Suppose you are in a hallway lined with 100 closed lockers. You begin by opening all 100 lockers. Next, you close every second locker. Then you go to every third
locker and close it if it is open or open it if it is closed (call this toggling the locker). You continue toggling every nth locker on pass number n. After your hundredth
pass of the hallway, in which you toggle only locker number 100, how many lockers are open?
In a hall with k lockers, how many lockers remain open after pass k?