Two guards, two doors
Two doors: one leads out, one leads to a dead end. Each door has a guard. One guard always tells the truth and the other always lies, but you do not know which is which.
You may ask one guard one yes-or-no or "which door" question. What do you ask?
Show hint
Make your question pass through both guards, so the truth and the lie are both applied.
Show solution
Ask either guard: "If I asked the other guard which door leads out, which door would they point to?" Then take the other door.
If you asked the truth-teller, they honestly report the liar's wrong answer. If you asked the liar, they lie about the truth-teller's right answer. Either way you hear the wrong door.
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