Question

(Discrete Math)

Dean Keaton, a leader of the criminal underworld, was killed by one of his own henchman.
You are a special detective that has been called in to interview each of the men and determined
that all were lying except for one. He was able to deduce who killed Keaton based on the following
statements given by each of the henchmen.


Fenster: Soze killed Keaton.
Hockney: McManus was in a meeting with Fenster when Keaton was killed.
McManus: Soze didn’t kill Keaton.
Soze: McManus didn’t kill Keaton.


Who killed Keaton? Please explain your answer.

Answer 1

McManus killed Keaton

Explanation:

As we know that only one is saying the truth, let's analyze who might that be.

When we read the four statements, we notice that Fenster and McManus are saying exactly the opposite, so they can't be both lying. One of them is saying the truth, let's see who is.

If Fenster is saying the truth, Soze killed Keaton. But Soze said McManus didn't kill Keaton and he is lying (because just Fenster is saying the true), that means McManus killed Keaton. We have a contradiction here (we knew Soze killed Keaton), so Fenster can't be saying the true.

Therefore, McManus is saying the truth and the other three are lying. Let's see there's no contradiction here:

McManus said Soze didn't kill Keaton and that's true. Fenster is lying, so Soze didn't killed Keaton, that matches what McManus said.

Hockney said McManus was in a meeting when Keaton was killed, as that's a lie, McManus wasn't on a meeting so he could had killed Keaton. Finally, Soze is also lying so McManus did kill Keaton.