Professor Z was killed by one of his four students, who was helped by another of the four. His students declared:
A: If B is guilty of something, then C must be innocent.
B: If A is innocent, then C must be guilty.
C: If B was the killer, then D must have had nothing to do with the crime.
D: I am innocent.
As everybody should know, guilty parties always lie, and innocent people always tell the truth. Who killed the professor, and who was his accomplice?
(In reply to answer
by K Sengupta)
At the outset, let us suppose that C was guilty. If so, then by his false statement it follows that if B was the killer then D must have been connected with the crime. This suggests the complicity of three individuals connected with the crime, which leads to a contradiction.
Accordingly, it follows that C was innocent. ........(*)
Let us now suppose that B was innocent. If so, A could be either innocent or guilty. If A was guilty, then in terms of his false statement, it follows that each of B and C must also be guilty. This is a contradiction. On the other hand, if A was innocent, then in terms of his statement, it follows that C was guilty, and this contradicts (*).
Accordingly, it follows that A couldn't have been either innocent or guilty. Therefore, the original supposition that B was innocent is false, and hence B must be guilty. Since by (*), we know that C was innocent, it follows from B's false statement that A must be innocent. Thus remaining individual, that is D, must be guilty.
Now, C was innocent. Since, both B and D were guilty, it follows from C's true statement that B couldn't have been the killer. Consequently, D was the killer and B was his accomplice.
Edited on May 15, 2008, 6:20 am