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hallway that is infinitely long

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There is a hallway that is infinitely long, with a series of lightbulbs that are all turned off. Someone enters and pulls the string on every light bulb, turning them all on. Another person enters, pulling the string on every other lightbulb. A third person enters, pulling the string on every third bulb. This continues indefinitely, a person pulling the fourth, then the fifth, etc. Looking from the entrance of the hallway, what lights are on?

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Solution Summary

An infinitely long hallway is analyzed. A series of lightbulbs are given.

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In this case the bulbs which are a perfect Square will be on and the rest will be off.

So bulbs 1 , 4 , 9 , 16 , 25.....and so on ...

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