i.e., Any of the gods can answer your questions.

You assume that True and False cannot know how Random will answer. But they are gods, and as far as we know their only limitations are that True always speaks truthfully and False always speaks falsely. So it is at least possible that True and False can know beforehand how Random will answer.

The fact of their knowing beforehand how Random will answer does not affect the randomness of whether his answers are true or false. Randomness only indicates that there is no pattern in his answers from which it would be possible to calculate the probability of his answer to any particular question being true or false.

Ask god A, “Will you answer ‘yes’ to this question?” Since an answer of “yes” will be true and an answer of “no” will also be true, if the god answers at all he must be either True or Random.

Remember, the problem does not stipulate that the god MUST answer; it only stipulates that True always speaks truly, False always speaks falsely, and Random speaks truly or falsely at random. Thus, if False ALWAYS speaks falsely, and the question does not permit a false answer, then he must remain silent when asked.

So, if god A replies, then god A is either True or Random. Then, ask god B, “Will you answer ‘yes’ to this question?” If god B replies, then god B is either True or Random, and god C is thus False.

Now, for the third question ask god A, “Will you answer ‘no’ to this question?” Any answer to this question will be false, so if god A answers, then god A is Random and god B is True.

This solution works whether or not any particular god answers any particular question. You just have to alter the order of the questions and who you ask, depending on whether or not the god answers.

Concerning the god Random: You are not affecting his freedom to answer “da” or “ja”–he still may answer either one, no matter which means yes or no. However, you are ensuring that whether he answers da or ja, you know he’s either not False (if you ask the ‘yes’ question) or not True (if you ask the ‘no’ question).

If the god answers at all, that god is Random. The other two gods would be unable to answer, due to their commitment to answering only truthfully or only falsely, since they cannot know what Random’s answer would be, and thus do not know which answer to give in order to be truthful or false.

Let’s say you asked god A, and he could not answer. We now know he is not Random.

2nd Question: Now ask god A “If I asked god B if YOUR (god A’s) name is True, would he say “ja”?

If god A is unable to answer, god B is Random, and neither of the other two are revealed.

If god A says “da”, he is True, god B is False, and god C is Random.

If god A says “ja”, he is False, god B is True, and god C is Random.

3rd Question: Assuming the 2nd question only revealed that god B is random, the identity of the other two gods remains unknown. Repeat question 2, now referring to god C: Ask god A “If I asked god C if YOUR (god A’s) name is True, would he say “ja”?

If god A says “da”, he is True, god B is Random, and god C is False.

If god A says “ja”, he is False, god B is Random, and god C is True.

Why This Works: Once you identify which god is Random, you are only working with the standard always lies /always tells the truth logic problem, except you don’t understand the language being spoken. This can be overcome using the following example:

Assume A is True, B is False

If Ja is yes, Da is no:

Ask A : “If I were to ask B if YOUR (god A’s) name is True, would he say ja?”

A answers: “da”

Ask B: “If I were to ask A if YOUR (god B’s) name is True, would he say ja?”

B answers: “ja”

If: Da is yes, Ja is no

Ask A: “If I were to ask B if YOUR name is True, would he say ja?”

A answers: “da”

Ask B: “If I were to ask A if YOUR name is True, would he say ja?”

B answers: “ja”

In both cases, False repeats “ja”, regardless of whether it means yes or no. In both cases, True says “da”, regardless of whether it means yes or no.

coolgenius

Ask A, “Would the meaning of True’s answer to this question be “No”?”
If A responds, ask B the same question. (We now know that A isn’t True.)
If B responds, and A’s answer doesn’t equal B’s answer, ask C, “Does one plus one equal two?” (We now know that B isn’t True, which leaves C.) Based on C’s answer, we now know what “da” and “ja” mean, information we can use to figure out which of A and B is False based on their previous answers.
On the other hand, if A’s answer equals B’s answer, we know that their answers meant “Yes”.So, ask C, “Is A False?” If C gives the same answer as A and B, then A is indeed False. Otherwise, B is False.

Now to backtrack, assume B never responded to the first question (in which case, B is True). Then, ask A, “Would the meaning of False’s answer to this question be “Yes”?” If A answers, A is not False, so A is Random. If A doesn’t answer, it’s because A is False and therefore cannot answer, leaving C to be Random.

To backtrack further, assume that A never responded to the first question (in which case A is True). Ask A, “Does one plus one equal two?” (or whatever). (From this we know the meaning of “da” and “ja”.) Then, ask A, “Is B False?” We now know which of B and C is False and which is Random.