MathDB

Let

K

be a cube with edge

n

, where

n>2

is an even integer. Cube

K

is divided into

n^3

unit cubes. We call any set of

n^2

unit cubes lying on the same horizontal or vertical level a layer. We dispose of

\frac{n^3}4

colors, in each of which we paint exactly

4

unit cubes. Prove that we can always select

n

unit cubes of distinct colors, no two of which lie on the same layer.

Problem Statement