Can you repeat that in English please? :lol2:
English??? You are having the want I say the logic theorem she be the English??? So yes, now I try to say what she want to say, the logic theorem...
The terms of the problem are: you get one question, only one, and it has to be of the yes/no variety. Sigh... that limits your choices a lot. And it's worse than that. If you ask a question which separates the truth teller from the liar, that doesn't help with the third sister, because her answer might be the truthful one, in which case it'll be the same as that of the truth teller. And you don't get a second question to sort those two out. If she decides to lie, her answer will be the same as that of the compulsive liar sister. And again, you don't get to sort the two out with a followup question.
The only way you can get at the true/false sister, so far as I can see, is to ask a question which, whether she's telling the truth or lying, results in a different answer than the compusive truth-telling sister and compulsive liar will give. Yes? So there are two parts to this trick (I
think):
Part 1: figure out a question that both the truth-teller and the liar will give the same answer to. Now one thing about them (something the original question shoves in your face): they're at least consistent—you `know where you stand' with them. And the point is, the sisters know who tells the truth, who lies, and who does both. So the strategy is, ask the question
about the sisters and what they know from each other's answers. The question has to allow us to group the two `extreme' sisters together—well, since all the sisters know what the true answer is from either the truth-teller's or the liar's answers (because they know who is who), make your one shot at the answer a question which, no matter which of the sisters you ask, will yield the same result for the liar and the truth teller.
So here's a question Q. And the truth teller will always answer Q truthfully (A = 1) and the liar will always answer Q falsely (A = 0). But in both cases, the sisters all know how to get at the truth. Take the truth-teller's answer's literally, but flip the value of the liar's answers. In one case, a literal answer is necessary, in the other, a flip is necessary. Think of my bolded question as, `can you take my answer literally?' The truth teller says, truthfully, yes you can take my answer literally. The liar says—because she's a liar—yes, you can take my answer literally. So for both of them, the answer is `yes—take my answer literally'.
Part 2: Make sure that the true/false sister has to answer differently from the other two, whether or not she's telling the truth. And here the idea is, you have to play on the fact that unlike the first two, the third sister's answers can't automatically be used as pointers to the truth, because no one knows (including her sisters) what she's doing in any given answer.
That means, if she answers the bolded question truthfully, she has to admit that no, her truthful answer
cannot be taken as a literal truthful answer to the question Q, because her sisters know she might be lying, hence they cannot answer the statement `we can infer the correct answer' with a `yes'. So even though her answer is truthful, her sisters cannot make the right inference automatically; hence: is she telling the truth—yes!Can her sisters know that for sure?—no! Therefore her truthful answer tow whether the truthfulness of her answer and the truthfulness of `your sisters know what the truth is from your answer' are identical has to be `no': you cannot take my truthful answer to the particular question you're asking literally as what my sisters can say about the answer to the question.
But if she's lying when she answers, it means that the truth value of her answer (false) is the same as the truth value of the statement that her literal answer to the question is truthful—namely, uh-uh. Under no circumstances do we, or her sisters, know what she's up to, hence we can't conclude that what she says is true. So the statement that we can would be false, just as her answer to Q is false. So the two overlap, and when she's lying, she knows that the two overlap. But because she's lying, she can't answer Q truthfully, by saying yes, the two overlap. On the contrary: by assumption, since she's lying, she has to claim that the two
don't overlap. In other words, she has to answer the statement contained in Q with a resounding `no'.
So the true/false sister always has to answer the bolded question with a big fat `no'. And the other two must answer it `yes'. And that's how you can tell 'em apart...
... does that help at all??
lol
), and (ii) that I have spent no more time in this thread at this moment than was required to upload the following text. 
