**100 closed lockers.**

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?