When they are done, which lockers will be open? Which lockers will be opened...

[shikshik_72]

...and shut only once? A middle school has an enrollment of 1000 students. The school has 1000 lockers, numbered 1 to 1000, one for each student. On Monday morning all 1000 lockers are closed and all 1000 students are outside. The first student enters and opens all of the lockers. The second student follows and closes every second locker, beginning with the second locker. The third students enters the school and reverses every third locker begining with the locker number 3 (that is, if a locker is open, she closes it and if it is closed, she opens it). This procedure continues until all 1000 students have entered the building and passed by all the lockers. When they are done, which lockers will be open? Which lockers will be opened and shut only once?