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Who's trustworthy?

  1. Aug 30, 2011 #1
    On a certain island, the inhabitants are divided into two types, those who always tell the truth and those who always lie. One day a vistor to the island stops three inhabitants of the island to ask for directions to a well known museum. "All three of us are liars," warns the first inhabitant, "not so, only two of us are liars," says the second. "Not so," says the third, "The other two guys are lying."

    Which, if any, of the three islanders can the visitor truth to give honest directions?

    The second, right?
     
  2. jcsd
  3. Aug 30, 2011 #2

    micromass

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    I think the second as well...
     
  4. Aug 30, 2011 #3
    My reasoning:

    The first: The assumption that he is telling the truth leads to a sort of paradox, since he claims that he himself is a liar. However he is still lying if less than 3 are liars. He must be lying.

    The second: "only two of us are liars." In no direct contradiction to anything.

    The third: "Not so, the other two guys are lying." He must be lying because he is claiming that the second is lying, while at the same time agreeing with him about the number of liars. His statement must be a false one.
     
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