a bored student walks down a hall of closed lockers, numbered 1 to 1024. they open the locker numbered 1 , and then alternate between skipping and opening each closed locker thereafter. when they reach the end of the hall, the student turns around and starts back. they open the first closed locker they encounter, and then alternate between skipping and opening each closed locker thereafter. the student continues wandering back and forth in this manner until every locker is open. what is the number of the last locker they open? (1996,