All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes > Geometry
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: How Leonhard would solve it | Comment 4 of 5 |
(In reply to How Leonhard would solve it by JLo)

The points are non-colinear.  Choose any point as the first and connect it to the three outside points; you have three triangles within the outer one.

Now within each triangle choose an arbitrary point; connect to the vertices of the second-level triangle it's in, for each.

Continue within each newly formed triangle until any triangle is formed with no point inside, but continue with any others.   The result will triangulate all the points.

It's just that I did not know if merely being a triangulation would guarantee the maximum number of lines.

  Posted by Charlie on 2006-08-19 00:03:53
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information