In a boarding school the students go into the locker room and stand by their closed lockers. At the first blow of a whistle, the students open every locker. At the second whistle, the students close every second locker (lockers 2,4,6 etc. are slammed shut). At the third whistle, the students toggle every third locker. To toggle means to close it if it's open, and to open it if it's close. They toggle lockers 3,6,9 etc. At whistle four they toggle every fourth locker. At the whistle 5, they toggle every 5th locker, and so on....
There are 100 lockers, at the 100th whistle, the student standing next to locker 100 (and only that student) toggles his locker. How many lockers are then opened?