How do you solve the locker problem?

The locker problem typically involves determining how many lockers remain open after a certain number of students toggle them. Each locker is toggled (opened or closed) by students whose numbers are divisors of the locker number. For example, locker 12 is toggled by students 1, 2, 3, 4, 6, and 12. Ultimately, a locker will remain open if it is toggled an odd number of times, which occurs only for lockers with an odd number of divisors—specifically, perfect squares. Thus, the open lockers correspond to the perfect square numbers up to the total number of lockers.