Find the maximum possible number of intersection points between the diagonals of a 13-gon.
Since it is not specified that the 13-gon is regular, then we can assume the 13-gon is irregular, so there will not be any set of three diagonals which intersect at a common point.
Consider any pair of diagonals that intersect. They are also the two diagonals of the quadrilateral defined by the set of four vertices. There are 13C4=715 ways to choose a set of four vertices, and each set will have a different intersection, so the answer is that number 715.
Solution