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a circle has 1500 chords draw in it so that the maximum number of non overlapping regions is obtained. find the difference between the number of points of intersection of the chords and the number of polygons formed by the chords inside the circle.

I've been trying to figure this out for what seems like hours now. Anyone have an idea?

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    $\begingroup$ I do have some ideas, but since it sounds like this is homework or something similar I'm not going to tell you what to do. I will make a suggestion, though, which you will find useful in many problems of this kind: try finding the answer in some simpler cases. What if the number of chords is much smaller? 1, 2, 3, 4, ... ? Don't just look at the numbers that come out; it may be easier to see why the answer is what it is in these simpler cases. $\endgroup$
    – Gareth McCaughan
    Oct 24, 2018 at 1:01
  • $\begingroup$ Gareth McCaughan no its not homework, but a puzzle given to my class from my teacher for fun $\endgroup$
    – user53382
    Oct 25, 2018 at 0:42

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