Find a set of 8 points with no three collinear
such that no subset of 5 forms a convex pentagon.
(In reply to possible real solution (not proven yet)
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