Truth or Liar

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John and Jacob are twin brothers. One of them is a liar whereas the other one is a truth-teller.

I called their home number and one of them picked up.
I asked. ‘Does John lie?’ The person replied with a yes.

Whom did I talk with, John or Jacob?

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    Jacob

    We have two possibilities:
    (1) John is the liar and Jacob says the truth OR
    (2)  Jacob is the liar and John says the truth.

    In both the cases, we have two possible outcomes of the call:
    (a) John attended the call OR
    (b) Jacob attended it.

    Assuming (1) was correct, i.e., John is the liar:

    If (a) were correct, i.e., John attended the call, then he would have said ‘no’ because he’s the liar, and hence wouldn’t have admitted it. But the person who attended the call said ‘Yes’. So, it can’t be John who picked the call. i.e., it must be Jacob.

    Now, if we assume that (2) was correct, i.e., Jacob is the lair. Then:

    If (a) were correct, i.e., John attended the call, he would have told the truth – that he does not lie. But the person said ‘Yes’. So, it can’t be John who attended the call. It must be Jacob,

    Thus, in either case, it must be Jacob who attended the call.

    Viji_Pinarayi Expert Answered on 24th March 2023.
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