[lit-ideas] Re: Try a Logic Problem

  • 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

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.


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