Chapter SR24, Problem 4P

Solution

How many total squares does the grid have?

204 Squares.

Given:

The 8X8 grid at the right has some 1X1 squares, some 2X2 squares, some 3X3 squares, and so on.

  

Calculation:

As given the 8X8 grid at the right has some 1X1 squares, some 2X2 squares, some 3X3 squares, and so on.

The total squares does the grid have -

  $\begin{array}{l}=8\cdot 8+7\cdot 7+6\cdot 6+5\cdot 5+4\cdot 4+3\cdot 3+2\cdot 2+1\cdot 1\\ =64+49+36+25+16+9+4+1\\ =204\end{array}$

So, there are 204 squares in grid.