A new high school has just been opened, with an enrollment of 1000 students. The school has 1000 lockers, numbered 1 to 1000, to accommodate them. On the first day of school all 1000 lockers are closed. The first student enters the school and opens all of the lockers. The second student follows and closes every second locker, beginning with the second locker. The third student enters the school and reverses every third locker beginning with the third. This procedure continued until all 1000 students have passed by all of the lockers. When they finish, which lockers will be open?
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I think all of the lockers will be open at the end
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