two doors, two guards, one question
You are standing in front of two identical doors. One leads to a castle (freedom), and the other to certain doom. Each door is guarded by one guard.
One guard always tells the truth.
The other always lies.
You don’t know which guard is which.
You may ask one question to one of the guards.
You can point to either door when asking.
What question do you ask to guarantee finding the door to the castle?
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You ask either guard: “If I asked the other guard whether the door on the left leads to the castle, what would they say?”
Then:
If the guard answers “yes”, go through the right door.
If the guard answers “no”, go through the left door.
You’re essentially inverting the answer twice; once by asking what the other guard would say, and again by the behavior of the guard you’re speaking to (who might be lying or telling the truth).
In every case, the guard gives you the opposite of the truth.
So, to simplify:
Whatever the answer is, the truth is the opposite.
If they say “no”, it does lead to the castle.
If they say “yes”, it does not lead to the castle.
