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The two doors

Pure logicLevel 2 · Core · ●●○○○

You are in a room with two doors. One leads to freedom, the other to death.

There are two guardians: one always tells the truth and the other always lies, but you don't know which is which. You can only ask ONE question to ONE of the guardians.

What question would you ask to know for sure which door to choose?

Hints

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  1. Key idea: The question “nests” one lie within another: Truthful honestly reports the other's lie.
  2. Then choose the door opposite the one they tell you.
  3. Key idea: The question “nests” one lie within another: Both actions produce the same erroneous result.

Solution

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Answer: Ask any of the guardians:

"If I asked the other guardian which door led to freedom, what would he tell me?"

Then choose the opposite door to the one they tell you.
Explanation:
This question works because whatever guardian you choose will always point you to the wrong door. That's why, in the end, you choose the opposite.
Analysis by case:

Case Answer you get Point out
Truthful "The liar would say: right" Right
Liar "The truthful would say left; I lie" Right

Result: They both point you to the WRONG door → You choose the opposite → Freedom!
Key idea: The question “nests” one lie within another:

  • Truthful honestly reports the lie of the other
  • Liar lies about the truth of the other
  • Both actions produce the same erroneous result

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