The Two Gatekeepers
You, Merlin and your friend, Albert approach two doors guarded by two gatekeepers of the deadly castle. You know that one door leads to the exit, and the other leads to death, but you don't know which is which. You also know that one of the gatekeepers always tells the truth, and the other always lies, but you don't know which is which. You get one question to ask one of the gatekeepers to figure out which door leads to the exit. What do you ask?
Next Question : The Next Gatekeeper
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1 solution
In order to arrive at the correct answer, let's analyze the information given. We know that we can't tell which gatekeeper is which, so we need to think of a question that gives the same answer when a gatekeeper lies, and when a gatekeeper tells the truth.
One way to do this is to "link together" the truth-teller and the liar. Then, the question goes through both a truth teller and a liar, and you'll get the same answer no matter who you ask. To do this, we would need to ask one of the gatekeepers about the other.
If we ask one gatekeeper, "What would the other gatekeeper say is the door that leads to the exit?", the truth-teller, knowing that the other gatekeeper would say the bad door, would tell us the door that leads to death. The liar, knowing that the other gatekeeper would tell us the good door, would tell us the door that leads to death.
Since we have just found a question that gives the same answer no matter who we ask, we have just solved the problem, and should go through the opposite door of whatever the gatekeeper gives us.
Q . E . D .
Next Question : The Next Gatekeeper