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Math Help - logic word puzzle

  1. #1
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    logic word puzzle

    hey guys. who is interested in a logic puzzle? i still cant work it out help me please

    four suspects W,X,Y and Z were rounded up for questioning conserning a break in. it was known that at least one was guilty, and that no on outside the 4 was involved. the following facts were established:

    a) W is definatelly innocent
    b)if X was guilty, then he had exactly one accomplice
    c) if Y was guilty, then he had exactly two accomplice

    is Z guilty or not?
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  2. #2
    MHF Contributor
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    Quote Originally Posted by boomshine57th View Post
    hey guys. who is interested in a logic puzzle? i still cant work it out help me please

    four suspects W,X,Y and Z were rounded up for questioning conserning a break in. it was known that at least one was guilty, and that no on outside the 4 was involved. the following facts were established:

    a) W is definatelly innocent
    b)if X was guilty, then he had exactly one accomplice
    c) if Y was guilty, then he had exactly two accomplice

    is Z guilty or not?
    If X is guilty, then his accomplice could be Y or Z
    If Y is guilty, then his accomplices can only be X and Z

    Is Z guilty?

    Not sure. Because X could be the guilty person and Y is his accomplice.
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  3. #3
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    z is guilty

    if y is guilty then so are x and z

    if x is guilty then so is z ( because if y was guilty al three would be guilty)
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  4. #4
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    Hello, boomshine57th!

    Four suspects W,X,Y\text{ and }Z were rounded up for questioning concerning a break-in.
    It was known that at least one was guilty, and that no one outside the 4 was involved.
    The following facts were established:

    (a) W is definitely innocent
    (b) if X was guilty, then he had exactly one accomplice
    (c) if Y was guilty, then he had exactly two accomplices

    Is Z guilty or not?

    From (a), the only suspects are: . X,Y,Z

    If (c) is true, then Y is guilty, and X and Y were accomplices.
    . . Then all three are guilty. ( X had two accomplices; Z had two accomplices.)
    Hence, (b) is not true.

    Therefore, (c) is not true: Y is innocent.
    . . The only suspects are: . X\text{ and }Z


    X is either (1) guilty or (2) innocent.

    (1) If X is guilty, then (b) says he had one accomplice; it must be Z.
    . . Hence, Z is guilty.

    (2) If X is innocent, then Z is the only remaining suspect.
    . . Hence, Z is guilty.


    Therefore, Z is guilty.

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  5. #5
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    i love your logic! thats really good! thank you ever so much! (star)
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