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From: terryl@tekcrl.UUCP
Newsgroups: net.puzzle
Subject: Re: another puzzle (SOLUTION***SPOILER)
Message-ID: <527@tekcrl.UUCP>
Date: Fri, 14-Feb-86 04:51:57 EST
Article-I.D.: tekcrl.527
Posted: Fri Feb 14 04:51:57 1986
Date-Received: Sun, 16-Feb-86 04:06:22 EST
References: <1645@hound.UUCP>
Lines: 42

> 
> 
>      Three men are in a room. The room has no mirrors and the three men
> are in a straight line such that the person in the back of the line
> can see the two people in front of him, the middle person can see
> only the person in front of him, and the person in front can't see
> anyone. Another person walks in with a bag containing 3 black hats
> and two red hats. The man pulls three hats at random out of the bag
> and places them randomly on the three men. He walks out of the room.
> The man in the back says,"I don't know what color hat I'm wearing."
> The man in the middle says,"I don't know what color hat I'm wearing, either."
> Now tell me what color hat the man in the front of the line is wearing
> and why.
> 

     The first man is wearing a black hat. At first, this looked impossible
to figure out, but once you look at it logically, you'll say "WOW!!! I coulda
had a V8!!!".

     Here's the reasoning:

     From the vantage point of the men in the back of the line, there are
three possibilities: The two men in front both have black hats, or both have
red hats, or one has a red hat and one has a black hat. We can immediately
dismiss the "both have red hats" case, since if that were true, then the
man in the back of the line would have a black hat. That leaves either "both
have black hats" case, or "one has a red hat and the other has a black hat"
case. We only need to consider the "one has a red hat and the other has a
black hat" case, since if both the man in front and the man in the middle had
a black hat, then obviously the man in front would be wearing a black hat.

     Assume the man in front had a red hat. Now the man in the middle AND
the man in the back can both see this. If this were the case, then the man
in the middle can immediately claim that he is wearing a black hat, because
by what the man in the back said. So the man in front cannot be wearing a
red hat, because the man in the middle claims that he doesn't know what color
hat he is wearing; therefore, the man in front must be wearing a black hat. QED.


				Terry Laskodi
				     of
				Tektronix