3. Alice, Bob, Charlie and Eve are having a conversation. Each of them knows who are honest and who are liars. The conversation goes as follows:
Alice: Both Eve and Bob are liars.
Bob: Charlie is a liar.
Charlie: Alice is a liar.
Eve: Bob is a liar.
Who is/are honest?
Answer: Charlie and Eve
Solution: We consider two cases:
Case 1: Alice is honest.
If Alice is honest, both Eve and Bob must be liars. If Eve is a liar, then Bob must be honest. This cannot be the case.
Case 2: Alice is a liar.
If Alice is liar, then either Eve is honest or Bob is honest. Suppose Eve is honest. Then, Bob is a liar. If Bob is a liar, Charlie must be honest, and Alice is a liar. This is a possible case.
Suppose Eve is a liar. Then, Bob is honest. Since Bob is honest, Charlie is a liar, and Alice is honest. This cannot also be the case.

Thus the only possible case is that Alice is a liar, Bob is a liar, Charlie is honest and Eve is honest.