Two doors: one leads to freedom, one to doom. One guard always lies, the other always tells the truth. You don't know which is which. You can ask one guard one question. What do you ask?
Hint: Make both guards point the same way.
Ask either guard: 'Which door would the other guard say leads to freedom?' Then pick the opposite door.
The question passes through both a liar and a truth-teller, so the answer is always the wrong door. Choosing the other one gets you out.
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