MathDB

Let

n

be positive integer.A square

A

of side length

n

is divided by

n^2

unit squares. All unit squares are painted in

n

distinct colors such that each color appears exactly

n

times. Prove that there exists a positive integer

N

, such that for any

n>N

the following is true: There exists a square

B

of side length

\sqrt{n}

and side parallel to the sides of

A

such that

B

contains completely cells of

4

distinct colors.

Problem Statement