You face two identical doors. Behind one is safety, behind the other a trap. Two guards stand in front of you; one always tells the truth, the other always lies. You may ask one guard one question to determine the safe door. What do you ask?
Hints
Let the liar and the truth-teller describe each other.
Answer
Ask either guard, 'If I asked the other guard which door leads to safety, what would they say?' Whichever door they point to is the trap, so take the other door. The truth-teller truthfully reports the liar's lie, and the liar lies about the truth-teller's truth, so both direct you away from safety.