Liars Everywhere!
You are travelling and come across a road division. You don't know which of the two roads to take. You see two people around there. One of them always lies and the other always speaks the truth, whatever you ask them. Now what is the minimum number of total questions you need to ask them to get your correct path if we assume that they both know the correct answer and you don't know who speaks truth and who lies?
P.S. You can ask yes/ no questions ONLY. i.e., questions with answer either yes or no. You can't ask other type of questions.
C'mon.. You obviously don't have and maps (not even google maps!) Otherwise you'll get the answer wrong.
And oh. please! You can't test who is the liar and who is the truthful one by asking questions like are you a man and all... Otherwise you'll get the answer wrong.
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9 solutions
CLAIM: the one question "What would the other person say if I ask him if this if the correct path?" suffices.
Now here we have 4 possible things which can happen. Lets look at them one by one.
You approach the liar. What would the other person (here, the truthful person) say if I ask him if this if the correct path? (pointing at one of the roads.
The road is correct. The liar knows the truthful person would say yes, but he himself always lies, so he would say NO. Now you know that if the liar said no, it is the correct path.
The road is not correct. The liar knows the truthful person will say no, but he himself will say YES. Now, you know that if the liar said yes, the other path is the correct one.
Now if you approach the truthful person and ask him the same question,
If the road is correct. The truthful person knows the liar would say no, but he himself always speaks truth, so he would say NO. Now you know that if the truthful person said no, it is the correct path.
The road is not correct. The truthful person knows that the liar would say yes, but he himself always speaks the truth. So he would say YES. If he says yes, you know that it is the wrong path.
So even if you don't know who lies and who speaks truth, you know what common question you can ask so that you get an answer which will always lead you to the correct path. If you get a no from either of them, take that path, and if you get a yes from either of them, take the other path.