Step-by-Step Square Counting

To find the total number of squares, we need to systematically count all squares of different sizes and orientations.

1. Axis-Aligned 1x1 Squares:

   These are the most obvious squares that make up the main grid. There are 4 columns and 2 rows.

   4 * 2 = 8 squares
2. Axis-Aligned 2x2 Squares:

   These are larger squares formed by combining four 1x1 squares. We can find 3 of them by shifting a 2x2 window across the grid.

   3 squares
3. Small Tilted Squares:

   Inside each of the 8 small 1x1 squares, the diagonals form a smaller, tilted square.

   8 squares
4. Medium Tilted Squares:

   These are squares of size 1x1, tilted at 45 degrees. They are formed by connecting two adjacent grid points (like B and I) and the centers of the two squares next to that line.

   • There are 3 such squares in the top row (centered around points B, C, and D).
   • There are 2 such squares in the bottom row (centered around points I and H).
   3 + 2 = 5 squares

Total Count

Finally, we add up the counts from all categories:

Final Answer: The total number of squares is 24.