Question

The new runway at Middle East International Airport has 200 high intensity lights, all along its edges, for easy navigation. The lights are labelled as 1 to 200. The ground operators at the airport test the lights using the following protocol. 1. First, they switch off all the 200 lights. 2. Next, they switch on all lights labelled with numbers that are divisible by 2. 3. Then, they flip the switch for every light whose number has 3 as a factor. (Flip means if a light is on, they turn it off and if the light was off, they turn it on.) 4. Next, they flip the switch for every light whose number is divisible by 4. 5. They then flip the switch for every light whose number is divisible by 5. . . . 200. Finally, they flip the switch for every light whose number is divisible by 200. How many lights are switched off at the end of the test? 1

Answer 1

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