One question, and you only need one man of any type: "If I were to ask you whether the left fork leads to Someplaceorother, and you chose to answer that question with the same degree of truth as you answer this question, would you then answer 'yes'?"

The truthteller will say "yes" if the left fork leads to Someplaceorother, and "no" otherwise. The liar will answer the same, since he will lie about where the left fork leads, and he will lie about lying. The randomizer may either lie or tell the truth about this one question, but either way he is behaving like either the truthteller or the liar and thus must correctly report the road to Someplaceorother.

If however the third person randomly answers yes or no it is clear that you must ask at least two questions, since you might be asking the first one of the randomizer and there is nothing you can tell from his answers.

Start by asking A "Is B more likely to tell the truth than C?"

If he answers "yes," then
If A is truthteller, B is randomizer, C is liar. If A is liar, B is randomizer, C is truthteller. If A is randomizer, C is truthteller or liar.
If he answers "no," then
If A is truthteller, B is liar, C is randomizer. If A is liar, B is truthteller, C is randomizer. If A is randomizer, B is truthteller or liar.

In either case, we now know somebody (C or B, respectively) who is either a truthteller or liar. Now, use the technique for finding information from a truthteller/liar, viz., you ask him the following question: "If I were to ask you if the left fork leads to Someplaceorother, would you say 'yes'?"

If the answer is "yes," take the left fork, if "no" take the right fork.

If you just want to identify the three men, there are several ways to proceed. Perhaps the simplest is to ask the man identified as either a truthteller or a liar some question like "Is one plus one equal to two?" If he answers "yes," then he is the truthteller, else he is the liar. If he is the truthteller, ask him if another man is the liar. By process of elimination you know the identity of the third man. If he is the liar, ask him the same question, but disbelieve the answer. Then again by process of elimination you know the identity of the third man.

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