What is the most popular ISL problem in the last decade?
People like to discuss about which is the best problem in a contest, specifically from the IMO shortlist (ISL), but that usually ends up in an argument about what even makes a problem “better” – there are so many factors to consider and everyone values different things.
One day, during one of these conversations, a different question caught my attention – what is the most well-known ISL problem? The distinction here is that this is a purely objective question – we could (theoretically) take a random sample of humans, feed them every ISL problem, and ask if they have seen it before.
But I did not have access to random samples of humans, so I did the next best thing – track view counts on AoPS.
For the uninitiated, if you hover your cursor over a thread, it will show you the number of views1:
Being the bored NSF I am (common theme), I decided to collect the view count of all ISL problems from 2015 to 20222 and rank them according to number of views.
Before we see the results, here’s a short digression: try to match the 4 topics (Algebra, Combinatorics, Geometry, Number Theory) to the colours blue, green, yellow, red based on your gut feel. Here’s a helpful diagram:
The first time I came across this question was during IMO training in 2023. I can’t remember if I came up with it or someone else, but it provoked some interesting discussions.
And I bet you put algebra as red (based on my sample size of like 4).
I’m not so sure why, but if I were to guess, it’s because algebra questions often involve messy expressions. It’s lifeless, it’s bloody, it’s gory, and it provokes visceral hatred (for the algebra fans out there, I’m joking). In Evan Chen’s MOHS rating sheet, algebra is red too.
Anyways, here’s the rest of my answer: combinatorics is yellow because it makes me happy. Geometry is green because they both start with “g”.
So that leaves us with the following:
- Algebra: red
- Combinatorics: yellow
- Geometry: green
- Number theory: blue
Back to business.
Here’s the top 40 questions as of May this year. The darker the background, the harder the question.
Expectedly, the top 40 are dominated by IMO questions. I was personally expecting 17C5 to be at the top because of just how infamous it is, but I guess 4th is not bad too.
If there’s anything that surprises me the most, it’s that the top 2 questions and top 2 non-IMO questions are all functional equations. I cannot really explain this, perhaps it is so easy to forget the solution to an FE that people keep re-viewing it.
Just for fun, let’s look at the bottom too.
I have to admit this seems pretty accurate. I hardly see these problems being discussed anywhere, except maybe 15N7.
There are some problems with this ranking though. Most prominently, questions that are older would have had more time to be viewed. To fix this, all I had to do was to wait 6 months, recollect the total number of views, and resort based on the difference. Well…
Some of these really shocked me. 22A1, 22N8?
Then I realised, there’s now a bias in the other way, because people are more likely to try questions from more recent ISLs. In order to counter this, what I need to do is to compute, for each question posted at year 
In the end, I decided that total views is still a much better indication of popularity. Questions that are older are more likely to be known by more people simply because they are older, so I do not have to try so hard to remove the time factor.
To pretend I have a definitive answer posed at the start would be a lie, but if I had to provide one, it would be 19A1, and 15A2 among non-IMO questions.
Thanks for reading 🙂
As usual, here’s the data:
Gabriel Goh Hao Xiang 
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