1. At a math teacher. conference, 100. teachers lined
At a math teacher conference, teachers lined up in a hall right in front of a row of lockers.  The first teacher ran down the hall opening all 100 lockers.  The second teacher then proceeded to run down the hall closing every 2nd locker. The third teacher ran down the hall doing the opposite to every 3rd locker (meaning the teacher closed the third locker because it was currently open, and then opened the 6th locker because it was closed).  The 4th teacher did the opposite to every 4th locker (meaning if a locker was closed the teacher opened it and if a locker was open the teacher closed it). 

2. If this process repeats all the way down to the 100th teacher, how
many lockers would remain open
after all 100 teachers had gone down
the hall? and which ones?