5. The Case of Brown, Jones, and Smith. One of them committed a crime. During the investigation, each of them made two statements:

Brown: 1. I am not the criminal. 2. Neither is Jones.

Jones: 1. Brown is not the criminal. 2. Smith is the criminal. Smith: 1. Brown is the criminal. 2. I am not the criminal.

During the investigation, it was established that one of them lied twice, another told the truth twice, and the third one lied once and told the truth once. Who committed the crime?
5. The culprit cannot be Jones, because in this case none of the defendants would have lied twice, which contradicts the condition of the problem. It cannot be Smith either, because in this case there is no defendant who lied exactly once. The only possible option is that the crime was committed by Brown.