For positive integers n consider the lattice points Sn={(x,y,z):1≤x≤n,1≤y≤n,1≤z≤n,x,y,z∈N}. Is it possible to find a positive integer n for which it is possible to choose more than nn lattice points from Sn such that for any two chosen lattice points at least two of the coordinates of one is strictly greater than the corresponding coordinates of the other?[I]Proposed by Endre Csóka, Budapest combinatoricslattice points