(A map of the cave)
| | | | | | ___| |___ | _____ | | | | | | | | | | |_____| | | # | |____#____|
You tell your claim to another person, who is interested but wants proof that you know the secret. You want to show you know, but don't want to share the secret with a stranger. How can you prove to him beyond a reasonable doubt that you know the secret password?
(Assume the other person must stay in the entrance tunnel of the cave.)
Note: In case you can only open it one way, you would like the observer not even to learn which way you can open it.