Amber: Maybe number theory or logic puzzles! Anything that you can come up with from basic principles without needing to use fancy tricks.

Jake: I think probably combinatorics problems. There are just so many interesting counting tricks, and creative insights everywhere you look. I think most combinatorics problems make whoever's solving them feel accomplished.

And finally… If you could talk to any mathematician in history, who would it be?

Jake: I think my answer would me Ramanujan. His mind just worked in a different way from everyone else, and I've always been fascinated by him.

Mason: Karl Weierstrass. I’m interested in analysis in my more “professional” math career, so I’d be really interested in his motivations for all the cornerstones of analysis he developed. Also, all of my encounters with German mathematicians so far have been thoroughly enjoyable.

——

That’s all for today. We hope you enjoyed this window into the BrUMO team and process, and don’t forget to sign up for the 2026 edition :)