PROBLEM NUMBER TWO ANSWER
Buffalo Museum of Science
Fill the maze with water. Put the ping pong ball into the starting hole, attach a hose and blow it through. It works because water is incompressible, and the ball just follows the current.
I know, I know, sometimes it doesn't and gets caught in a side alley, but this is the answer anyway. (Maybe attach a small handkerchief to it to catch the current.)
Of course this is not a real np hard solution, since filling the maze with water is a way to explore all dead-end alleys by sending a probe (the water column). But it is a solution to the mechanical puzzle of the maze and the ping pong ball. Doubtless there are other solutions.
R. Zander, Sept. 20, 2001