Chessboard Problem

Hello Everyone!

So I decided to use different colors to solve this problem. As we can all see there is a big 8 by 8 chess board that is a square itself, no one needs more explanation on that. However, it gets a little trickier when we start thinking about a 7 by 7 chess board. Now it may be a little difficult to picture a 7 by 7 chess board out of an 8 by 8 chess board; therefore, I decided to use four different colors to picture all different squares possible. As you can see below, there are 4 different ways of drawing a square that has 7 by 7 smaller squares in it (pink, red, green, blue). If we keep going further we will see that there are 9 squares for a 6 by 6 chess board out of an 8 by 8 chess board.

Therefore, as we go on we start to see a pattern and instead of counting all 200 plus squares, we use our mathematical skills to follow the pattern and fill in the blanks such as follows:

8 by 8 chess board- 1 square

7 by 7 chess board- 4 squares

6 by 6 chess board- 9 squares

5 by 5 chess board- 16 squares

4 by 4 chess board- 25 squares

3 by 3 chess board- 36 squares

2 by 2 chess board- 49 squares

1 by 1 chess board- 64 squares

Total number of squares= 1+4+9+16+25+36+49+64= 204

As a teacher, I would ask my students to find a pattern after they have solved the problem if they did not see a pattern while solving it. However, if they did see a pattern already then I would ask them to work on an 8 by 7 chess board problem.