I am always harping on my students to write solutions well rather than aiming for just mathematically correct, and now I have a pair of problems to illustrate why.

Shortlist 2011 N1

Here is Shortlist 2011 N1, proposed by Suhaimi Ramly:

For any integer $d > 0$, let $f(d)$ be the smallest positive integer that has exactly $d$ positive divisors (for example, $f(1)=1$, $f(5)=16,$ and $f(6)=12$). Prove that for every integer $k \geq 0$, $f(2^k)$ divides $f(2^{k+1})$.

I like this problem, so try it out if you haven’t. This is a problem …

The application

During this year’s MOP, we used the following procedure to divide some of our students into two classes:

Let $p = 7075374838595186541578161$ be prime. Take the letters in your name as it appears on the roster, convert them with A1Z26 and take the sum of cubes to get a number $s$. For example, EVANCHEN corresponds to $s = 5^3 + 22^3 + \dots + 14^3 = 16926$. Then you’re in Red 1 (room A155) if $s$ is a quadratic residue modulo $p$, and Red 2 (room A133) otherwise.

The students were understandably a bit confused why the prime was chosen. It turned out to be a prank: if you ran the calculation on the 30-ish students in this class, it was …

OTIS 2025-2026 applications are due August 1, 2025. The usual fare.

https://web.evanchen.cc/otis.html#apply

One of my favorite Djikstra programming quotes is about thinking via “lines of code spent” rather than “lines of code produced”. I started using this as a philosophy in my writing too: words spent.

Background

One of the things that’s surprised me about student writing is how poorly words are spent. You’ll have a solution where the trivial boilerplate steps are painfully verbose, and then the actually important parts are missing all the critical details.

I wonder how much of this is because of crummy writing advice. In school essays, even when you have nothing meaningful to say, teachers often impose a minimum word countIn ninth grade, my English teacher preferred the euphemism “develop your ideas” for “write more words”. It wasn’t until halfway through the year I realized why she kept writing that on all my essays. as a “proof of work”. The implied conclusion …

Thanks to Olga and Holly for factchecking a draft of this post. Remaining errors are my responsibility of course.

The recent 2025 Teammate Hunt just finished, which went really well. See the link to the wrapup. I was a minor supporting character in the organizing team, mostly just taking care of writing a few puzzles here and there. This post is about the creation stories behind all those puzzles.

(Puzzle links only work if you’re logged in for now; public access is coming later.)

Stories of my puzzles

Black or White and Black or White or Moon or Sun (from the control panel round)

This was a puzzle that worked because of our hunt structure (control panel puzzles come in pairs). Masyu is a common logic puzzle genre, and I was curious if there was another standard Nikoli genre that also involved a closed loop. That’s how I …

A lot of you have been asking me what comes after my PhD. Continuing my post-OTIS entrepreneurial adventures (see BOATIS in 2023 and (EC)⁵ in 2024), I’m happy to announce the next chapter: I will be moving to Seoul later this year to start a career in fashion design!

New York would have been the obvious choice, except I hate New York, and I thought it might be good to spend some time out of the country. I’ll be chilling in the fashionable 한남동, sketching ideas for blazers (and calling it “gender-neutral epistemology” or whatever gets clicks). I haven’t decided on a name yet for my future brand, suggestions welcome.

Please buy my brand when it comes out!

Korean translation

ㅎㅎㅎ 난 농담해. 이것은 번역이 아니야. OTIS 수달을 위한 퍼 …

Happy Pi Day! Here’s a quick summary of some recent things going on with me:

• I got my PhD! (I defended my thesis last December.)

• My multivariable calculus (18.02) notes are published on MIT OpenCourse Ware.

• The 2025 Teammate Hunt runs from March 28 to April 6. Please check it out! (Yes, I’m on the organizing team.)

• USEMO 2025 is open to all middle and high school students now (the US requirement has finally been dropped). Problem proposals are open now and are due on May 10, 2025; see the USEMO page for submission instructions.

• After being in development hell for 10 years, the silly weekend project I put together in 2015 is finally up: Olympiad GeoGuessr, a dumb game where you can try to guess collinear and concyclic points from real MO diagrams. Thanks to Abdullahil Kafi for contributing a lot of the recent levels.

  We …

I recently had a student writing to me asking for advice on problem-solving. The student gave a few examples of problems they didn’t solve (like I tell people to). One of the things that struck me about the message was their description of their work on USAMO 2021/4, whose statement reads:

A finite set $S$ of positive integers has the property that, for each $s\in S$, and each positive integer divisor $d$ of $s$, there exists a unique element $t\in S$ satisfying $\gcd(s,t) = d$. (The elements $s$ and $t$ could be equal.) Given this information, find all possible values for the number of elements of $S$.

Roughly (for privacy reasons, this isn’t exactly what …

There are a lot of different kinds of math enrichment activities now, ranging from olympiads to math circles to tons of summer programs and so on. I work in the competition sphere, and I used to spend a lot of time worrying about whether I took the right side.

Now that I’m a bit older, I came to the realization that maybe I don’t need to be so intent on comparing my work to others (even though I realize comparing yourself to others is human nature, haha). I eventually told myself: there are lots of people who don’t like olympiad exams; there are also lots of people who do, and it’s just okay for them to co-exist. We don’t need to decide which of the N systems is the best and kill the other N-1, because “best” is so different from person to person anyway …

Two pieces of news for high school math contest enthusiasts:

OTIS Mock AIME 2025

We’re running the OTIS Mock AIME again this year! It’ll go from December 19, 2024 to January 20, 2025.

New this year is that we’re offering two tests, I and II, and you can try either or both. However, unlike the real AIME, the two versions are intentionally different:

1. The OTIS Mock AIME I is going to be tough. It will definitely be harder than the actual AIME, by perhaps 2 to 4 problems. But more tangibly, it will also have significant artistic license. Problems will freely assume IMO-style background throughout the test, and intentionally stretch the boundary of what constitutes an “AIME problem”.
2. The OTIS Mock AIME II is meant to be more practically useful. It will adhere more closely to the difficulty and style of the real AIME. There will inevitably …