The webcomic version is easily solvable with counterfactuals (I think -- I could be wrong).
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.
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.
Sounds like the equivalent of its head exploding, albeit somewhat slower and more painfully...
The solution proposes that for the first question, I turn to god A and ask "Hey, A, if I were to ask you 'Are you Random', would you say 'ja'?"
Either A is Random or is not - we have those two cases to consider. Let's consider the case where A is, in fact, Random - only I don't know it yet.
The problem, as stated, says that since A is Random, for each question posed to him, he "mentally flips a coin" and then answers as if he were Truth or as if he were Falsity. So while we're considering the case that A is Random, we have two sub-cases to consider: that he will answer as Truth or that he will answer as Falsity. Let us consider the sub-case where A, although Random, will answer as Truth.
Finally, we have sub-sub-cases more: perhaps 'ja' means "yes" or perhaps it means "no". And so, we'll consider the sub-sub-case where 'ja' means "yes".
So A is Random, has chosen to answer my first question as Truth, and 'ya' means yes. My question (in the bogus solution) is:
"Hey, A, if I were to ask (in your current mental state) 'Are you Random?' would you say 'yes'?"
God A (who is Random and who will answer this one question as Truth) reasons thusly. He thinks to himself:
"If this guy had asked me 'Are you Random', since I have decided to tell Truth, I would answer 'yes' ('ja').' However, that was not the question put before me - a different question was put before me.
Random (that's me, A) flips the coin once per question asked. If he were to have asked 'Are you Random' that would have entailed a coin flip separate from the current coin flip. That other coin flip could have gone either way and so, really, I might have answered 'yes' or 'no' ('ya' or 'da').
In other words, we made it clear to this guy that he was supposed to ask a simple yes or no question and instead he asked a question to which the only True answer would be 'dajadaja' [god-speak for 'maybe']."
At that point, god A would produce from his sleeve the Magic Wand of Heyting (which was manufatured during the god-wars recorded in the book of RejectingTheLawOfTheExcludedMiddle) and smite me for failing to ask a yes/no question after being clearly instructed to do so.
In other words, with the proposed (bogus) answer, should A happen to be Random, and his coin come up Truth, and should 'ja' happen to mean 'yes' -- then I will go to my grave never knowing which god is which. (Similar analysis probably applies to other sub-sub-cases.)
Very badly framed puzzle (but one that would be hard to frame soundly without giving away the intended answer).
This is in fact quite clearly described in the section Random's Behaviour about a third down the page...
If I were to ask you if A is random, would you say ja?
That's why B is justified in smiting the asker for not asking a yes/no question.
I would expect this problem to be accessible to most people with a basic grasp of logic, hence the generic title.
i'd say the average code base works your brain harder.
There are four gods:
One always tells the truth.
One always lies.
One always chooses a random answer.
One always stabs people for trying to be clever or asking tricky questions.