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Math Help - [SOLVED] Logic Question

  1. #1
    TGS
    TGS is offline
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    [SOLVED] Logic Question

    Sharky, a leader of the underworld, was killed by one of his own band of four henchmen. Detective Sharp interviewed the men and determined that all were lying except for one. He deduced who killed Sharky on the basis of the following statements:

    a) Socko: Lefty killed Sharky.
    b) Fats: Muscles didn't kill Sharky.
    c) Lefty: Muscles was shooting craps with Socko when Sharky was knocked off.
    d) Muscles: Lefty didn't kill Sharky.

    Who killed Sharky??

    Please help...

    I've set variables for each statement.

    p - Socko Killed Sharky
    q - Fats killed Sharky
    r - Lefty killed Sharky
    s - Muscles killed sharky
    t - Muscles was shooting with Socko when Sharky was killed
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  2. #2
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    Hello, TGS!

    Sharky, a leader of the underworld, was killed by one of his own band of four henchmen.
    Detective Sharp interviewed the men and determined that all were lying except for one.
    He deduced who killed Sharky on the basis of the following statements:

    a) Socko: Lefty killed Sharky.
    b) Fats: Muscles didn't kill Sharky.
    c) Lefty: Muscles was shooting craps with Socko when Sharky was knocked off.
    d) Muscles: Lefty didn't kill Sharky.

    Who killed Sharky?

    (a) Socko said: .Lefty is guilty.

    (b) Fats said: .Muscles is innocent.

    (c) Lefty said: .Muscles and Socko are both innocent.

    (d) Muscles said: .Lefty is innocent.



    The fact is: exactly one told the truth, the other three lied.


    Note that (a) and (d) are contradictory.
    They cannot both be true and they cannot both be false.
    One of them told the truth, the other one must have lied.

    Suppose (a) is true: Lefty is guilty.
    . . Then (b) and (c) are also true.


    Hence, (d) is true: .Lefty is innocent.

    Then: .(a) "Lefty is guilty" is a lie.

    . . . . . (b) "Muscles is innocent" is a lie.

    . . . . . (c) "Muscles is innocent and Socko is innocent" is also a lie.


    Therefore: .Muscles is guilty.

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