MathDB

Let

ABC

be a triangle. Take

n

point lying on the side

AB

(different from

A

and

B

) and connect all of them by straight lines to the vertex

C

. Similarly, take

n

points on the side

AC

and connect them to

B

. Into how many regions is the triangle

ABC

partitioned by these lines?
Further, take

n

points on the side

BC

also and join them with

A

. Assume that no three straight lines meet at a point other than

A,B

and

C

. Into how many regions is the triangle

ABC

partitioned now?

Problem Statement