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?

×

Problem Loading...

Note Loading...

Set Loading...