You have a thousand kids that go to highschool. In this school, there are 1000 lockers, so each kid has a separate locker. Now, All the kids , numbered 1-1000 line up outside of the school. The first kid comes in a opens all the lockers. The second kid comes in a shuts all of the even number lockers. The third kid comes in and changes (if it's open, he shuts it, and vice versa) all the lockers that are multiples of 3. The forth kid comes in and changes all the lockers that are multiples of 4. And so on and so forth, with the 1000th kid changing the locker that is a multiples of 1000. The question? After the 1000th kid changes the locker, how many lockers are left open? Make sure you prove it. Paden Roder P.S.-If you need any more explaination, tell me. I may have left some small details out on accident.