Question 14
In a regular tetrahedron $ABCD$ consider planes that are parallel to its faces such that each edge is divided into 6 equal segments. These planes determine, on the edges of the tetrahedron, on its faces and in its interior a set consisting of 80 points of intersection. Denote this set by $V$.
Find the maximum number of elements of a subset $W$ of the set $V \cup \{A, B, C, D\}$, having the property: any three points of $W$ are not collinear and the plane generated by them is neither parallel with any of the faces of the tetrahedron $ABCD$, nor contains one of his faces.
Mihai Monea
Find the maximum number of elements of a subset $W$ of the set $V \cup \{A, B, C, D\}$, having the property: any three points of $W$ are not collinear and the plane generated by them is neither parallel with any of the faces of the tetrahedron $ABCD$, nor contains one of his faces.
Mihai Monea