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Solution to: Troubled Traveler

The question that the traveler should ask is: "Does the left road lead to Eindhoven 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 Eindhoven. The truth-telling brother knows that his lying brother would say that the left road does not lead to Eindhoven, and so he answers "No".
  2. The traveler asks the question to the truth-telling brother, and the right road leads to Eindhoven. The truth-telling brother knows that his lying brother would say that the left road leads to Eindhoven, and so he answers "Yes".
  3. The traveler asks the question to the lying brother, and the left road leads to Eindhoven. The lying brother knows that his truth-telling brother would say that the left road leads to Eindhoven, and so he lies "No".
  4. The traveler asks the question to the lying brother, and the right road leads to Eindhoven. The lying brother knows that his truth-telling brother would say that the left road does not lead to Eindhoven, and so he lies "Yes".

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