George Boolos' enigma has no possible logical answer !

[Phaéris]

the enigma is this :
“Behind three characters A, B and C hide the gods True, False and Random. True always answers the truth, False always answers the opposite of the truth, and Random chooses its answers at random. Your task is to reveal the identities of A, B and C by asking only three questions whose answer is true or false. The gods understand but they will answer your questions in their own language, that is, by da and ja. You do not know what these answers correspond to.

- You can question a god more than once (and then a god will not be questioned at all).
- The second question and to whom it is addressed may depend on the answer to the first question. Likewise for the choice of the third.
- Random can be considered as deciding its answers to any true-false question by a coin toss up or down."

So ; If I ask to the god B, "If I asked you 'Is A Random', would you answer ja? " If B answers ja, then where B can be Random (and answered at random), so A and C can't be random BUT B can be non-random so it means that A or C can be random....
There is at the begining of the resolve a contradiction and a impossibility to continue and resolve the puzzle ...Because it's impossible to isolate one god because there is always 2 possibilities.

Conclusion : This enigma cannot be resolved logically .