Question 73
A school has 100 students and 100 lockers numbered 1 to 100. Initially all lockers are closed. The first student opens every locker; the second closes every even-numbered locker; the third changes the state of every locker whose number is a multiple of 3, closing open lockers and opening closed ones. The fourth student changes the state of every locker numbered by a multiple of 4, and so on, through the hundredth student, who changes the state of lockers numbered by multiples of 100. After all the students have passed, how many lockers are closed?