The Locker Problem

The Locker Problem

Every day, 100 students enter a school that has 100 lockers. All the lockers are closed when they arrive.

Student 1 opens every locker.

Student 2 closes every second locker.

Student 3 changes the state of every third locker, i.e., he opens it if it is closed and closes it if it's open.

Student 4 changes the state of every fourth locker and so on... so that student $n$ changes the state of every nth locker.

Once all 100 students take their turns, how many lockers will be left open?