Problem:Closed Locker
School is about to begin. The janitor has all the lockers closed. All 1000 of them.
Student .1 comes along and opens ALL of the lockers.
Student .2 comes along and closes doors 2, 4, 6, 8, 10, etc....
Student .3 comes along and changes the state of every 3rd locker ( 3, 6, 9, 12, 15).
Student .4 comes along and changes the state of every 4th locker (4, 8, 12, 16).
Student .5 comes along and changes the state of every 5th locker (5, 10, 15, 20)
Student .6 comes along and changes the state of every 6th locker (6, 12,18. 24)
It keeps going until all 1000 students go through. What lockers are closed?