Let T be the set of all lattice points (i.e., all points with integer coordinates) in three-dimensional space. Two such points (x,y,z) and (u,v,w) are called neighbors if ∣x−u∣+∣y−v∣+∣z−w∣=1. Show that there exists a subset S of T such that for each p∈T , there is exactly one point of S among p and its neighbors. combinatoricsIMO Longlist