When a psychiatrist was found murdered in his apartment, 4 of his patients were questioned about his death.
I. The police knew from the testimony of witnesses that each of the 4 patients had been alone with the psychiatrist in his apartment just once on the day of his death.
II. Before the 4 patients were questioned they met and agreed that every statement each patient made to the police would be a lie.
Each of the patients made 2 statements, as follows:
Avery - 1. None of us 4 killed the psychiatrist. 2. The psychiatrist was alive when I left.
Blake - 3. I was the second to arrive. 4. The psychiatrist was dead when I arrived.
Larry - 5. I was the 3rd. to arrive. 6. The psychiatrist was alive when I left.
David - 7. The killer did not arrive after I did. 8. The psychiatrist was dead when I arrived.
Which one of the 4 patients killed the psychiatrist? Explain your reasoning.