Riddle Light Bulbs

THis is a math problem i cant figure out. It deals with 1000 light bulbs turning on and off.?

SO here is the problem. There are 1000 light bulbs. First , you pull every chain turning all the lights on.Next, you pull every second chain, and those lights(half of the lights will be off) will turn off. THen, you pull every third chain, and then fourth, and fifth, and so on until you pull the thousandth chain, which will be the last. Can someone please help me figure out this riddle? I need a good way of solving this, a plain number answer wont help.

If you draw out a series of lights on a paper (up to even like 20) then step through each iteration you will notice a pattern starts emerging. The answer is that every light where pass number P divides the number N will the light be on.

So on pass P if you change light N, on the pass where P/N you will change it to the opposite. This leaves a pattern of lights on.

In short, only the lights that lead to exact squares will be on. So lights… 1, 4, 9, 16, 25, 36, 49… up to 31 X 31 or 961 will be on. This is a total of 31 lights.

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