MathDB

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

T

such that for each

p \in T

, there is exactly one point of

S

among

p

and its neighbors.

Problem Statement