*From*: Paul Stone <pas@xxxxxxxx>*To*: lit-ideas@xxxxxxxxxxxxx*Date*: Fri, 23 Jun 2006 11:20:45 -0400

`At 11:10 AM 6/23/2006, you wrote:
`

Paul Stone wrote:

"and yesterdays answer ... was correct and pretty much exactly the same as yours."

The part I didn't get was:

"Since neither prisoner 1 or 2 knows which colour hat they have on, they must BOTH be wearing red ones because, if 3 had a red hat on, prisoner #2 would KNOW that he has a white one on"

I don't see why P1 and P2 must both be wearing red hats. Why can't they both be wearing white hats? Or why can't P1 be wearing white and P2 red? Or vice versa?

Okay, this is the verbose answer:

1) P1 says he doesn't know:

THEREFORE, P2 and P3 must be collectively be wearing either 1R/1W or 2W

2) P2 says he doesn't know either:

THEREFORE, P1 and P3 must ALSO be collectively be wearing either 1R/1W or 2W

So it's the elimination of the possibility of his red hat wearing that allows P3 to know that he must be wearing a white hat. It makes no difference what P1 and P2 have on, they could very well both be wearing white.

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**Follow-Ups**:**[lit-ideas] Re: Try a Logic Problem***From:*Phil Enns

**[lit-ideas] Re: Try a Logic Problem***From:*Lloyd Mitchell

**References**:**[lit-ideas] Re: Try a Logic Problem***From:*Paul Stone

**[lit-ideas] Re: Try a Logic Problem***From:*Phil Enns

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