For example, take Locker 12.It is visited by students 1 & 12, 2 & 6, and 3 & 4. Since everyone has a partner to "undo" their work, the door ends up closed.The exceptions are Perfect Squares (like 9, 16, 36).Take Locker 9: It is visited by 1 & 9 (who cancel each other out) and Student 3. Since 3 times 3 = 9, Student 3 has no partner to close the door back. That "odd man out" leaves the locker open.
