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Math Help - What road to take? Knights and Knaves puzzle.

  1. #1
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    What road to take? Knights and Knaves puzzle.

    At each fork of roads on the island, exaclty one road is safe to take; the other roads lead to dragons and very sharp sticks and whatnot. Luckily, there are signs posted for each possible direction you could choose. Unluckily, at each intersection, at least one of these signs is a lie. While walking down the road one day you come to a place where the road splits into three directions, labeled A, B, C. From the statements on the signs below, determine which road is safe to take.

    Road A:
    "You can believe what is written on signs B and C."

    Road B:
    "You should take road A. Or maybe road C. One of those."

    Road C:
    "Whatever you do, do not take road B!"
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  2. #2
    Junior Member
    Joined
    Jan 2009
    Posts
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    Let's see. I'm sorry if I missed something.

    If sign A is true, then signs B and C must also be true. But this leads to a contradiction, since at least one sign must be lying. So, sign A is actually false. But if it's false, then I cannot believe what's written on signs B and C. Therefore, all three signs are lying.

    Sign C says that I shouldn't take road B, but since it is lying, I choose road B.
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