So, there are three suspects. They are John, Bob and Mary. They all make 3 statements each.
Bob says: John is innocent. Mary is the murderer. Mary hated the victim.
John says: I am innocent. On the night of the murder, me and Mary were together. The victim was best friends with Bob and Bob was best friends with the victim.
Mary says: I am innocent. I was never with John, on the night of the murder. I did not see Bob on the night of the murder, either.
It could be any one of them, all of them, two of them or none of them. The liar(s) are the murderers. Solve it.
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So, if the murderers were lying, then that means we have to twist everything around. Let’s start with Bob. He says that John is innocent, Mary is the murderer and Mary hated the victim. When we twist it around, he is saying that actually, John is guilty, Mary is not the murderer and Mary loved the victim. Let’s go to John. He says I am innocent, on the night of the murder, me and mary were together and Bob was best friends with the victim and the victim was best friends with Bob. When we twist it around, it mean he is guilty, he and Mary were not together on the night of the murder and Bob was enemies with the victim and the victim was enemies with Bob. Mary says I am innocent, I was never with John on the night of the murder and I never saw Bob on the night of the murder. Twisting it around, it means that she was not innocent and she was with John on the night and she saw Bob on the night of the murder.
We still need to find out, though, who the murderer(s) is or if it’s murderers are. So if it is murderers, they would try to help each other as they are in it together. In Bob and John’s statements, they are helping each other, when John says Bob was best friends with the victim and when Bob says that John was innocent. This means that they were the liars and they are the murderers. Mary is innocent and did not lie. We also know it was Bob, more so than John, because he has more of a motive if the victim was his enemy.