Understanding the Chessboard
A standard chessboard consists of 8 rows and 8 columns, creating a grid of squares.
Total Number of 1x1 Squares
- The most straightforward calculation is for the 1x1 squares.
- There are 8 rows and 8 columns of 1x1 squares.
- Thus, 8 x 8 = 64 squares.
Counting Larger Squares
In addition to the 1x1 squares, there are also larger squares:
- 2x2 Squares:
- Can be formed by choosing 2 adjacent rows and 2 adjacent columns.
- There are 7 rows and 7 columns that allow for this, resulting in 7 x 7 = 49 squares.
- 3x3 Squares:
- Similarly, these can be formed by choosing 3 rows and 3 columns.
- This results in 6 x 6 = 36 squares.
- 4x4 Squares:
- Can be formed by choosing 4 rows and 4 columns.
- This results in 5 x 5 = 25 squares.
- 5x5 Squares:
- Results in 4 x 4 = 16 squares.
- 6x6 Squares:
- Results in 3 x 3 = 9 squares.
- 7x7 Squares:
- Results in 2 x 2 = 4 squares.
- 8x8 Square:
- This is the entire chessboard itself, which counts as 1 square.
Final Calculation
- Adding all the squares together:
- 64 (1x1) + 49 (2x2) + 36 (3x3) + 25 (4x4) + 16 (5x5) + 9 (6x6) + 4 (7x7) + 1 (8x8) = 204 squares.
However, the question specifically asks for the 1x1 squares on a chessboard, which is 64. Thus, the correct answer is option 'A'.