MathDB

6

Part of 1997 Chile National Olympiad

Problems(1)

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

Source:

11/23/2021
For each set CC of points in space, we designate by PCP_C the set of planes containing at least three points of CC. ∙\bullet Prove that there exists CC such that ϕ(PC)=1997\phi (P_C) = 1997, where ϕ\phi corresponds to the cardinality. ∙\bullet Determine the least number of points that CC must have so that the previous property can be fulfilled.
combinatorial geometrycombinatorics