MathDB

min no of points, set of 1997 planes with at least 3 points (1997 Chile NMO P6)

Source:

November 23, 2021

combinatorial geometrycombinatorics

Problem Statement

For each set

C

of points in space, we designate by

P_C

the set of planes containing at least three points of

C

\bullet

Prove that there exists

C

such that

\phi (P_C) = 1997

, where

\phi

corresponds to the cardinality.

\bullet

Determine the least number of points that

C

must have so that the previous property can be fulfilled.