The number of diagonals in an octagon is

$A$ parallelogram is cut by two sets of $m$ parallel lines,each set being parallel to one of its sides. How many parallelograms are formed in total?

How many chords can be drawn through $21$ points on a circle?

Let $p_n$ denote the total number of triangles formed by joining the vertices of an $n$-sided regular polygon. If $p_{n+1} - p_n = 66$, then the sum of all distinct prime divisors of $n$ is:

Suppose that $20$ pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars,then the total number of beams is

How many parallelograms can be formed by a set of $4$ parallel lines intersecting another set of $3$ parallel lines?