MathDB

Each of the

{4n^2}

unit squares of a

{2n \times 2n}

board

{(n \ge 1) }

has been colored blue or red. A set of four different unit squares of the board is called pretty if these squares can be labeled

{A,B,C,D}

in such a way that

{A}

and

{B}

lie in the same row,

{C}

and

{D}

lie in the same row,

{A}

and

{C}

lie in the same column,

{B}

and

{D}

lie in the same column,

{A}

and

{D}

are blue, and

{B}

and

{C}

are red. Determine the largest possible number of different pretty sets on such a board.
(Poland)

Problem Statement