A school has 1.000 students and 1.000 lockers. The lockers are numbered from 1 to 1.000. The students enter the building one at the time. The first student open all the lockers. The second student begins with the second locker and closes all the lockers with even numbers.
The third student begins with the third locker and changes-either by opening closed doors or closing open doors-all lockers with numbers that are multiples of 3. The fourth students begins with the fourth locker and changes all lockers with numbers that are multiples 0f 4. This pattern continues until all the students walk past all the lockers. After the last student has gone by the lockers, which lockers are open ?
