ALEGEBRA
posted by HALIS .
The new school has exactly 1000 students and 1000 lockers.On the first day all the students meet outside and agree on the following plan: the first student will enter the school and open all the lockers.The second student will then enter the school and close every locker with an even number (2,4,6,8..).The third student will the reverse every third locker (3,6,9,12...).That is if the locker is closed,he/she will open it ,and if is open ,he/she will close it.The 4th student will then reverse every fourth locker and so on until all 1000 students in turn have entered the building and reversed the proper lockers.

A very old problem
Here is a great explanation
http://www.daniweb.com/forums/thread217790.html#