Contributed by Robert Orenstein

A hallway in a school has 100 lockers. A student runs down the hall and opens each locker. A second student runs down the hall and closes every other locker. A third student runs down the hall and "changes the state" of every third locker (i.e., if the locker is open, he closes it; if it's closed, he opens it). This continues for 100 students -- the N-th student changes the state of each N-th locker.
After all 100 students have run through the hall, which lockers are open?

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