[Psycho]

My calculus teacher introduced this as a bonus problem, don't worry, it doesn't involve calculus, just some hard core algebra!

At some random highschool there are 1000 students, and 1000 lockers. At the beginning of the day, all of the lockers are closed. The first kid comes in, and opens every locker. The second kid comes in and reverses the order of every 2nd locker, 3rd kid reverses the order of every 3rd locker, (reverses the order meaning if its open the kid will close it, if it is closed, the kid will open it) 4th kid reverses the order of every 4th locker - all the way to the 1000th kid that reverses the order of locker #1000, the question is, how many lockers are open, and how many are closed at the end of the day? (Hint look at the multiples) This is a fun one!