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Math Help - Three People Stand In Line

  1. #1
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    Three People Stand In Line

    This is a beginner question I just got today. Could anyone give me an idea how to solve this?

    Three people stand in line, one after the other. A hat is placed on the head of each one of them from a set of three white and two black hats. Each person can see only the hats of the persons standing around them, and not his own. They all know there are three white hats and three black hats. Show at some point in time that one of them knows the color of his own hat.

    thanks in advance.
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  2. #2
    Senior Member DivideBy0's Avatar
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    So... is it three blue and three black, or three blue and two black? The question also seems quite undeveloped, by 'some point in time' what do you mean? Do they switch hats around after a period of time etc.?
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  3. #3
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    Hello, Edbaseball17!

    I agree with Divideby0 . . . Your wording is vague.


    Three people stand in line, one after the other.
    A hat is placed on the head of each one of them from a set of 3 white and 2 black hats.
    Each person can see only the hats of the persons in front of him, and not his own.
    They all know there are three white hats and two black hats.

    Show at some point in time ? that one of them knows the color of his own hat.

    Do you mean: eventually one of them will have a divine revelation? .I don't think so!
    This is a classic problem, but you've omitted some important details.


    The three men are intelligent and logical.

    They are instructed: When you know the color of your hat, say "I know."

    After a few minutes of silence, the man in front (who sees no hats
    . . and who, incidentally, is blind) says, "I know!"

    What color is his hat, and how did he know?


    He reasoned as follows.

    If the man at the back saw two black hats,
    . . he'd know immediately that he has a white hat.
    Since he didn't answer, he must have seen at least one white hat.

    The man in the middle knows this.
    So if he saw a black hat in front of him,
    . . he'd know immediately that he has white hat.
    Since he didn't answer, he must have seen a white hat.

    The man in front knows all of this
    . . and concluded that he must have a white hat.

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