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Problems(1)

Inequality on number of points and planes

Source:

1/3/2011
Let PP be a set of nn points and SS a set of ll segments. It is known that: (i)(i) No four points of PP are coplanar. (ii)(ii) Any segment from SS has its endpoints at PP. (iii)(iii) There is a point, say gg, in PP that is the endpoint of a maximal number of segments from SS and that is not a vertex of a tetrahedron having all its edges in SS. Prove that l≤n23l \leq \frac{n^2}{3}
inequalitiesgeometry3D geometrytetrahedrongeometry unsolved