3

Part of 2011 Miklós Schweitzer

Problems(1)

hyperplane covering

Source: miklos schweitzer 2011 q3

R^d

n^d

points of an n × n × ··· × n cube grid are contained in 2n - 3 hyperplanes. Prove that n (

n\geq3

) hyperplanes can be chosen from these so that they contain all points of the grid.

algebraic combinatoricsEuclidean spacereal analysis