Maybe I'm just not seeing the logic the way you do, but to me random means it really doesn't matter what the question is, because the answer is err.. random.
The cleverness of this natty logic puzzle gets hung up on the semantic difference between "answering randomly" and "answering each (whole) question truthfully or liarly on a random basis."(1) Unfortunately, if you didn't get that when the puzzle was presented, you didn't stand a chance.
Another way to solve your problem, assuming the identities of the three being interogated are known might be first to ask each individual, "Is your name variable?" where the variable is equal to the suspects own name.The one who's compelled to tell the truth will do so, the one who lies will lie, the one that's compelled to be random could go either way, but at the least if he answers truthfully, you know who the liar is. If he answers falsely, you know who the truth-teller is.Once you know either which prisoner always lies, or which always tells the truth you could ask "did prisoner x commit the crime?".If you're asking the known truth-teller and he answers 'yes' you've now solved the crime. If he says 'no', then you ask "did prisoner y commit the crime?" If he still says 'no' then you know the truth-teller himself is the one who did it. If you're asking the known liar the same question, the first time if he says 'yes' you know he's lying so you know prisoner x didn't do it. if he says 'no' then you've solved the crime, because prisoner x did do it.Of course I've just realized that this doesn't account for the additional twist of solving for whether 'ja' or 'da' means 'yes'.
Let's allow our Random answer individual to be truly random - that is, regardless of the question posed of him, he simply answers "ja" or "da", as if flipping a coin, to use Nehetsrev's example. The puzzle is still solveable - but the questions become a bit trickier...."But," I hear you protest, "What if Andrei is the Random one?" Well, let's change what the statements above mean, then. An answer of "da" means that Cedrick is not random, and "ja" means that Barda is not random. And this doesn't change if Andrei is the random one!
Isn't this dependent on the outer questions being answered as modifiers to the inner question, rather than being answered in a truly random(1) fashion?Because when answering in a truly random fashion, you can get two different answers when asking the same question multiple times.
Was killing all three and then acting all righteous and indignant an option?
Nope, not dependent. If Andrei's the liar, "da" means Cedrick's the truthteller. If he's the truthteller, "da" means Cedrick's the liar. If he answers "da" or "ja" at random, whether or not he's lying, for any component of the question, doesn't matter. If Andrei's the random one, then regardless if his answer is "da", or "ja", the person who would be indicated as non-random if Andrei were non-random is guaranteed to be non-random; because if Andrei is random, both of the others are non-random.So if he is Random, you're guaranteed that the others are not. If he's not Random, then you have a question that will give you another one that isn't as well.
How do you recognise a random answer from a non random answer?
So you don't need to know whether he's answering randomly or non-randomly, only that both random and non-random answers are possible.
And the Rofirienite Judges shall be executed for heresy against the supreme will of Sulterio in allowing this madness to continue.