Pow #2 locker vandalismLong ago,Aptos wasn’t the nice,friendly school as we know of today.One day,these wicked adolescents decided to play a trick on the principal.They decided to vandalize the school’s 1,000 lockers by opening and closing them one after another.They had a love of mathematics,so they devised a plan to open and close the lockers in a systematic pattern.Here was their plan:the lockers were numbered 1-1,000.The first student would start

Pow #2 locker vandalism
Long ago,Aptos wasn’t the nice,friendly school as we know of today.One day,these wicked adolescents decided to play a trick on the principal.They decided to vandalize the school’s 1,000 lockers by opening and closing them one after another.They had a love of mathematics,so they devised a plan to open and close the lockers in a systematic pattern.
Here was their plan:the lockers were numbered 1-1,000.The first student would start with locker #1 to open every locker.The second student would then go to locker #2 and close every other locker all the way to locker #1,000.The third student would then take her turn.Starting with locker #3,she would change the position of the door to every third locker all the way to #1,000.That is,if the door were open,she’d close it,and if it were closed,she’d open it.Then the fourth student could go to locker #4,change its position,and change its position,and change its position of every fourth locker through #1,000.This pattern continued until all 1,000 students had taken a turn.
When they finished,they looked over what they had done,hoping to see utter chaos… But they were shocked!
What did they see?
Which lockers were open and which lockers were closed?