A LOCKER PUZZLE: On graduation day, 1000 seniors line up outside the school. As they enter the school, they pass the school lockers, aptly numbered 1 to 1000. The first student opens all of the lockers. The second student closes every other locker beginning with the second locker. The third student changes the status of every third locker beginning with the third one (if opened, the student closes it; if closed, the student opens it). The fourth student changes the status of every fourth locker, and So on. Which lockers remain open after all 1000 students have entered the school? (show how you came up with an answer). It would be nice to include the formula used as well.