n points in space, 3d combo geo - All-Russian MO 1999 Regional (R4) 10.3
Source:
September 25, 2024
geometrycombinatoricscombinatorial geometry
Problem Statement
There are points in general position in space (no three lie on the same straight line, no four lie in the same plane). A plane is drawn through every three of them. Prove that If you take any whatever points in space, there is a plane from those drawn that does not contain any of these points.