Let n⩾3 be an integer. Let A1A2…An be a convex n-gon. Consider a line g through A1 that does not contain a further vertice of the n-gon. Let h be the perpendicular to g through A1. Project the n-gon orthogonally on h.
For j=1,…,n, let Bj be the image of Aj under this projection. The line g is called admissible if the points Bj are pairwise distinct.
Consider all convex n-gons and all admissible lines g. How many different orders of the points B1,…,Bn are possible? combinatorics proposedcombinatorics