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?
Finding the number of intersections of chords within a circle
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combinatorics
geometry
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1What 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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0My guess is that the most "regular" arrangement should give the minimum... – 2012-11-06
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0For 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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0@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