Question

Challenge: You are investigating a murder on the island of liars and truth tellers. You have assembled a group and you want to know

Answer 1

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.

1. Q1 - Are you the group leader ?
2. Q2 - Does the group have 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?

• You speak the truth
• There is a murderer in the group.

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".