[lit-ideas] Re: Try a Logic Problem

  • From: Paul Stone <pas@xxxxxxxx>
  • To: lit-ideas@xxxxxxxxxxxxx
  • Date: Thu, 22 Jun 2006 16:53:48 -0400


> > Here, as promised, for all the bored and lonely souls, is a problem I
> > offer my students. I often get e-mail
> > requests years after the course from students who have forgotten the
> > solution and desperately need it for their Saturday evening escapades and
> > reflections. I am informed that some have made quick money in pubs with it
> > and/or gotten lucky in some other manner. However, I ask for no
> > commission.
> >
> >
> The guard now asks prisoner #1 "Can you tell me the colour of the hat
> > you're wearing. The prisoner responds "No, I cannot."
> >
> > The guard then asks prisoner #2 the same question and he receives the same
> > answer.
> >
> > Finally, the guard asks prisoner #3 and prisoner #3 replies that he does
> > indeed know the colour of the hat he's wearing.
> >
> > The problem, should you decide to accept it, is: what is the colour of the
> > hat #3 is wearing, and more importantly, in logic as in love, how did he
> > figure it out?
> >
> > I forgot to mention one small detail here. Prisoner #3 is completely
> > blind. This is a problem in strict logic, nothing up my sleeves, Rocky 


The blind guy has a white hat on.

1) Prisoner 1 can see both 2 and 3's hats. He doesn't know what his hat is, therefore, their hats have to be white and red or two whites.

2) Prisoner 2 can see both 1 and 3's hats. He doesn't know what his hat is, therefore 1 and 3 must be wearing either W/W or R/W.

3) 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 -- since both 2 and 3 can't both have Reds or number 1 would know that he has a white one on.

paul

##########
Paul Stone
pas@xxxxxxxx
Kingsville, ON, Canada 

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