Zero-knowledge proof
First, Victor waits outside the cave as Peggy goes in. They label the left and right paths from the entrance A and B. Peggy randomly takes either path A or B. Then, Victor enters the cave and shouts the name of the path he wants her to use to return, either A or B, chosen at random. Providing she really does know the magic word, this is easy: she opens the door, if necessary, and returns along the desired path.  Note that Victor does not know which path she has gone down.