You have 100 lockers, all closed, and 100 students. The first student goes and opens every locker. The second student toggles every second locker (i.e., closes lockers 2, 4, 6, …, 100). The third student toggles every third locker (i.e., opens if closed, closes if open, for lockers 3, 6, 9, …, 99), and so on, until all 100 students have passed.

At the end, which lockers will remain open?

Previous iteration: #749797 (several stackers answered correctly this time). I also updated the full answer to the integral problem from two days ago (see #750702).