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3 Hats...


Best Answer phaze, 17 December 2012 - 01:09 AM

Spoiler for Seems to work

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8 replies to this topic

#1 Anza Power

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Posted 15 December 2012 - 07:56 PM

Sorry if this has been posted before, a friend texted me this saying he needed the solution ASAP, I can proudly say I replied in a very timely manner... :D

Again it's that psycho warden with the obsession with hats and logic coming up with a new challenge, 3 prisoners, each gets a hat, the hats can be colored red green or yellow (no one knows how many hats in total there are of each color) each prisoner can see the hats of the other two but not his...

Each must write down the color of their hat on a piece of paper, if at least one of them is correct they all go free, what should they do?

(btw there's the usual rule if they talk or anything they all get executed, they may agree on a strategy before but that's it)
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#2 ReverseCausality

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Posted 16 December 2012 - 03:43 AM

Spoiler for Problem and Solution


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#3 wolfgang

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Posted 16 December 2012 - 07:09 PM

Spoiler for Let me suppose that


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#4 flamebirde

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Posted 16 December 2012 - 10:02 PM

That can't be right because there could be two yellow and one green, with no red. Then if they all pick red, no one gets it right and they all die.


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Mafiosos and mafiosas of the world, unite! And then kill each other in a particularly tricky move that everyone suspects but never anticipates.

stand back. I'm going to apply logic.

 

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#5 phaze

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Posted 17 December 2012 - 01:09 AM   Best Answer

Spoiler for Seems to work


Edited by phaze, 17 December 2012 - 01:10 AM.

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Perfecting Mafia suicide since August 2008

#6 bushindo

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Posted 17 December 2012 - 01:20 AM

Sorry if this has been posted before, a friend texted me this saying he needed the solution ASAP, I can proudly say I replied in a very timely manner... :D

Again it's that psycho warden with the obsession with hats and logic coming up with a new challenge, 3 prisoners, each gets a hat, the hats can be colored red green or yellow (no one knows how many hats in total there are of each color) each prisoner can see the hats of the other two but not his...

Each must write down the color of their hat on a piece of paper, if at least one of them is correct they all go free, what should they do?

(btw there's the usual rule if they talk or anything they all get executed, they may agree on a strategy before but that's it)

 
Here's how I believe the prisoners should approach this
Spoiler for Approach

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#7 CaptainEd

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Posted 17 December 2012 - 06:59 PM

Kudos to Anza Power and Bushindo! It is surprising just how much can be performed by a team in collusion, but incommunicado!
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#8 Anza Power

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Posted 17 December 2012 - 07:40 PM

phaze and bushindo are both correct, my solution was the same as bushindo's one, phaze's solution is a little harder to understand why it works but it's exactly the same as the arithmetic one just worded differently...
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#9 CaptainEd

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Posted 17 December 2012 - 08:43 PM

Indeed, The solution discovered by you and Bushindo is immediately applicable to N colors and prisoners for any N, while Phaze's solution requires some additional conditions.


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