Thursday, 13 February 2014

logical deduction - Find the correct door!


This is my first puzzle but I hope it will work out well and that everyone can enjoy it.


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 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 are all knowing and willing to answer any questions you might ask by "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.


Oh yeah, one more thing, one of them always lies.



Is there a fail proof way to find the good door? If so say how you would proceed.
If not, explain why.


HINT



Read carefully what was asked of you from this puzzle.
Success can sometime be found in failure.



CONGRATULATION to Geliormth for finding the exact answer I was looking for and apologize for any mistakes or badly explained details there might have been withing my puzzle.


Please leave me comments on how you liked my puzzle and its "twists". If the twists and/or the answer were more irritating than fun, I will try to improve on that next time.



Answer




For clarification, I'll repeat the exact formulation of the question asked here:



Is there a fail proof way to find the good door? If so say how you would proceed. If not, explain why.



After reading the hint I came to the following conclusion: yes, there is a fail proof way to find the good door. (multiple solutions for this are given already, my solution looks like the one given by ffao)


But as stack reader pointed out to the ones finding the good door they were still stuck inside the room. So then the answer would be: no, there is no fail proof way to find the good door and open it.


As the valid questions can only halve the numer of options we need 3 questions to find the good door out of the 5 possible doors. But in order to know what the answers we get (yes/no) actually means we need one more question to make sure we know wether the guard we are questioning is telling the truth or telling lies. (ask a guard if the guard next to him tells the truth: yes -> both tell the truth, no -> one of them lies).


This means that we need 4 questions in total to find the good door but we need a 5th question to ask the guard to open that door.


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