A school has exactly 50 lockers, numbered 1 to 50. On the first day of school, the custodian opened all the lockers. When the janitor came, he closed every
locker with an even number. When the principal arrived he "reversed" every fifth locker. That is, if the locker is, close, he opens it. If the locker is open, he closes it. How many lockers remained open when the principal left? What are the locker numbers?