Question: There were 1000 rooms in a school all with doors closed initially. One day 1000 students were called and numbered from 1 to 1000. Now, each student was sent one by one and could change the status of room only if his own number divides the room number perfectly. Means, for example, student number 1 could open all the rooms which were closed initially since 1 divides all 1 to 1000. Similarly student 2 could change the status of only even room numbers since only room numbers 2,4,6,8,10,12,..,1000 are divisible by
2. Changing the status of room means if the room is closed make it open and vice verse. So after 1000 students done their jobs, how many rooms will be remained open?