Mr. Smith works on the 13th floor of a 15 floor building. The only elevator

Moves continuously through floors 1, 2, . . . , 15, 14, . . . , 2, 1, 2, . . . , except that it stops on a floor on which the button has been pressed. Assume that time spent loading and unloading passengers is very small compared to the travelling time.

Mr. Smith complains that at 5pm, when he wants to go home, the elevator almost always goes up when it stops on his floor. What is the explanation?

Now assume that the building has n elevators, which move independently. Compute the proportion of time the first elevator on Mr. Smith's floor moves up.