Question 68
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)
(Poland)