The impossible chessboard puzzle

An information puzzle with an interesting twist Solution on Stand-up Maths: https://youtu.be/as7Gkm7Y7h4 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: https://3b1b.co/chess-thanks Home page: https://www.3blue1brown.com Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ 0:00 Introduction 3:58 Visualizing the two-square case 5:46 Visualizing the three-square case 12:19 Proof that it's impossible 16:22 Explicit painting of the hypercube ------------------ Thanks to everyone who endured me probing them with this puzzle and provided helpful discussion, especially Cam Christensen, Matt Parker, and Mike Sklar. Mike, by the way, deserves credit for coming up with the particularly clean way to see that it's impossible when n is not a power of 2. 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/subs