A typical Mensa riddle. Who is the murderer?

Five murder suspects, including the guilty party, are being interrogated by the police at the scene of a brutal murder. Of the five statements made, just three are true.
 
Alf White: "David Dark is the murderer."
Barry Gloomy: "I am innocent."
Cyril Shady: "It wasn't Ernie Black."
David Dark: "Alf White is lying."
Ernie Black: "Barry Gloomy is telling the truth."

Only one of the five suspects is the murderer. Who is the murderer?

                                                          

Problems like this can be effortlessly solved once you know the pattern. We should first note that three of the five statements are true. This is a crucial piece of information. As the famous quote in the video game Trials and Tribulations goes, reverse your thinking. The fact that three of the five statements are true means that we can mark as false any statement whose validity necessitates more than or fewer than three true statements. Hopefully the following walkthrough will clear things up a bit.

Before I start, for those who are actually planning to read this entire post, I recommend copying and pasting the above problem to a separate word document or a notepad file so that you can easily refer to it while reading the rest of the post.

I. Alf White is lying. David Dark is telling the truth.

Suppose that White is telling the truth. Then David Dark would be the murderer. Barry Gloomy would indeed be innocent, because there can only be one murderer and that’s David Dark. So Gloomy would be telling the truth. We can see that Cyril Shady’s statement would also be true.

So far we already have three true statements. According to our premise, Alf White, Barry Gloomy, and Cyril Shady are the ones who are telling the truth. For the logic to be complete, we must conclude that David Dark and Ernie Black must be lying. This, however, is invalid. Black says that Gloomy is telling the truth, which is true. Since the premise that Alf White’s statement is true leads to the conclusion that four people are telling the truth, we can deduce that Alf White is not telling the truth. Hence David Dark is not the murderer.

We can also conclude that David Dark is telling the truth. He is simply stating the fact that we have just shown to be true.

II. Barry Gloomy and Ernie Black are a package deal.

Suppose Gloomy is telling the truth. This automatically means that Ernie Black is also telling the truth—he is saying that Barry Gloomy’s statement is true, which is our premise. Now suppose Black is telling the truth. According to his statement, Gloomy’s statement would also be true. Applying contrapositive (“If A --> B, then ~B --> ~A) to these deductions, we can see that Gloomy and Black are sort of like a package deal. If one is lying, so is the other one. If one of them is telling the truth, the other one is as well.

III. Cyril Shady is lying.

Since we already know that White is lying and Dark is telling the truth (from I), the third truth-teller would have to be either Gloomy or Black and not both. This contracts the second underlined portion in II. Shady’s statement cannot be true.

IV. We now have the two liars: White and Shady. This means we know who the truth-tellers are.

All we have to do now is figure out who the murderer is. This can be easily done. Shady is a liar (from III), and she is claiming that Black is innocence. This means that Black is guilty.

Gloomy, Dark, and Black are telling the truth, while White and Shady are lying. The murderer is Ernie Black.