Counting Colorful Squares!

How squares are arranged?

The tabletop measures 3n × 3n, so we can divide it evenly into n² ( 3 × 3) squares that together tile the surface completely.

Let's consider a piece of square of size 3 x 3. For each such unit of 3 x 3 -

1. If the center of the square is red square, then there are 5 blue squares and 3 red squares surrounded with it. 

2. If the center is blue square, then there are 4 blue and 4 red squares surrounding that square. 

In any case, for 3 x 3 = 9 squares, there are 5 blue and 4 red squares. 

Therefore, for tabletop of 3n x 3n, there will be 5n² blue squares and 4n² red squares.