MathDB

3

Part of 1973 Kurschak Competition

Problems(1)

3d combo geo with (2n-3)/4 tetrahedra

Source: 1973 Hungary - Kürschák Competition p3

10/15/2022
n>4n > 4 planes are in general position (so every 33 planes have just one common point, and no point belongs to more than 33 planes). Show that there are at least 2n−34\frac{2n-3}{ 4} tetrahedra among the regions formed by the planes.
combinatoricscombinatorial geometry