Solve this hard Deduction Problem?

Jimmy claims that either Michelle or Toni tells the truth. Toni says that either Michelle or Jimmy tells the truth. Michelle says that neither Toni nor Jimmy tells the truth. Who, if anyone, is truthful?

3 Answers

  • 2 months ago

    Since all three statements are "claims" only, we can't rely on any of them being true, so we can't know in this case who, if anyone, is being truthful.

  • 2 months ago

    Suppose Jimmy is lying. Then Michelle must be lying, else Jimmy's claim is true. But Michelle says Jimmy is lying, which is true, so she isn't lying. So assuming that Jimmy is lying leads to a contradiction.

    Suppose Jimmy is telling the truth. Then Toni is telling the truth and Michelle is lying, which does not contradict Jimmy's claim. That works.

  • 2 months ago

    Jimmy tells truth (he said Toni tells truth and Michelle lies)

    Toni tells truth (she said Jimmy tells truth and Michelle lies)

    Michelle lies (since she said neither above tells truth)

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