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Knight and knaves and distant planet puzzle

  1. Jan 15, 2010 #1
    A distant planet is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie.

    Eight inhabitants of the planet: Marge, Mel, Betty, Bob, Bill, Carl, Zeke and Alice are busy at a conversation, when a visitor from a neighboring planet stops by and asks each of the eight inhabitants their respective identities. They say:

    Marge: “It's not the case that Bob is a knave.”

    Mel: “Bill is a knave.”

    Betty: “Carl and Zeke are knights.”

    Bob: “Neither Mel nor Bill are knaves.”

    Bill: “Only a knave would say that Carl is a knave.”

    Carl: “I know that Alice is a knave and Zeke is a knight.”

    Zeke: “Of Carl and I, exactly one is a knight.”

    Alice: “Zeke and Marge are both knights.”

    Determine the type of each of the inhabitants from the abovementioned statements.
     
    Last edited: Jan 16, 2010
  2. jcsd
  3. Jan 15, 2010 #2

    D H

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    Mel is a knight; all of the rest of are knaves.

    This assumes that knaves can tell the truth so long as they do so in a compound statement and so long as the compound statement is false.
     
  4. Jan 15, 2010 #3

    CRGreathouse

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    From Zeke's statement, we deduce that Carl is a knave. Then from Bill's statement we deduce that Bill is also a knave. Thus Bob is a knave and Mel is a knight. Thus Marge and Betty are knaves. Thus Alice and Zeke are also knaves.

    It's a pretty easy puzzle.
     
  5. Jan 15, 2010 #4
    Just a persnickity bit-- I don't like the way Carl's statement is phrased. It's arguable as to whether or not he's making a compound statement "X and Y", or two separate statements "X" and "Y". Assuming the former, everything's peachy. But assuming the latter, it's impossible. I know it's a sticky point of grammar, but the current phrasing translates to:

    Carl: “I know that Alice is a knave and I know that Zeke is a knight.”

    I would recommend changing it to:

    Carl: “I know that Alice is a knave and Zeke is a knight.”

    DaveE
     
  6. Jan 15, 2010 #5

    D H

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    I had the same persnickity problem with Carl's statement.
     
  7. Jan 16, 2010 #6
    I confirm having made the requisite amendment in the original post in conformity with the foregoing.
     
    Last edited: Jan 16, 2010
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