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[cerapa]

You're teleported to a magic realm where there are three gods in front of you, one of them always lies, one always tells the truth, and one randomly alternates between truth and lies

What do you mean by "randomly alternates"?

As in, it alternates, but the starting state is randomized, or that it is random each time?

[Darvi]

It means you can't tell whether he's lying or tell the truth, regardless of how often you ask. Except by observation,I guess.

[MonkeyHead]

It would be trivial to determine which one were the alternating one though by asking the same question and waiting for contradictory responses.

[Flying Dice]

How, exactly, does the random alternation work? Do you just mean simple alternation with a randomized starting point/answer, or is it supposed to be a randomized answer for each question?

[Darvi]

It presumably means that for any given question there's a 50% chance that he lies.

[Frumple]

I'd be more curious about potential variate state truth statements, in that case. What if you ask a yes/no question that can be answered yes or no and be equally truthful or false? Or have the true/false value dependent on axiom bases or other data you might not hold or have? The latter bit is particularly easy in english where you've got words that are spelled/sound the same but have different meanings only discernible by context; who's to say this alternative language isn't structured so almost the entirety of their language functions so? Yes or no could be almost entirely meaningless on their own in the unknown language

[Darvi]

Suggested addendum 1: Asking grammatically ambiguous questions or questions that they cannot answer ("Will I punch you in the face?") is punishable by smiting.

[Neonivek]

They answer in a language you can't understand, the language has yes or no, but you don't know which is which

Goodness if Yes and No is a homynym (or however you spell two words that sound the same) then I am doomed!

Also I am guessing these "gods" are all knowing?

[Darvi]

Homophones.

[Itnetlolor]

I remember seeing the Mythbusters deal with this before. Switching yielded higher positives than sticking.

[Lectorog]

Homophones sound the same; homonyms do too, but they're also spelled the same, so they could be homophones or homonyms (for whatever that matters).

Also I am guessing these "gods" are all knowing?

If the puzzle is like the one I've heard, the answer doesn't involve asking them trivia questions, so you could assume so.

We had an old thread, if anyone's interesting in browsing it.
http://www.bay12forums.com/smf/index.php?topic=75636.0

I remember seeing the Mythbusters deal with this before. Switching yielded higher positives than sticking.

Because testing through repeated trial is so much more valid than mathematical proof.

[Neonivek]

Because testing through repeated trial is so much more valid than mathematical proof

I still remember the math I needed to disprove the 1 = 2

[GlyphGryph]

1. You may only ask yes or no questions.
2. They answer in a language you can't understand, the language has yes or no, but you don't know which is which.
3. You may only ask three questions, the first may be directed at all of them, the second and third may only be directed at one of them.

So, let's work this out with a few test cases and some of the more obvious questions. Out gods will be 1,2, and 3, and our potential answers will be "a" and "b"

Question one: Are there three of you? (Or some other easily verifiable, such as "are you gods?")
Possible answer results, assuming 1 is liar, 2 is truthteller, 3 is random (but we don't know which is which):

Truth?	MR.LIE	TRUTHY	RANDOMGUY
A	b	a	a
A	b	a	b
B	a	b	a
B	a	b	b

So, we have three answer groups - baa, bab, abb, but no idea which represents truth.

However, we know this - whichever one is the odd one out is NOT the random guy.

More later.... I don't know if I'm going down the right track here, but I feel like that's a valuable piece of information.

[Neonivek]

Generally speaking you can narrow who flipflops quite easily.

The person who switches from truth or lies will be the one who shares an answer

So if you ask "Is the sky blue?" you will get the ABB or AAB

You can isolate that extra guy by asking the same question to one of the duplicates. (If he isn't the one who flipflops he will say the same thing... if he is he will switch)

Of course to isolate which is lies and which is the truth is another question though, and I am not sure if I could do it in one additional individual question. So likely what you would have to do is adjust the first question or somehow eliminate the middle man.

However in order to find out which tells the truth and which lies... I guess you need to establish with a question which is yes and which is no.

[Lectorog]

The one doesn't go back and forth evenly, it's random. He may answer truthfully to all three questions, or lie on all three.