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Math Help - Enigme !

  1. #1
    Junior Member
    Joined
    Dec 2009
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    Enigme !

    Hii !

    Three prisoners are one behind the other. Each wearing a hat on the head fired at random from 2 white hats and 3 blacks. Thus, the first sees the hats of 2 next, the 2nd, only the following and the 3rd see nobody. That devine the color of his hat is released.One who gives a false response is dead, but the one who do not know will remain prisoner. Request that prime (who sees the 2 other) if he knows the color of his hat. He replied that not. We are asking the 2nd (who cannot see that the next), it also responds not. We are asking the 3rd who does not see person and knows how to answer. How is this possible ?

    Have Fune
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, Perelman!

    This is a classic (very old) problem.


    Three men are lined up in a single file.
    Each is wearing a hat chosen at random from 2 white hats and 3 blacks.
    The rear man sees the hats of the other two,
    . . the middle man sees only the front hat,
    . . the front man can see no hats.

    The rear man is asked if he knows the color of his hat. He replies "No."
    The middle man is asked if he knows the color of his hat. He replies "No",
    The front man is asked if he knows the color his hat. He replies "Yes," and correctly names the color.

    How is this possible?
    Spoiler:

    If the rear man saw two White hats, he'd know he was wearing a Black hat.
    Since he didn't know the color of his hat, he must have seen at least one Black hat.

    The middle man knows this.
    So, if he saw a White hat on the front man, he'd know that his hat is Black.

    Since the middle did not the color of his hat, he must have seen a Black hat.

    Therefore, the front man concluded that he is wearing a Black hat.


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