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Guest Message by DevFuse
 

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Hats on a death row!! One of my favorites puzzles!


Best Answer bonanova, 08 January 2008 - 06:25 PM

Spoiler for Here's my idea
Go to the full post


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#11 Ploper

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Posted 30 December 2007 - 01:34 AM

wow this sounds like a really fun one
I'm busy right now but I'm gonna sleep on it and tell you if I've found anything tomorrow... mK
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#12 unreality

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Posted 30 December 2007 - 01:58 AM

I just figured out how to save 19 people FOR SURE I think. Maybe 18
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#13 unreality

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Posted 30 December 2007 - 02:15 AM

Okay I was wrong- it saves 15 people FOR SURE and the other 5 each have a 50% chance of survival, meaning on average there will be 17.5 survivors (2 short of the 19.5 of the "perfect solution" of this problem), or a 1/32 that all 5 will make it.

Spoiler for solution


It may be possible to expand on my technique. I tried but this seemed to make the most of it, and it seems that 15 people guaranteed is the best you can do- though stwalk thought 13 people was, so I'll keep working for that 19
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#14 roolstar

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Posted 31 December 2007 - 10:18 AM

With no other information present, I don't see how this is solvable. What strategy would allow you to say the word "red" or the word "black" and tell nineteen people which of two colors each was wearing? I believe it is impossible; you cannot convey that much information in a simple binary choice.



You are on the right track in your reasoning spoxjox.

The most reliable and correct method should devide the big universe of possibilities of the 20 prisoners into 2 possibilities

And I assure you there is a way: don't give up yet guys...

I'm will not post a spoiler just yet. Finding the solution of this puzzle is a lot more fun than discussing the solution.

PS: The answer may surprise you with its simplicity. (OK enough hints for now)
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#15 bonanova

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Posted 31 December 2007 - 02:35 PM

Spoiler for solution

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#16 Ploper

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Posted 31 December 2007 - 04:44 PM

yeah, I'm havin trouble with this one..
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#17 unreality

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Posted 31 December 2007 - 10:03 PM

Spoiler for solution

In mine (a few posts up) I saved all but 5. Hmmm I must rethink this...
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#18 unreality

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Posted 31 December 2007 - 10:04 PM

I hope its not something stupid like "Oh to make it a fair challenge the evil king makes everyone's hat color the same", I highly doubt it.

Is my answer on the right track at least?
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#19 bonanova

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Posted 01 January 2008 - 10:24 AM

I hope its not something stupid like "Oh to make it a fair challenge the evil king makes everyone's hat color the same", I highly doubt it.
It's not. The strategy works for any distribution of colors.

Is my answer on the right track at least?
Yes. The survival of the first prisoner to speak cannot be guaranteed.
The others, if they follow the strategy and listen to all of the previous speakers, will know their hat color.


Roolstar gave a good clue:

The most reliable and correct method should devide the big universe of possibilities of the 20 prisoners into 2 possibilities
The first speaker tells which of these possibilities is true. What are the possibilities?


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#20 PDR

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Posted 01 January 2008 - 09:26 PM

Your hint about 2 possibilities made it suddenly clear. Try this:
Spoiler for solution

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