The unexpectedly hard windmill question (2011 IMO, Q2)

The famous (infamous?) "windmill" problem on the 2011 IMO
An equally valuable form of support is to simply share some of the videos.

The author of this problem was Geoff Smith. You can find the full list of problems considered for the IMO that year, together with their solutions, here:

You can find data for past IMO results here:

Viewer-created interactive about this problem:

And another:

I made a quick reference to "proper time" as an example of an invariant. Take a look at this minutephysics video if you want to learn more.

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

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If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.

Music by Vincent Rubinetti.
Download the music on Bandcamp:

Stream the music on Spotify:

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.

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Various social media stuffs:

[rigira]

“I know what you’re thinking, those do happen to be all prime numbers”

nah I wasn’t thinking that

[SlackwareNVM]

The clicking sound when a point gets hit is really satisfying.

[ojotabe]

"If a made up windmill prepares you for a real problem, who cares that it's a fiction?"

Wise words man

[tacticaltaco]

I paused this video months ago trying to solve it. I ran into all the traps you listed out after giving about the solution, and ultimately gave in and watched the video. This is one of the most unique failures I've had when trying to solve a problem and an incredible lesson. Thank you.

[maltml]

Came for 3Blue1Brown, stayed for 5Blue5Brown

[lokoroko]

Let's just take a minute to appreciate how much effort was put into creating such a well animated video.

[maxliu]

I remember attending a math camp and my instructor was one of the contestants of the 2011 IMO and he got this question on the test. This has one of the best solutions that I’ve seen

[QuintessentialWalrus]

I can't help but think the reason so many participants struggled with this problem is because it's so difficult to visualize. The graphics in this video make discovering the solution seem almost obvious, but with a pencil and paper? And a question written in that kind of language? It's very far removed from what you typically see in the study of mathematics.

[spicyjew]

Came for the video, stayed for the dope clicking noises

[MaxxTosh]

For your 2M subscriber special, can we see you tackle an IMO problem you’ve never seen before, to see how your brain works without having a ton of time to animate and think? You are incredibly insightful!

[Danny-qhsu]

The click every time the pivot passes off is god tier

[haxney]

On the "social" point, I've noticed this phenomenon in all sorts of things I've taught to people: programming, dance, woodworking, video games, etc. For human beings, it seems like an essential part of learning something is forgetting what it was like not to know that thing.

[John.]

See Y’all In 5 Years When This Is In Everyone’s Reccomended

[johannesbrahms]

3Blue1Brown: "I guess I will try to exite people with this maths problem"
Internet: "thAt CLickIng nOISe Is SatiSFyIng"

[purvanshbhatia]

after watching your videos for a year, i’m baffled at how you consistently explain not only the solution to a math problem, but the process of thinking for an entire topic within math. Props

[efulmer]

3Blue1Brown
As a non-mathematician I greatly appreciate the Don Quixote reference you made at the end of a very satisfying mathematical puzzle. I love your videos. You provide just enough information in one moment that I can make the stab at your next point before you quite get there in your video. Very satisfying, even when I get it wrong, but especially that one or two times I've actually gotten it somewhat right.

[benjaminblackwell]

The inclusion of the animated graphics makes this much easier to understand. It’s good to remember that the kids taking the test didn’t have this advantage. Anyway fantastic videos they let my feel smarter than I am.

[iamasquidinspace]

As a physics student, I really appreciate the take-away message of "look for an invariant". Really good advice!

[hurbig]

Now I know why my university adjusts the grading scale according to the number of points students were able to get. I always thought it is to limit the number of people who pass since the first year is a sort of entrance exam. Now I think it is reasonable to think that sometimes a problem is just way harder than they anticipated so they are more merciful on grading that one.

I am often amazed by the fact that we are expected to be able to prove theorems that mathematicians a few decades ago were unable to proof and I am just a student. Of course, it is easier for us because we know that it is provable and we know that we probably need to use the tools that were presented to us in the course, but a few mathematicians died without ever seeing the solution to this problem.

[shreyjha]

I liked how you added a philosophical aspect to this problem because what you said at the end is so true. Your solution seemed easy to me, but then again how would I know to go with that solution, and how would I know to look for a constant.