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There are n points on a circle that are pairwise connected by a chord in the circle. What is the maximum and the minimum number of points within the circle that are intersections of the chords?

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    What progress have you made? You really ought to be able to answer one part of the question very easily.2012-11-06
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    My guess is that the most "regular" arrangement should give the minimum...2012-11-06
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    For the maximum, try starting like this: if you choose any 4 from the $n$ points on the circumference, and join those 4 with chords, how many intersections do you get?2012-11-06
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    @HerngYi For the regular $n$-gon the number of intersections is given by sequence [A006561](http://oeis.org/A006561) but I don't believe that is the minimum e.g. for $n=7.$2016-08-04

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To form a pair of chords that intersect, you need 4 points. Hence, that can be done in nC4 ways. There is only way to join the 4 points with two chords and form an intersection. Hence, the final answer is nC4.

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    Please improve it's format.See:http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference2016-08-04
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    That's the answer to the question about the **maximum** number of intersections. What about the **minimum**?2016-08-04
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    This doesn't answer the question because in some configurations the chords do not intersect inside the circle.2016-12-08