How many squares are there on a checkerboard?

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- Apr 6th 2009, 06:28 AMphillyfan09Checkerboard
How many squares are there on a checkerboard?

- Apr 6th 2009, 08:32 AMstapel
- Apr 6th 2009, 10:46 AMGrandadSquares on a Checkerboard
Hello phillyfan09Of course, there are little squares, but we suspect that this isn't the answer that we're supposed to come up with!

There's one very big square , of course, and there will be some number between and squares with a size between these two. So how do we find out how many there are in an organised way? Well, look first at the next size square down: . You'll see that you can find of these.

Then look at a size square. There's one up in the top left-hand corner, and two more along the top row of the board. If we move down a square there are another ; and a final row of along the bottom of the board. That's altogether.

Can you see a pattern emerging? We have

square.

squares

squares

...

squares

So all you have to do is work out the numbers in between and add them together to get your answer. If you want to use a formula, you might like to know that the sum of the first square numbers is

Grandad