Unexpected Solution to a Counting Puzzle π€
Discover the surprising answer to a counting puzzle and explore light-based solutions. Support future projects on Patreon!

3Blue1Brown
14.2M views β’ Jan 13, 2019

About this video
Solution: https://youtu.be/6dTyOl1fmDo
Light-based solution: https://youtu.be/brU5yLm9DZM
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/clacks-thanks
New to this channel? It's all about teaching math visually. Take a look and see if there's anything you'd like to learn.
NY Times blog post about this problem:
https://wordplay.blogs.nytimes.com/2014/03/10/pi/
The original paper by Gregory Galperin:
https://www.maths.tcd.ie/~lebed/Galperin.%20Playing%20pool%20with%20pi.pdf
Evidently, Numberphile also described this problem (I had not known):
https://youtu.be/abv4Fz7oNr0
You'll notice that video has an added factor of 16 throughout, which is not here. That's because they're only counting the collisions between blocks (well, balls in their case), and they're only counting to the point where the big block starts moving the other way.
Thanks to these viewers for their contributions to translations
Bengali: Prayas Sanyal
Hebrew: Omer Tuchfeld
Italian: @Deye27, @hi-anji
------------------
These animations are largely made using manim, a scrappy open source python library: https://github.com/3b1b/manim
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:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
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: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Light-based solution: https://youtu.be/brU5yLm9DZM
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/clacks-thanks
New to this channel? It's all about teaching math visually. Take a look and see if there's anything you'd like to learn.
NY Times blog post about this problem:
https://wordplay.blogs.nytimes.com/2014/03/10/pi/
The original paper by Gregory Galperin:
https://www.maths.tcd.ie/~lebed/Galperin.%20Playing%20pool%20with%20pi.pdf
Evidently, Numberphile also described this problem (I had not known):
https://youtu.be/abv4Fz7oNr0
You'll notice that video has an added factor of 16 throughout, which is not here. That's because they're only counting the collisions between blocks (well, balls in their case), and they're only counting to the point where the big block starts moving the other way.
Thanks to these viewers for their contributions to translations
Bengali: Prayas Sanyal
Hebrew: Omer Tuchfeld
Italian: @Deye27, @hi-anji
------------------
These animations are largely made using manim, a scrappy open source python library: https://github.com/3b1b/manim
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:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
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: http://3b1b.co/subscribe
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Instagram: https://www.instagram.com/3blue1brown_animations/
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Video Information
Views
14.2M
Likes
320.2K
Duration
5:13
Published
Jan 13, 2019
User Reviews
4.9
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