An amusing riddle for intellectual masochists.

[Odin1199]

So there's no more ways to find out which one is which, like their placement? Is there a sure way to solve this or do you need to take chances? Even if you make both of truth and lies say yes, if chaos says yes and then you're screwed. I didn't get what you said about Eris not saying yes/no but truth/lies.

[Heartless Angel]

Nope, nothing that you can sense will tell you who is who, your only way to find out is through your three questions. It can be solved without any luck factoring in, though obviously there would be multiple ways the solution could play out, based on the answer to the first question there are a couple possibilities for the second, and so on. But you can get the right answer 100% of the time with the proper method without any guessing. As for making everyone say yes, that was a hint on how to translate the words. If you can come up with a question that has to be answered 'yes' whether you're telling the truth or lying, whatever answer any Goddess gives to that question definitely means yes. However translating the words is not necessary to solve the puzzle.

As for Eris, this may be important to some solutions, she does NOT choose to say yes or no at random. She chooses whether to tell the truth or lie at random. Basically you can think of Eris flipping a coin before answering a question. If she were choosing her answer at random, it would be something like heads means yes, tails means no. But what she actually does, is decide at random whether or not to tell the truth, so something like heads means tell the truth, tails means lie. This is important if you come up with a question that must be answered the same way regardless of whether or not you're telling the truth. If you come up with a question that would have to be answered "yes" by both truth tellers and liars, Eris would also have to answer "yes", because she is choosing between truth and lies, not yes and no.