The lockers are numbered 1 to 1000. Student 1 runs through and opens every locker. Next, Student 2 changes the state of lockers 2, 4, 6, 8, and so on....

The lockers are numbered 1 to 1000. Student 1 runs through and opens every locker. Next, Student 2 changes the state of lockers 2, 4, 6, 8, and so on. Then, Student 3 changes the state of every locker numbered 3, 6, 9, and so on. Which locker doors are open when every student finishes? If this pattern continues, what do you think Student 4 does? Which students touched Locker 12? Which lockers were touched by both students 6 and 8? Which lockers were touched by exactly two students? Which lockers were touched by exactly three students? What questions do you still have about the Locker Problem? What, if anything, is still unclear?