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A wicked master

  1. Sep 9, 2004 #1
    a wicked master captures a boy, and tells him he will work for one of his two sons. He is allowed to make one statement - if this statement it true, he will work for Terrence the Terrible. If the statement is false, he will work for Angus the Awful.

    What can the boy say so that he will not work for either of the wicked master's two sons?
  2. jcsd
  3. Sep 9, 2004 #2
    I will work for Angus the Awful.
    I think that does the job
  4. Sep 28, 2004 #3
    Using symbolic logic...

    p: The statement is true (~p: the statement is false)
    q: He will work for Terrence (~q: he will NOT work for Terrence)
    r: He will work for Angus (~r: he will NOT work for Angus)
    s: He will work for neither (~s: he will work for one of them)

    Conditional (p -> q) Hypothesis #1
    Conditional (~p -> r) Hypothesis #2
    Therefore (p -> s) v (~p ->s) ?

    Construct truth table with conclusion (p -> q) ^ (~p -> r) -> (p ->s)
    and you will find that there is no true statement or false statement that can be made to avoid working for one or the other. Therefore, the statement he must make to escape working from both is to not speak at all, to say NOTHING.
  5. Sep 28, 2004 #4


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    I think Poolwin has it. If you say you will work for Angus, then if you are sent to work for Angus, the statement is true. But, you can only work for Angus if the statement is false. If you go to work for Terrence, then the statement is false, but you can't work for Terrence if the statement is false, you should have worked with Angus.
  6. Sep 28, 2004 #5
    huh? :confused: :confused:
  7. Sep 28, 2004 #6


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    Poolwin's right.

    divib, saying nothing does not save you because there is no stated outcome for that choice of action. Perhaps, if you say nothing, the wicked master makes you work for him until you finally open your mouth. Your truth table approach doesn't account for the possibility that the outcome can alter the truth of the statement.

    So using p -> q and ~p -> r , the solution is simply one that makes r -> p. Why ? Because r -> p and p - > q means that r -> q, but r and q are mutually exclusive, hence you have a contradiction. And clearly, Poolwin's answer is an example of r -> p.
  8. Sep 29, 2004 #7
    my friend sandeep here, gives another answer which is similar to the answer already given. the sentence is:

    "im a perennial liar".

    kind of a paradox.
  9. Sep 29, 2004 #8
    a similar sort of question was posted here a few days back, the only difference was that it said that a man is going to be killed by an executioner and the executioner asks him to say something. if it is true he will be hanged to death and if false he will be drowned to death.

    see!! pretty much the same.
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