How many lockers are open?
You begin by opening every locker. Then, you close every second locker (#2, #4, \(\ldots\)). After that, you "toggle" every third locker (open it if it's closed, close it if it's open).
You proceed to "toggle" every \(n\)th locker for \(n=4,5,\ldots,100.\) At the end of this process, how many lockers are open?