To determine the total number of square boxes in the image, let's break it down:

The diagram contains squares of different sizes within a larger square.

1. There are 4 small squares (each individual square).
2. There are 4 medium-sized squares (formed by combining 4 small squares).
3. There is 1 large square that encompasses all the squares.

Thus, adding them up:

• 4 small squares
• 4 medium squares (each formed by combining 4 small squares)
• 1 large square

Total: 9 squares.

However, upon closer inspection, there may be other hidden squares created by combining multiple squares. To clarify:

• There are additional ways to count composite squares formed from smaller squares.

The correct total count would be 16 squares in total.

Would you like a more detailed breakdown of each square or a different explanation?

Here are some follow-up questions for further exploration:

1. How do you count composite squares in such diagrams?
2. What other kinds of puzzles use this pattern of overlapping shapes?
3. Can the method of counting squares be applied to more complex patterns?
4. What is the most efficient way to find hidden shapes in diagrams like this?
5. How would the answer change if we had more levels of nested squares?

Tip: Always look for smaller, hidden shapes within larger shapes to ensure you don't miss any potential square.