There are n lockers in a hallway numbered sequentially from 1 to n. Initially, all the locker doors are closed. You make n passes by the lockers, each time starting with locker #1. On the ith pass, i = 1, 2, ..., n, you toggle the door of every ith locker: if the door is closed, you open it, if it is open, you close it. For example, after the first pass every door is open on the second pass you only toggle the even-numbered lockers (#2, #4, ...) so that after the second pass the even doors are closed and the odd ones are opened the third time through you close the door of locker #3 (opened from the first pass), open the door of locker #6 (closed from the second pass), and so on. After the last pass, which locker doors are open and which are closed? How many of them are open?

-There are n lockers in a hallway numbered sequentially from 1 to n. Initially, all the locker doors are closed. You make n passes by the lockers, each time starting with locker#1. On the ith pass, i = 1, 2, ..., n, you toggle the door of every ith locker: if the door is closed, you open it, if it is open, you close it. For example, after the first pass every door is open　on the second pass you only toggle the even-numbered lockers (#2,#4, ...) so that after the second pass the even doors are closed and the odd ones are opened　the third time through you close the door of locker#3 (opened from the first pass), open the door of locker#6 (closed from the second pass), and so on. After the last pass, which locker doors are open and which are closed? How many of them are open?