Suppose you're in a hallway lined with 100 closed lockers. You begin by opening every locker. Then you close every second locker. Then you go to every third locker and open it (if it's closed) or close it (if it's open). Let's call this action fiddling a locker. Continue fiddling every nth locker on run-through number n. After 100 run-throughs, where you fiddle only locker number 100, how many lockers are open?