## Tuesday, February 28, 2006

### How many squares would there be?

If you were to construct a 7 x 7 checkered square (i.e., a 7 x 7 chess board), how many squares would there be in total? (Hint: it's not 49)

1. Is it 140??

2. Here's how I did it. There is one 7 x 7 square. There are 4 6 x 6 squares. ...
5 x 5 = 9
4 x 4 = 16
...
1 x 1 = 49

For a total of 1 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 = 140 squares.

So I got the same answer as you did tjb.

3. you have to count the numbers of it and the larger sized number and the larger larger and then count the whole big square as one.

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