To approach this problem, I started writing out the end result (whether the locker remained open or closed) starting at locker #1. As I continued the process, in my head I would have to recall what had happened to the locker previously to determine the end result. Recalling what had happened previously to the locker, and what number of student did it, made me realize that changes to the locker happened at numbers that that locker # is divisible by. If the locker # has an even number of factors, then the end result of the locker is open. If the locker # has an odd number of factors, then the end result of the locker is closed. Thus it is possible to determine the end result of the locker if you know how many factors that locker number has.
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