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Points on a plane (Posted on 2006-08-18) Difficulty: 3 of 5
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?

No Solution Yet Submitted by atheron    
Rating: 4.0000 (1 votes)

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A guess | Comment 1 of 5

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

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