SOLUTION to the Impossible Chessboard Puzzle
ฝัง
- เผยแพร่เมื่อ 16 ส.ค. 2020
- SPOILER ALERT - This video contains my solution to the "Almost Impossible Chessboard Puzzle" as presented to me on the 3Blue1Brown channel video "The impossible chessboard puzzle" ( • The impossible chessbo... ). You will get the chance to pause the video. And you may gamble my solution is not correct. But if you want to get a go on this problem yourself you are hereby warned not to watch this video ;)
- วิทยาศาสตร์และเทคโนโลยี
Fascinating how you explained this solution! I have one question that may seem too simple to even consider but for this riddle and your solution, it would be THE paramount piece of information to make this work. If the chess board is sitting in the middle of a table with no chair (or alone on the ground) how do you communicate the direction from which to view the board to the second prisoner?
i guess the letters and numbers on a chessboard
An excellent meta question. Strictly speaking, 3Blue1Brown should’ve explained that the board orientation is a “given”, and that the prison authority would not mess with the board orientation between the two prisoners, etc. 👍🏻
The prisoners can also communicate before hand. They might determine the orientation of the board by relating it to some invariable component of the room. The door for example. Now if the jail keepers were to turn the board 😭 idk
Kudos to you, man!
I didn't understand the solution of 3blue1brown , you explain it very well now it is crystal clear. Thanx
You have interesting videos
Subscribed
Wow, thank you very much :). If what I have to say is of even the slightest value to anyone that is more than enough for me to keep doing videos. Take care!
I find it unlikely that a pair of prisoners that are smart enough to figure this out aren't also smart enough to avoid going to jail.
got a point! XD
Thanks! very well explained :) subscribed.
Warm thanks for your kind feed back :). I wish you all the best of success with your own puzzle solving :)
Ok but what if the board already have the key under the right square if you flip a coin it will give a new answer and you have to flip a coin
Sucks that nobody has answered this. I have the same question. Warden has a 1:64 chance of picking the location that's randomly encoded. How to not change the encoding if must flip one?
In that case we just flip the top-left corner position, the zero.
I'll explain it first then verify against the XOR logic. Remember that to determine if a bit position (bi) is set or not (set means equals 1) we count the number of heads in the positions where the i-th bit is set, if it's even it's set. This means we never count the first position no matter what it is because it's binary representation is all zeros, you can also rewatch the video to see that the top-left corner is never counted as part of the sets identified.
Now to prove this, let's say you find the board pointing at position 0100101 and the key is in that position, then you want to encode from 0100101 to (itself) 0100101 to know the position you want to change we use XOR, and anything XOR itself is 0 (0000000), because nothing changes and that's the position you want to flip 🙃
the only problem is that this assumes both prisoners are aware of this agreed upon communication method or encoding, but there's no way for prisoner one to convey the info to prisoner two so unless they had prep time for the puzzle to establish that it still seems impossible
Covered in the 3Blue1Brown video at around 01:10 - The 2 prisoners may conspire ahead of time if they want, but the Warden also knows exactly their strategy.
Does this method still work if we operate under the original premise that 3blue1brown posed though with the "Warden" Being able to play defense by listening in to the strategy before he arranges the board? Couldn't he just make every Coin be heads or all of them be tails and it would throw off the encoding?
It will work no matter what the warden does. If the warden sets it all heads, which is 000000, then just flip the coin on the key.
Hinged on the edge of a knife.
If you don’t know the orientation of the board when it was flipped it doesn’t work…
But what if it doesnt start with 50 heads and 50 tails? it never said it would
Its random so i guess it might be aligned
The second player can see the configuration BEFORE the flip(the configuration that is different from the final one only for that single flip)?
No, the second player can see only the final board :). But both players has worked out the scheme to decode the board information. The trick is to find that scheme so a single flip is enough to change the encoded number to anything between 1 and 64. This puzzle is a good one! I wish you all the best wrapping your head around a solution that fits your way of thinking :)
@@kjell-olovhogdahl6557 Thanks!
This is pretty big-brain
what if the key is allready under the square, that the board is presenting before the flip? can you change a coi s value without changing the 010110 outcome?
You would flip the coin in the top left corner, representing the value 000000. This would not affect the value of our board
Is this correct?
This would be a fantastic way to solve thee puzzle if you were both thinking the same way. But imagine for a moment that you hadn't explained your solution and instead had given us the board (post-coin flip) to look at in your video. Would you reasonably expect that anyone in the comments could guess your intentions with the message you've left before your explanation, and find the key?
What?
Thanks!
You are welcome. Glad if I could provide any information of value to you :)
Each was carefully placed. Carelessly turn over the coin on the key.
Thanks 🥰
Thanks for your kind feed back. You are welcome :)