FILE No.51Unsolved
In a hidden underground room there are two doors. One leads to the exit; the other leads to a dead-end trap. A guard stands in front of each door.
One guard always tells the truth. The other always lies. You do not know which is which. Both guards know which door is the exit.
You may ask one guard a single question, once. The answer will be "yes" or "no".
What should you ask to be certain of the safe exit?
If you get stuck, open the hints one at a time, in order.
Think about the case where you ask the truth-teller, and the case where you ask the liar, separately.
What happens if you ask what the other guard would say?
Both guards will give you the same answer to this question.
What should you ask to be certain of the safe exit?
Choose the answer closest to the truth.
"If I asked the other guard whether this door is the exit, would he say yes?"
The answer is: "If I asked the other guard whether this door is the exit, would he say yes?"
If you ask the truth-teller, he truthfully tells you what the liar would say (a lie). If you ask the liar, he lies about what the truth-teller would say (the truth), so he also gives you a lie. Either way, you get the opposite of the correct answer.
So if this door really is the exit, you will always hear "no". If it is not, you will always hear "yes". Take the door opposite to the answer you hear.
Asking "Are you the truth-teller?" tries to identify the guard, but it never tells you anything about the doors.
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