Imagine a long hallway, with 500 lights attatched to the ceiling, all turned off. Each light has a pull string which turns it on or off with one pull. You start with the first light and pull every string, turning on all the lights. A friend comes behind you and, starting with the second light, pulls every other string, turning those lights off but leaving others on. ANother friend comes along and, starting with every third light, pulls every third string, now turning some lights on and some lights off again. A fourth person comes and pulls the fourth light, and then pulls every fourth string. SO on and So fourth until the 500th person comes and pulls on just the very last string. How many lights will be turned on? Whcih ones, and why?