We don't know anything about the members of the group. They can be liars/truthful and murderers/Not murderers. While asking a question to the group leader, one thing is for certain, we know that he is the group leader. So the first question to be asked should be whether he is the group leader or not. This will immediately tell us whether the leader is a liar or a truth-telling person "if his answer yes I'm the leader that's mean he telling the truth". Then we can ask the question if the group has the murderer.
Q1 | Q2 -Yes | Q2-No |
Yes | Verdict - Yes | Verdict - No |
No | Verdict - No | Verdict - Yes |
The table kind of gives us a hint on that the question is based on XOR logic. Now try this:
Asking the following question to the leader:
Is exactly one of the following true?
Now we haven't asked two questions, we have just asked a single question on whether exactly one of these is correct. Following is a table of Actual Answers of the two subparts and what the final answers of a truth-telling and liar would be.
a | Yes | Yes | No | No |
b | Yes | No | Yes | No |
Final answer- Truth-telling | No | Yes | X | X |
Final answer- Liar | X | X | No | Yes |
The Xs are situations that don't arise because of our assumption that the person is a Liar/Truth-telling. Therefore, if the answer to the question is "No" - irrespective of whether the leader is a liar or truth-teller, we can say that there is a murderer in the group, and the opposite if the answer is "Yes".
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