Billy "The Knife," the infamous tough guy, was found murdered one night in an alleyway behind the nightclub he used to frequently visit. The police brought in three suspects on the next morning. One of the officers interrogated the three men and noted down the following statements.
Alex:
1. I did not kill Billy.
2. Jimmy is not my friend.
3. I knew Billy.
Jimmy:
1. I did not kill Billy.
2. Alex and Dexter are friends of mine.
3. Alex did not kill Billy.
Dexter:
1. I did not kill Billy.
2. Alex lied when he said that Jimmy was not his friend.
3. I do not know who killed Billy.
Only one of the three is guilty, and only one of each man statements is false. Who killed Billy the Knife ?
Jimmy
It is not Alex because if it was, Alex 1 and Jimmy 3 would both be false, which would make Alex 2 and Jimmy 2 both true which is a contradiction.
It is not Dexter because if it was, Dexter 1 and Dexter 3 would both be false, which is not possible.
Therefore, it must be Jimmy.
