Here's a section from the H-group Hanabi strategy page: LINES During your turn, part of figuring out the best move involves looking into the future to see what the next player will do. If they discard, will it be okay? Is there some obvious clue that they will do? And so on. As you get… Continue reading Foresight
Category: Mathematics
2011 N1 = 2024 A2
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 $latex {d > 0}&fg=000000$, let $latex {f(d)}&fg=000000$ be the smallest positive… Continue reading 2011 N1 = 2024 A2
A stupid “real-life” application of quadratic reciprocity
The application During this year’s MOP, we used the following procedure to divide some of our students into two classes: Let $latex {p = 7075374838595186541578161}&fg=000000$ 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 $latex {s}&fg=000000$.… Continue reading A stupid “real-life” application of quadratic reciprocity
Getting to know problems
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 $latex… Continue reading Getting to know problems
Imperative statements in geometry don’t matter
There's this pet peeve I have where people sometimes ask things like what kind of strategies they should use for, say, collinearity problems in geometry. Like, I know there are valid answers like Menelaus or something. But the reason it bugs me is because "the problem says to prove collinearity" is about as superficial as… Continue reading Imperative statements in geometry don’t matter
A proof of Poncelet Porism with two circles
Brian Lawrence showed me the following conceptual proof of Poncelet porism in the case of two circles, which I thought was neat and wanted to sketch here. (This is only a sketch, since I'm not really defining the integration.) Let $latex {P}&fg=000000$ be a point on the outer circle, and let $latex {Q}&fg=000000$ be the… Continue reading A proof of Poncelet Porism with two circles
Brianchon is fair game
About five years ago I wrote a blog post warning that I thought it was a bad idea to design math olympiads to be completely untrainable, because I think math olympiads should be about talent development rather than just talent identification, yada yada yada. So now I want to say the other direction: I also… Continue reading Brianchon is fair game
New handout: Intro to Proofs for the Morbidly Curious
Downloadable at https://web.evanchen.cc/handouts/NaturalProof/NaturalProof.pdf. I don't know why I thought to write this, but it's been bugging me for a year or two now that I've never seen the answer to "what is a proof" written out quite this way. So here you go. It's a bit weird for me to be writing an article that… Continue reading New handout: Intro to Proofs for the Morbidly Curious
Everything I need is on the ground
For me the biggest difference between undergraduate math and PhD life has been something I've never seen anyone else talk about: it's the feeling like I could no longer see the ground. To explain what this means, imagine that mathematics is this wide tower, where you start with certain axioms as a foundation, and then… Continue reading Everything I need is on the ground
A common type-error on the OTIS application
There's a common error I keep seeing on OTIS applications, so I'm going to document the error here in the hopes that I can pre-emptively dispel it. To illustrate it more clearly, here is a problem I made up for which the bogus solution also gets the wrong numerical answer: Problem: Suppose $latex {a^2+b^2+c^2=1}&fg=000000$ for… Continue reading A common type-error on the OTIS application
Power Overwhelming 