Five people are sitting around a circle. Some always tell the truth, whilst others always lie. Each person claims to be sitting between two liars. How many of them are telling the truth?
A 0
B 1
C 2
D 3
E 4
1: LTL <-- sure
2: LLTLL <-- adjust
3: LLTLT <-- final
To solve this problem, let's examine the statements made by each person.
First, let's identify the possible positions of the truth-tellers around the circle. Since each person claims to be sitting between two liars, anyone claiming to be sitting between two liars must be telling the truth. In other words, only truth-tellers can sit next to two liars.
Let's consider each position and the corresponding statements made by the people sitting there:
Position 1: The person in this position claims to be sitting between two liars. If this statement is true, then the person must be telling the truth, making this position a truth-teller.
Position 2: The person in this position claims to be sitting between two liars. However, we already know that person in Position 1 is telling the truth. Therefore, the person in Position 2 cannot be telling the truth because they would have to be sitting next to two liars. Thus, this position cannot have a truth-teller.
Position 3: Similar to Position 2, the person in this position claims to be sitting between two liars. However, the person in Position 1 is a truth-teller, which means the person in Position 3 cannot be telling the truth since they would have to be sitting next to two liars. Therefore, this position cannot have a truth-teller.
Position 4: The person in this position claims to be sitting between two liars. We have already determined that both Positions 1 and 2 cannot have truth-tellers, which means the person in Position 4 cannot be telling the truth either. This position cannot have a truth-teller.
Position 5: The person in this position claims to be sitting between two liars. Since Positions 2, 3, and 4 cannot have truth-tellers, the person in Position 5 must be telling the truth, as there are no other positions left.
Based on our analysis, only one person is telling the truth, which corresponds to Position 5.
Therefore, the correct answer is:
B) 1