There are 268 lockers at Kortright Hills which are numbered from 1 to 268. All the locker doors are shut. On the first day of school, imagine that there are 268 students waiting out.

• The first student goes in and opens all the locker doors.
The second student goes in and closes every other locker door, starting with locker 2.

The third student goes in and changes every third locker, starting with locker 3 (If the do
open, it is closed. If the door is closed, it is opened.

The fourth students goes in and changes every fourth locker, starting with locker 4.

· This continues for all 268 students.

After all 268 students have entered the school, which locker doors will be open?