there are 100 lockers lined up in a row, and for some unknown reason they are unlocked. for a similarly unknown reason there are 100 students lined up outside the hallway containing the 100 lockers. the first student goes and opens all the lockers. the second then goes and closes every second. the third either opens or closes every third locker, (changes the "state" of it) for example, the 6th locker is closed when the 3rd guy comes to it, so he opens it. after all 100 students go by, what lockers are open/closed? please note i dont think that you should list out all 100 lockers and their state, there is a pattern.