IMO 2007 Shortlist A7
Let n > 1 be an integer. In the space, consider the set S = (x,y,z) | x,y,z ∈ {0,1,...,n}, x + y + z > 0 . Find the sm...
Category: Algebra
Problem
Let n > 1 be an integer. In the space, consider the set S = (x,y,z) | x,y,z ∈ {0,1,...,n}, x + y + z > 0 . Find the smallest number of planes that jointly contain all (n+1)3 −1 points of S but none of them passes through the origin. (Netherlands)