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Rabia

The Room of Doors

You find yourself in a mysterious room with three doors. Each door leads to a different path, but only one path will take you to safety. The other two paths are extremely dangerous and will lead to certain doom.

In front of each door, there is a guard. You know the following about the guards:

  1. One guard always tells the truth.
  2. One guard always lies.
  3. One guard alternates between telling the truth and lying (you don’t know in which order).

You can ask one question to any one of the guards to determine which door leads to safety. What question do you ask to ensure you choose the correct door?

Answer:

You ask any guard the following question: “If I were to ask the guard who always tells the truth which door leads to safety, what would he say?”

  • If you ask the truth-telling guard: He will truthfully tell you which door the truth-telling guard would say, which is the safe door.
  • If you ask the lying guard: He will lie about what the truth-telling guard would say, but since he always lies, his lie will correctly point you to the safe door.
  • If you ask the alternating guard: Regardless of whether he is currently lying or telling the truth, his answer will still mislead you about what the truth-telling guard would say, leading you to the correct door.

By following the answer given by any guard to this question, you can safely determine which door leads to safety.