*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 > > ------------------------------------------------------------------ > To change your Lit-Ideas settings (subscribe/unsub, vacation on/off, > digest on/off), visit www.andreas.com/faq-lit-ideas.html > ------------------------------------------------------------------ To change your Lit-Ideas settings (subscribe/unsub, vacation on/off, digest on/off), visit www.andreas.com/faq-lit-ideas.html

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

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

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

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