# Lockers

**Number Theory**Level 3

There are 1000 lockers in a hallway, and 1000 students. All of the lockers in the hallway are closed. The first students runs down the hallway and opens every single locker. The second student runs down the hallway and closes every other locker, starting at the second locker (2,4,6,8,etc). The third student runs down the hallways and inverts every third locker (if a locker is closed, the third student opens it, if a locker is open, it gets closed). How many lockers are open after the 1000th student finishes running down the hallway.

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