## [lit-ideas] Re: Try a Logic Problem

• From: "Lloyd Mitchell" <rmitchell@xxxxxxxxxxxx>
• To: <lit-ideas@xxxxxxxxxxxxx>
• Date: Fri, 23 Jun 2006 10:05:43 -0700

```OK, here's the solution.

#1 can know what color hat he's wearing only if he sees two red hats. (The
pool is 2 red, 3 white.) He does not know. So he isn't looking at 2 reds.

#2 doesn't need to bother looking at #1. If he sees red on #3, he knows he's
wearing white. (Otherwise #1 would be looking at 2 reds, and could have
answered.) He does not know. So he isn't looking at red on #3.

So #3 knows he's wearing white.

Lloyd Mitchell

----- Original Message -----
From: "Paul Stone" <pas@xxxxxxxx>
To: <lit-ideas@xxxxxxxxxxxxx>
Sent: Friday, June 23, 2006 8:20 AM
Subject: [lit-ideas] Re: Try a Logic Problem

> 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
>
> 3) BUT, since P2 knows knowledge (1), if P3 was wearing a red hat, then P2
> would KNOW that he himself had a white hat on -- because, if P2 also had a
> red hat on, then it cascades back and P1 would have KNOWN that he (P1) had
> a white hat on.
> 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.
>
> Paul
>
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