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Red hat, blue hat


Best Answer Rainman, 24 October 2013 - 08:49 PM

Spoiler for simple example for 50 saves

Go to the full post


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18 replies to this topic

#1 bonanova

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Posted 23 October 2013 - 05:04 AM

First, the good news: Nobody gets killed. 100 prisoners are out on parole, and the those who guess wrong will simply have their parole revoked. No blood. What a relief. The children will sleep well tonight.

 

But a lot of the usual stuff in the red hat / blue hat genre still applies:

  • The Parole Officer (PO) will fit each parolee with a red hat or a blue hat.
  • Each parolee can see all the other hat colors, but not his own.
  • No communication is permitted. Just looking at hat colors.
    Seriously, no shouting, pausing, singing, pointing, facial expressions.
    If anything like that happens, then the PO will get PO'd and shoot everyone.
  • On a common signal, each parolee will simultaneously guess the color of her own hat.
  • Parolees initially meet, to formulate a strategy that dictates what color to guess, based on what she sees.
  • The object is to guarantee the most successful guessers, regardless of the hat distribution.

And here's a wrinkle. There is a spy who informs the PO of the strategy.

So in placing the hats, the PO does his best to foil it.*

How many parolees can be saved?

 

* For example, if the strategy is to "guess the majority color" the PO will place 50 red and 50 blue hats, and no parolee will be saved.


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#2 phil1882

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Posted 23 October 2013 - 05:20 AM

Spoiler for 50 prisioners saved

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#3 harey

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Posted 23 October 2013 - 10:31 AM

Spoiler for


Edited by harey, 23 October 2013 - 10:38 AM.

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#4 Rainman

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Posted 23 October 2013 - 11:06 AM

Spoiler for


Standing in a certain position based on what you see is a form of communication.
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#5 Rainman

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Posted 23 October 2013 - 11:14 PM

Spoiler for answer


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#6 ThunderCloud

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Posted 24 October 2013 - 01:08 PM

Spoiler for A way to free 49...


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#7 ThunderCloud

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Posted 24 October 2013 - 01:29 PM

Spoiler for 50 prisioners saved

 

Spoiler for Evil PO...


Edited by ThunderCloud, 24 October 2013 - 01:34 PM.

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#8 ThunderCloud

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Posted 24 October 2013 - 02:06 PM

Spoiler for Spoiler for 50


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#9 phil1882

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Posted 24 October 2013 - 03:06 PM

edit: never mind

 


Edited by phil1882, 24 October 2013 - 03:09 PM.

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#10 ThunderCloud

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Posted 24 October 2013 - 04:08 PM

Spoiler for Spoiler for 50

 

Actually, that conniving PO could foil this plan too, saving only 48...

 

Spoiler for But I think this approach might just do it


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