There are 4 doors to the secret Truth Club room, each one at the end of a tunnel leading there. Each of the members has a keycard to a different door. All the doors are unlocked from the inside, but to enter from the outside, one needs to swipe the door's keycard to open the door for a few seconds.

You have found a copy of one of these cards, and want to prove beyond a reasonable doubt to the club members that you can unlock one of the doors, however, you don't want to expose to anyone whose door it is. What can you do to show this? (preferably with no additional materials, and without anybody else inside the cave/tunnels)

(Assume the club members are honorable enough to follow their part of the plan you propose.)

Here is a map of the tunnels:

(In reply to re: possible solution -Oh that easy? by brianjn)

well then I suggest a slight modification to my solution.   Have the members stand right outside the cave and close your eyes, you enter the cave and stand next to the door you can open.  You then tell them to open your eyes and choose a path for you to return down.  You then enter the room and exit via the desired path.  Now the odds of them picking the path that you are in and thus allowing you to return thru it without being able to access the room is 1/4, and when this is repeated N times the odds of you not being able to enter the room is (1/4)^N so choose a N large enough to give a small enough probability for the members to consider it good enough.

Now the crux of my solution is that they can see all 4 tunnels from outside the entrance, from what I see of the layout of the cave, if they stand in the middle of the entrance right outside the cave then they should have line of sight on all 4 entrances, if by chance they can only see 2 or 3 tunnels then this still works but with different probabilities.  Only if they can see only 1 or none does this solution fail.  Of course there are certain aspects of the cave not given in the drawing that could cause them to not be able to see the tunnels, for instance if the entrance has a slope to it such that it blocks their line of sight. 

Posted by Daniel on 2008-12-27 05:30:52