A number of points (N) are distributed along the circumference of a circle. Every point is connected to every other point by a chord. The points are spaced unevenly such that no more than two chords intersect at a common point inside the circle.
As demonstrated in these figures, when there are 4, 5 and 6 perimeter points, there are 1, 5 and 15 internal chord intersections respectively.
If N=8 (circle with 8 points on the perimeter), how many internal cord intersections are there?
Extra Credit: Produce a simplified expression that represents the number of internal chord intersections as a function of the number of perimeter points (N).
As always, the answer with the best analytical content will be this month’s Geek Challenge winner!
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