As you walk along a path in a forest, the path splits in two. You do not know which way to go. At the junction, two solemn guards stand, ready to help any passersby.
It so happens that the guards only know the words yes and no. It also happens to be that the guards are twin brothers, impossible to tell apart. And, as twin brothers, the guards have developed a quite peculiar dynamic: One of them always tells the truth, while the other always lies.
You have one question, which you can ask only one of the guards. How do you determine how to continue on your path?
Answer
Since you don’t know who of the guards will tell the truth and who will lie, you need to ask a question to which both will answer the same. One such question is:
Would your brother say that I should continue on the left path?
Assume that the left path is correct. The liar will answer no, because his brother would have answered yes. The truth-teller would also answer no, since his brother would have lied and answered no.
It would be the other way around, with both guards answering yes, if the right path were correct.