7 Questions at most: you should Ask two of the three statues the same question at least twice, and for security 3 times. And then the final clincher question.
I guess you can do it in 5 if Random really switches between True/False every other chance it gets, but if Random has a streak you're fucked. The problem of Random is as follows: the chance random gives the same answer 3 times, therefore masquerading as eithet truth or falsehood is 1/8; small enough to take a chance (get it?) with it.
Ask the left most statue a question whose answer you know. Is 2+2 4?
Answer Uu/Ww
Ask the statue again: Is 2+2 4?
Answer UU/Ww. If the answer is twice the same, it's either a lie or the truth. It could be random 1 in 4 times though, which is why we could go for the insurance of asking it a third time.
Is 2+2 4?
Answer Uu/Ww. If it is the same, then we can safely assume it's either the truth or a lie. If the answers the first statue gives vary at any point, then you know that it is the Random statue, and now you have to ask the other statues to determine if Ww/Uu is truth or false.
On to the next statue. Is 2+2 4?
Answer Uu/Ww.
And again. Is 2+2 4?
Answer Uu/Ww.
This statue has to have at least one answer different from the previous statue. If all it's answers are different from the previous statue, then by POE you know which one is random. If at least one is different with others the same, then you know this is the random statue. Whichever it chooses, you should be now be easily able to determine what is "True" and What is "False". Next, you ask The third one is determined by process of elimination.
The 7th (or 5th, if you're a maverick and you fuck safety up its ass) is: Are you speaking the truth?
Answer Uu/Ww.
Again, by POE we can then determine which is which. By now you should already know which is the truth answer and which is the false answer. You should have been able to discern the Random statue as well. The answer of this final question is checkmate.
I assume that the statue can understand english and understan elemental math as well.
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