Peter and Paul are always lying and truth-telling twins. You ask one of them, "Is Paul the lying one?" And he answers, "Yes." Whom did you ask the question?
The Riddle of always lying and truth-telling twins
Peter and Paul are twin brothers who look exactly alike. one of them, though, always lies and the other always tells the truth.
Once you ask one of them out of curiosity, "Is Paul the one who always lies?" And he answered, "Yes."
Question is: Whom did you ask the question?
Time to solve: 5 minutes.
Solution to the riddle of always lying and truth-telling twins
It's confusing, isn't it? Decide to avoid confusion totally and imagine and analyze "What if" situations.
For example, you can assume Paul is the always lying brother and with this assumption it will be easy for you to jot down the consequences without any confusion.
First What if situation: Paul is the always lying brother
Hint: Just forget that you have to find whom you asked the question.
Why? Because, if you ask a question to Paul or Peter the answer will not depend on the fact that you have asked the question. Answer will depend on the question and nature of Peter and Paul.
Okay, so we assume that Paul is the lying twin.
What would be the answer from Paul then?
True to his nature, he must reverse the truth and must answer in this case, "No."
And answer from Peter? He will simply tell the truth and answer, "Yes."
Actual results tally with the imagined results in this first what if situation, but you won't assume that you have reached the answer.
Why? Because, as you are following a systematic path, you have to see the consequences of all possible what if situations. That is the hallmark of exhaustive systematic analysis.
Second What if situation: Peter is the always lying twin
Notice that we are focusing on the always lying property. We can be sure in this case that Paul must then be the truth-telling twin.
Peter being the always lying twin what would be his answer? The genuine answer to the question, "Is Paul the one who always lies?" being NO, Peter has to reverse the truth and must answer, "Yes." And that has been the answer you got.
What would Paul's answer be? He will simply tell the truth and answer, "No.".
As you have got the answer of "Yes.", you will be sure now that whomever of Peter or Paul is the always lying twin, you have asked the question undoubtedly to Peter.
In both "What if" situations, Peter answers with "Yes.". That confirms the solution as Peter.
Can there be any more "What if" situation? No, there cannot be. In the second "What if" situation, you have covered just the opposite of the first "What if" situation, which has been the only other possibility.
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