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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

18 replies to this topic

### #11 Rainman

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Posted 24 October 2013 - 08:49 PM   Best Answer

Spoiler for simple example for 50 saves

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### #12 bonanova

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Posted 25 October 2013 - 02:37 PM

Spoiler for 50 prisioners saved

Spoiler for Evil PO...

Good observation TC.

But in fairness to Phil, the PO, knowing that half will make blue=1, etc., may not know which half that is. The PO, I think, would only choose the distribution of red/blue, not the individuals that receive a certain color. I'm still thinking through Phil's solution before I declare the puzzle solved.

In addition to the solutions posted (Rainman's #11 is very concise, and I'm wondering whether it's equivalent to Phil's?) there is a another clever one, not yet posted.

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

### #13 ThunderCloud

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Posted 26 October 2013 - 12:21 AM

The PO, I think, would only choose the distribution of red/blue, not the individuals that receive a certain color.

The puzzle states: "There is a spy who informs the PO of the strategy. So in placing the hats, the PO does his best to foil it." I interpreted this to mean the PO placed the hats himself, as diabolically as he could.

Edited by ThunderCloud, 26 October 2013 - 12:26 AM.

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### #14 bonanova

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Posted 26 October 2013 - 04:40 AM

The PO, I think, would only choose the distribution of red/blue, not the individuals that receive a certain color.

The puzzle states: "There is a spy who informs the PO of the strategy. So in placing the hats, the PO does his best to foil it." I interpreted this to mean the PO placed the hats himself, as diabolically as he could.

I follow you. And the OP, again, to be fair to you, does not preclude your comment.

The difference I drew was between knowing the strategy in general terms and being privy to the details of its implementation. And that is a finer distinction than the OP makes.

BTW, This may distinguish between Phil's and Rainman's (post 11) approaches. I don't think your PO tactic can defeat Rainman's solution. Or can it?

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

### #15 Rainman

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Posted 26 October 2013 - 10:44 AM

Phil's post is equivalent to half of the prisoners guessing there is an even number of blue hats, and the other half guessing there is an even number of red hats. Which is equivalent to everyone guessing there is an even number of blue hats. A 51-49 distribution, for example, is enough to guarantee that everyone fails. He had the right idea, but switching between counting red as 1 and counting blue as 1 does not change the outcome of the guess.

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### #16 bonanova

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Posted 26 October 2013 - 11:56 AM

The classic solution I saw a while back is clever, but not as neat as Rainman's:

Spoiler for classic

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

### #17 ThunderCloud

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Posted 26 October 2013 - 01:14 PM

The PO, I think, would only choose the distribution of red/blue, not the individuals that receive a certain color.

The puzzle states: "There is a spy who informs the PO of the strategy. So in placing the hats, the PO does his best to foil it." I interpreted this to mean the PO placed the hats himself, as diabolically as he could.

I follow you. And the OP, again, to be fair to you, does not preclude your comment.

The difference I drew was between knowing the strategy in general terms and being privy to the details of its implementation. And that is a finer distinction than the OP makes.

BTW, This may distinguish between Phil's and Rainman's (post 11) approaches. I don't think your PO tactic can defeat Rainman's solution. Or can it?

The Evil PO would be out of luck with Rainman's approach, so far as I can tell.

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### #18 benjer3

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Posted 27 October 2013 - 11:58 PM

Spoiler for Not exactly a solution, but a thought.

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### #19 bonanova

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Posted 29 October 2013 - 05:29 AM

Spoiler for Not exactly a solution, but a thought.

I think you're correct in your last statement. You can, as far as I know. guarantee 50% but not more.

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

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