Answer to Question #5440 in Algebra for Kater

Question

Suppose I have 2011 numbered lights in a row, all of which are initially off. Then I toggle all of the light switches, so they are all on. So then I toggle all the even number light switches so the even numbered light are on and the odd number lights are still on. Then I toggle all the lights whose number is a multiple of 3. Then I toggle all the lights whose number is a multiple of 4. The I toggle all the lights whose multiples of 5, 6, 7 etc. I keep going until the last step, when I toggle the 2011th light by itself. At the end of this procedure, which lights are on? How many lights are on and how many are off?