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You are travelling down a road to a village. You reach a fork in the road and find a pair of identical twin brothers standing there. One of the brothers always tells the truth and the other always lies.

If you are allowed to ask only one question to one of the brothers to find which is the correct road to the village, what is your question ?

Answer:

Point to one of the roads in the fork and ask the following question to one of the brothers.

"If I ask your brother if this is the correct road to the village will he say yes or no?"

If he answers is "no" then it is the correct way to the village.

Think about it -

If the brother you are speaking to is the one who always lies, then he will say "no" as he knows that his brother who speaks the truth would anwser "yes". If the brother you are speaking to is the one who speaks the truth, he will say "no" as he knows that his brother will lie about it being the correct road. Either way an answer "no" tells you it is actually the right road. Similarly if you are pointing to the wrong road you will get the answer "yes".