## Troubled traveler

A traveler, on his way to Miami, reaches a road junction, where he can turn left or right. He knows that only one of the two roads leads to Miami, but unfortunately, he does not know which one. Fortunately, he sees two twin-brothers standing at the road junction, and he decides to ask them for directions.

The traveler knows that one of the two brothers always tells the truth and the other one always lies. Unfortunately, he does not know which one always tells the truth and which one always lies.

How can the traveler find out the way to Miami by asking just one question to one of the two brothers?

The question that the traveler should ask is: “Does the left road lead to Miami according to your brother?” If the answer is “Yes”, the traveler should turn right, and if the answer is “No”, the traveler should turn left.

Explanation: There are four possible cases:

1.The traveler asks the question to the truth-telling brother, and the left road leads to Miami. The truth-telling brother knows that his lying brother would say that the left road does not lead to Miami, and so he answers “No”.

2.The traveler asks the question to the truth-telling brother, and the right road leads to Miami. The truth-telling brother knows that his lying brother would say that the left road leads to Miami, and so he answers “Yes”.

3.The traveler asks the question to the lying brother, and the left road leads to Miami. The lying brother knows that his truth-telling brother would say that the left road leads to Miami, and so he lies “No”.

4.The traveler asks the question to the lying brother, and the right road leads to Miami. The lying brother knows that his truth-telling brother would say that the left road does not lead to Miami, and so he lies “Yes”.

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