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From: verma@ucla-cs.UUCP
Newsgroups: net.puzzle
Subject: Re: another puzzle (hats) (* spoiler *)
Message-ID: <8937@ucla-cs.ARPA>
Date: Thu, 13-Feb-86 10:52:12 EST
Article-I.D.: ucla-cs.8937
Posted: Thu Feb 13 10:52:12 1986
Date-Received: Sat, 15-Feb-86 06:22:30 EST
References: <1645@hound.UUCP>
Reply-To: verma@ucla-cs.UUCP (Thomas S. Verma )
Organization: UCLA Computer Science Department
Lines: 30

In article <1645@hound.UUCP> 5125kaf@hound.UUCP (K.FRIEDMAN) writes:
>
>
>     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 man in front is wearing a black hat.

        Why ---

        Since the man in the back did not know what color his own hat
        was, then at least one of the men in front of him was wearing
        a black hat.  For if both of the men in front of him were wearing
        red hats, then he would know his own hat was black (only 2 red
        hats).  Now the middle man still does not know his own hat's color;
        if the first man had been wearing a red hat, then the man in the
        middle (knowing one of the two had a black hat) would know he was
        the one.  But he didn't so the first man was not wearing a red
        hat, and therefore must have been wearing a black hat.  QED

                                                        TS Verma