Intersections between chords
On a circle circumference, we choose 50 points and draw all chords joining these points. Find the maximum number of intersections between these chords?
Hint: when the number of points is 5, the maximum number of line intersections is 5.
The answer is 230300.
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1 solution
The intersection point of two chords is defined by four points, namely the two end-points of one chord, and the two end-points of the other chord. Conversely, if we take any four points on the circle, then there is exactly one way to draw two chords so that they form an intersection point. This means that the intersection points are in 1-1 correspondence with the number of ways of choosing four points, which is ( 4 5 0 ) = 2 3 0 3 0 0 .
( @starwar clone )