# Find the number of triangles formed by the vertices of a polygon of $2n+1$ sides each containing the centre of the polygon.

Find the number of triangles formed by the vertices of a polygon of $2n+1$ sides each containing the centre of the polygon.

I found that for $2k+1$ sides it is coming $1^2+2^2+3^2+..k^2$.I wanted to try induction for $2k+3$, but I think there is some undercounting..

• The phrasing of this problem is horrible...does "each containing the center" refer to the edges, or does it narrow the set of polygons we care about? Also, assuming that the polygon is a regular $n$-gon, your answer for $n = 3$ is $1 + 4 + 9 = 14$, but the correct answer seems to be 1. Probably best not to try an inductive proof until you have a conjecture that works in the base case. – John Hughes Apr 19 '16 at 3:12