"Square,Square; Which Color?"

A square tabletop measures 3n × 3n. Each unit square is either red or blue. Each red square that doesn’t lie at the edge of the table has exactly five blue squares among its eight neighbors. Each blue square that doesn’t lie at the edge of the table has exactly four red squares among its eight neighbors. How many squares of each color make up the tabletop?

Here is correct way to count those!

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.