The Hardest Problem On The Hardest Test

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Rating: 96.63% (by 126203 users)
Downloads: 4.8M (4757008)
Duration: 9min 55sec
Definition: HD
Published: 08 December 2017 (1 year ago)
Author: 3Blue1Brown

A difficult geometry puzzle with an elegant solution.
Home page:
Brought to you by you:
And by Brilliant:

Solution to the puzzle mentioned at the end:

These videos exist thanks to Patreon:

A different write-up of this solution:

1992 Putnam with this problem:

A problem with a similar flavor came up on the 2005 Putnam A6. Give it a try! The solution for that problem, by the way, was written by Calvin Lin, a friend of mine who works at Brilliant. Small world!

Animations largely made using manim, a scrappy open source python library.

If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and 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.

3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that).

If you are new to this channel and want to see more, a good place to start is this playlist:

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Tags: three brown one blue putnam math contest geometry 3 brown 1 blue brown 3b1b blue Mathematics 3brown1blue three blue one brown three 3 blue 1 brown one