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**fifthrapiers** A high school has 1,000 students and it has 1,000 lockers in its main corridor. All of the lockers are initially open. The first student walks down the corridor and changes the position (open/close) of each locker. In his case, he closes all of the lockers since they are all open. Then the second student walks down the corridor and changes the position of every second locker (in his case he will open all of the even-numbered lockers). Then the third student walks down the corridor and changes the position of every third locker (in his case he opens some and closes some). Then the fourth student walks down and changes the position of every fourth locker, etc. How many lockers are closed after the one-thousandth student is done? (Remember that the last student changes the position of every one-thousandth locker, which means he only changes the position of the last locker.)