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 Murder by Logic (Posted on 2004-03-05)
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?

 See The Solution Submitted by Federico Kereki Rating: 3.6667 (12 votes)

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 Puzzle Solution Comment 23 of 23 |

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
 Posted by K Sengupta on 2008-05-15 06:17:09

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