# How many lockers are open?

Suppose you're in a hallway lined with 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?

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