## Puzzle Board

## Hint

How many 1 by 1 squares are there on a checkerboard? 2 by 2? 3 by 3? ..

A systematic way of counting the squares can be helpful. You can use this Polypad to help organize your thoughts.

To help you count the number of 2 by 2 squares in any given square, create a transparent 2x2 square and drag it over the sides of the main square. Then a 3x3, a 4x4, and so on.

What did you realize?

## Solution

For the 8 by 8 checkerboard:

The total number of squares is the sum of the first eight square numbers.

## More on the Checkerboard problem

How many cubes are there in an 8x8x8 cube such as this?

## Next

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