# How many light bulbs will be on?

A room has 100 light bulbs numbered 1 to 100. All the bulbs are initially in the "off" state. 100 persons go into the room one after the other. The first person changes the state ("off" to "on") of all the bulbs. The second person changes the state (switches it on if it is off, or switches it off if it is on) of all the bulbs which have even number (2,4, 6...100). The third person changes the state of all the bulbs which have a number divisible by 3 and so on. That is, the $$n$$th person changes the state of all the bulbs which have a number divisible by $$n$$.

How many light bulbs will be in the "on" state once all the 100 persons have done their job?

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