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8 points no convex pentagon (Posted on 2009-10-09) Difficulty: 2 of 5
Find a set of 8 points with no three collinear such that no subset of 5 forms a convex pentagon.

See The Solution Submitted by Jer    
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re: possible real solution (not proven yet) -counterexample | Comment 3 of 4 |
(In reply to possible real solution (not proven yet) by Daniel)

The problem just asks for a single arrangement of points that works.  You give so much leeway that there are arrangements that do form convex pentagons.

I think it may be that your description guarantees a convex pentagon:  Points 5 to 4 to 6 form an angle.  Extending the rays intersects two sides of the original triangle.  The two verticies of the triangle inside the angle along with 5, 4 and 6 forms a convex pentagon.

  Posted by Jer on 2009-10-09 15:32:22

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