MathDB

Let

P

be a non-selfintersecting closed polygon with

n

sides. Let its vertices be

P_1 , P_2 ,\ldots, P_n .

Let

m

other points,

Q_1 , Q_2 ,\ldots, Q_m

, interior to

P

, be given. Let the figure be triangulated. This means that certain pairs of the

(n+m)

points

P_1 ,\ldots , Q_m

are connected by line segments such that (i) the resulting figure consists exclusively of a set

T

of triangles, (ii) if two different triangles in

T

have more than a vertex in common then they have exactly a side in common, and (iii) the set of vertices of the triangles in

T

is precisely the set of the

(n+m)

points

P_1 ,\ldots , Q_m.

How many triangles are in

T

A3