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While trying to get out of a dungeon, you arrive in a circular room with 5 doors at equal distances from each other. The doors are numbered 1 to 5.

The doors are all locked, but fortunately, there is a nice guard in front of each door willing to unlock their door for you if you just ask them nicely. The problem is that only 1 of these doors is the exit while the others will send you to your certain death.

The guards only know about their own door and willing to answer any questions you might ask as long as it it can be answered as "yes" or "no".

Unfortunately the guards are very impatient and will only allow you to ask 4 things in total and your questions may not include multiple or conditional statements. Keep it short and sweet.

Also, you know for a fact that one of the guards always lies, the other four always speak the truth.

What is the minimum number of questions that you need to find the correct door?

This is part 1: Find the correct door!

Note: In part 1, the guards knew about each and every door. In part 2, they only know about their own door.

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    $\begingroup$ Do the guards know all of the information in the problem statement? Do the guards know who the liar is? Are the guards able to draw logical conclusions after hearing previous questions and answers? $\endgroup$ Commented 18 hours ago
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    $\begingroup$ Are you allowed to ask a question where "I don't know" is a valid response? And, if so, what would the liar's response be if they don't know the answer to a question? $\endgroup$ Commented 14 hours ago
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    $\begingroup$ Is @kagami's answer below within your rules? I'm not sure how you define "multiple or conditional statements". It would be helpful to be explicit about what counts as disallowed. $\endgroup$ Commented 13 hours ago
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    $\begingroup$ Also, @Hermant your profile picture is broken because all Facebook profile images are broken. Might want to upload your picture to a different service. $\endgroup$ Commented 12 hours ago
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    $\begingroup$ @Pranay if so, then it's a problem for many users - no one in the other Q&A mentioned being able to see the image. $\endgroup$ Commented 6 hours ago

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You can find the exit in

4 questions. To do so, simply ask each guard in sequence, "Does the exit door have an even number?"

Only the guard in front of the exit knows the exit door's number and whether it is even or not, allowing them to give a definitively true or definitively false response. Any guard in front of a non-exit door doesn't know the exit door's number or its evenness and cannot truthfully or falsely answer whether it is even or not - they can't answer "yes" or "no", and therefore must refrain from answering entirely. The guard who gives a definitive answer (it doesn't matter if it's a "yes" or "no", or if they're telling the truth or lying) is the one in front of the exit. If they're not found among the first 4 guards, the exit is the 5th door.

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It can be done in 4 questions for the case where only yes/no questions are permitted, assuming the request to unlock doesn't count.

"How would you answer the question 'is your door safe?'"

The answer will be "yes" for the safe door, regardless of the guard's truthiness, or four "no"s mean to use the final door.

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  • $\begingroup$ Wouldn't this fall under "multiple or conditional statements"? $\endgroup$ Commented 13 hours ago
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    $\begingroup$ @Someone maybe? I'm not sure what that means exactly. $\endgroup$ Commented 11 hours ago
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    $\begingroup$ A liar would answer yes if it's their own door. They would answer "no" if you asked them whether the door is safe, so they would.answer "yes" to the stated question. $\endgroup$ Commented 11 hours ago
  • $\begingroup$ If you ask the guars for doors 1-4, when door 5 is the right one, and one of the guards you asked is a liar, then you still wouldn't know. $\endgroup$ Commented 1 hour ago

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