My best friend told me a puzzle today. It's like this: there are 100 closed doors in a row. You go down the row, opening every single door. Then you return to the starting point and close every alternate door along the row. Then you return to the starting point and go to every third door, closing it if it's open or opening it if it's closed. You keep doing this until you go to the 100th door straight from the starting point. So, at the end of this exercise, how many doors are open and how many are closed?