3 points are drawn on a plane, and inside their triangular region, more points are added such that no 3 are collinear, such that there are n points in total. What is the maximum possible number of line segments one could draw connecting two of these points such that none intersect other than at their endpoints?

As a new point is added it can be connected to each of 3 points already on the plane.  At the end the whole region will be filled with triangles.

The initial 3 points define only 3 line segments; but each new point defines 3 more.  So it would come out to 3n-6, if this conjecture is correct.

Edited on August 18, 2006, 4:17 pm

Posted by Charlie on 2006-08-18 16:15:32