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The Two Doors and Two Guards Logic Puzzle - Complete Solution

Problem Statement

You are in a room with two doors. One door leads to freedom, the other to certain death. Guarding the doors are two guards: - One guard always tells the truth - One guard always lies You don't know which guard is which, and you don't know which door leads where. You can ask ONE question to ONE guard to determine which door leads to freedom. What question should you ask?

Answer

Ask either guard: 'If I asked the other guard which door leads to freedom, what would they say?' Then choose the opposite door.

Step-by-Step Explanation

  1. 1

    Let's call the doors A and B, and assume door A leads to freedom.

  2. 2

    If you ask the truthful guard: 'What would the other guard say leads to freedom?' The truthful guard knows the lying guard would point to door B (the wrong door), so the truthful guard honestly tells you 'door B'.

  3. 3

    If you ask the lying guard the same question: The lying guard knows the truthful guard would point to door A (the correct door), but because the lying guard always lies, they will say 'door B'.

  4. 4

    In both cases, you get the same answer: door B (the wrong door).

  5. 5

    Therefore, you should choose the opposite of whatever answer you receive.

  6. 6

    This works because you're essentially asking about a double negative: the liar lying about the truth-teller's answer, or the truth-teller truthfully reporting the liar's lie.

  7. 7

    Alternative solution: Ask 'Which door would you say leads to freedom if I asked you?' This forces the liar to tell the truth about their own lie.

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