The almost impossible chessboard puzzle

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From Standup Mathematician.

Check out the meta-solution on 3Blue1Brown: https://www.youtube.com/watch?v=wTJI_WuZSwE

Thanks to Gordon’ s Wine Bar for letting us film in their bar. Ha! It wasn’t a dungeon, it was a wine bar all along! (An amazing wine bar at that; definitely visit it next time you’re in London (and things are open again)). https://www.gordonswinebar.com/

Also: this was filmed back in February 2020 pre-coronavirus (at least before we knew about it). Which is why we’re sat so close together and not wearing masks. And people are phoning a wine bar.

For those of you want it all, and you want it now, we’ve put the complete, unedited footage of Matt and Grant completing the puzzle scenario on Matt’s second channel.
https://www.youtube.com/watch?v=CEDZyK8UL6M

We’ll put the deleted footage on the Stand-up Maths patreon page: https://www.patreon.com/posts/39003911

Sorry the audio is a bit hit and miss. Matt’s microphone dropped out for a bit so we tried to rescue the audio from Grant’s lapel mic. With some success.

Puzzle as emailed by Grant to Matt:
Prisoner 1 walks in, sees a chessboard where each square has a coin on top, flipped either to heads or tails. The warden places the key under one of the squares, which prisoner 1 sees. Before he leaves, he must turn over one and only one coin. Prisoner 2 then walks in and is supposed to be able to figure out which squares the key is in just by looking at the arrangement of coins.

This is the website Matt mentioned with a full breakdown of the solution and interactive boards you can play with.
http://datagenetics.com/blog/december12014/index.html

CORRECTIONS:
– At 20:42 when I (Matt) said "You’re now assigning a 64-dimension…" he meant to say "You’re now assigning a 6-dimension…". But that is a moot point because Grant can visualise cubes in all dimension spaces with equal ease.
– At 24:20 I said Venn and Euler the wrong way around. No one tell Steve Mould!
– Let me know if you spot anything else.

Thanks again, as always, for Jane Street being my principal sponsor.
https://www.janestreet.com/

Thanks to my Patreon supporters who help make these videos possible. Here is a random subset:

Willy Felton
Claire Carroll
Matt Langford
Steve Davidson
James Dexter
Stephen Hart
Philippe von Bergen
Alex Frieder
Eric Sexton
Matthew Schuster

Support my channel and I can make more maths videos:
https://www.patreon.com/standupmaths

Filming and editing by Alex Genn-Bash
Music by Howard Carter
Design by Simon Wright and Adam Robinson

MATT PARKER: Stand-up Mathematician
Website: http://standupmaths.com/
Maths book: http://wwwh.umble-pi.com
Nerdy maths toys: http://mathsgear.co.uk/

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