The chessboard and coins puzzle

(These description links aren't active in the shorts player, but you can follow the link on the bottom of the video screen itself)

This comes from a collaboration I did with Stand-up Maths, where on his channel we covered the solution, and here on 3blue1brown we analyze a meta-puzzle.

Editing from long-form to short by Dawid Kołodziej
This comes from a collaboration I did with Stand-up Maths, where on his channel we covered the solution, and here on 3blue1brown we analyze a meta-puzzle.

Editing from long-form to short by Dawid Kołodziej

[bluebrown]

It probably goes without saying, but the solution is a pure coin flip. No small adjustment, leaving one coin warm, or any meta-gaming stuff like that.

This was part of a collaboration with Matt Parker (i.e. Stand-up Maths). On his channel we talk about the solution, and how we each thought about it. On this channel, I show why for most chessboard sizes, it would be impossible.

[KillianTwew]

Thanks, I'll go let the guys in my basement know I have a new puzzle for them

[markmarinas]

Even if prisoner number 1 is a one in a billion genius, if I'm prisoner number 2 we're both fucked.

[ZeL-iqsf]

The warden pushes the table over as I try to balance the coin on its edge

[jaraxlebaenre]

*Picks up coin and sets it edge up.
Warden: No, this isn't how you play the game

[umloginqualquer]

Easy. When you flip the coin, flip it around an axis ensuring that the new side facing up will have the drawing upside dowm. So all coins will be oriented correctly, except one.

[iVirus]

Warden: Okay, you can only turn over one c--
Me, staring blankly while swallowing the last of the coins: ...

[Trees]

This will be so useful for when I get trapped in a chessboard room! Thanks so much!!

[thatonedudefurryrights]

Warden: I have here a chessboard full of coins—
Me: Dude just take me back to my cell.

[lakepants]

i came to the comments to say flip the coin above the key onto it’s side so it’s vertical unlike every other coin.. but now i saw the “pure coin flip” and idk anymore

[jaraxes]

"bro, key at C6"
"Thanks bro"
"Oh btw, I flipped a random coin, don't mind that"
"Aight bro"

[odvjetnikai]

This is my favourite video of yours. I still remember watching this in college with my roomate and trying to come up with a solution. This fascinated us to extent where we were awake till dawn, scribbling stuff on the whiteboard and ultimatley giving up and watching the video.

Thanks for the fun times 😊

[Shadow_figure]

The warden watches in horror as I balance the coin on its edge

[nirbhay_raghav]

When I walk into a room with chessboard that has coins on it, I am going out of the room😂

[Tom-gvsi]

I would rotate all the coin facing the right way when you're looking at it, then flip the coin that has the key under it and make that one upside down when looking at it, so that it would be the only one upside-down when looking at the board

[Valkies-zjbi]

Answer:
As player 1 you must calculate in binary the XOR of all of the tails in the position, for example let’s say there were only tails on positions 3, 4, and 10 the XOR would be 000011 XOR 000100 XOR 001010 which equals 001101 (25) using this lets say the key was on 32, we would flip 011101 (57) so when player 2 XORs them they get 32

[Bolpat]

Better way to phrase it: Player 1 gets to tell the warden a chess square (e.g. b4) and the warden turns the coin. This takes away all shenanigans a player could employ touching the setup.

[suyuhao]

Do four million jumping jacks, wring your drenched shirt over the chessboard, and flip the coin with the key under it so only that will be dry.If your friend doesn't get it, at least you are ready to beat up the warden

[TheHerbalistaa]

I would wait until dust builds up on the coins, it may take a while but its a hypothetical answer, and then flip over the coin. No dust will be on that coin but there will be dust on all the others.

[polarbear]

Depends if all the coins are arranged in the same upright position. If all coins have the top facing north, flip the coin to be upside down compared to the rest