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I'm confused; what are the right answers for the following question under each of the 4 different conditions listed below?

“Are you Lala, or lying today, but not both?”

  1. If you are Lala, and you are a liar, what is your answer? (Yes/No)
  2. If you are Lala, and you are a Truth teller, what is your answer? (Yes/No)
  3. If you are not Lala, and you are a liar, what is your answer? (Yes/No)
  4. If you are not Lala, and you are a Truth teller, what is your answer? (Yes/No)
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  • $\begingroup$ "What is the right answer for this question" could / should be the title of all Stack Exchange questions. ;-P $\endgroup$ – palsch Oct 2 '16 at 22:23
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This is what's called an exclusive or condition: the correct answer is yes if and only if exactly one of the statements "you are Lala" and "you are lying today" is true. However, matters are further complicated by the fact that if you are a liar, you will not give the correct answer.

  1. If you are Lala, and you are a liar, what is your answer?

    The correct answer is no, because then the "and not both" condition of the question isn't satisfied. So your answer is yes, because you are a liar.

  2. If you are Lala, and you are a Truth teller, what is your answer?

    The correct answer is yes, because you are Lala but you are not both Lala and a liar. So your answer is yes, because you are a truth teller.

  3. If you are not Lala, and you are a liar, what is your answer?

    The correct answer is yes, because you are a liar but you are not both Lala and a liar. So your answer is no, because you are a liar.

  4. If you are not Lala, and you are a Truth teller, what is your answer?

    The correct answer is no, because you are neither Lala nor a liar. So your answer is no, because you are a truth teller.

Thus this question provides a way to

extract the answer to a yes/no question from a person who may either be a liar or a truth-teller by asking them a single, albeit tricky, question.

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  • $\begingroup$ Does this take into account that if you are lying today, then you lie for the answer? $\endgroup$ – Beastly Gerbil Oct 2 '16 at 13:46
  • $\begingroup$ I just think you must not give this question, because if you are a liar, you will not confess. so for the second condition you will say no, But the liar can also lie about the condition (exclisive or), so you will get uncertain answer. the liar can answer Yes or No whatever he like.. $\endgroup$ – Jamal Senjaya Oct 2 '16 at 13:47
  • $\begingroup$ @Jamal But you asked for the right answer, not the person's (possibly false) answer! :-) Will edit. $\endgroup$ – Rand al'Thor Oct 2 '16 at 13:48
  • $\begingroup$ @Beastly I was answering the "what is the right answer?" part and not the "what is your answer?" part - maybe because I've seen too many of TheBitByte's liar puzzles ;-) I've now edited to address both. $\endgroup$ – Rand al'Thor Oct 2 '16 at 13:52
  • $\begingroup$ @randal'thor I asked this because in puzzling.stackexchange.com/questions/43528/… puzzle, someone give me this in his answer. $\endgroup$ – Jamal Senjaya Oct 2 '16 at 13:54

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