A long hallway has 1000 light bulbs with pull strings, all in the off position. At the beginning of the hallway, 1000 people wait, each numbered 1 to 1000. Each person takes a turn walking down the hallway pulling the string for the lights numbered a multiple of their number. For example, the first person, numbered 1, will pull all of the strings. The second person, numbered 2, will pull 2, 4, 6, 8... etc.
Which lights will be on after every person has walked? After only the even numbered people have walked? After only the prime numbers have walked?
Which lights will be on after every person has walked? After only the even numbered people have walked? After only the prime numbers have walked?