[Karzyn]

I'm pretty sure that the webcomic is flawed.

In the last panel the center head says "Yes. I was lying." A head that always tells the truth would never say this because they weren't lying before and wouldn't lie about not lying. Conversely, a lying head would lie about lying and say that they weren't lying. Thus, the center head must be the random one. However, in the first panel both the right and the left heads agree that the hero may only ask one question. Since the right and left are both either truth-telling or a liar they cannot agree with each other.

Thus, the puzzle is flawed and probably just a joke.

[epochwolf]

Given that the comic has a punch line in the bottom of the last panel, the comic is definitely a joke.

The question becomes is the author trying some subtle play or unaware of the error? (Or are you incorrect about the comic being incorrect)

Either way, it was amusing and has value.