squares

Here is an easy one I remember from school.

How many squares are there on a chess board ?

Originally posted by Jay Peatea
Here is an easy one I remember from school.

How many squares are there on a chess board ?

8x8 + 7x7 + 6x6 + 5x5 + 4x4 + 3x3 + 2x2 + 1x1
I think.
No idea what it adds up to!

Right on...of course there must be 64+49+36+25+16+9+4+1=204 squares . incidentally, when summing consecutive square number like this, there is a simple formula. Can anyone figure it out?

Originally posted by Jay Peatea
Here is an easy one I remember from school.

How many squares are there on a chess board ?

After long thinking...8 times 8 = 64...that times 2 beacuse a chess bord has two sides = 128!

Olav

A similar thread on this which I thought quite interesting: http://www.redhotpawn.com/board/showthread.php?id=3567

Originally posted by LivingLegend
After long thinking...8 times 8 = 64...that times 2 beacuse a chess bord has two sides = 128!

Olav

Ah..I didn't understand the question...😕 There can also be squares of 2x2 and 3x3 etc.....don't have time to calculate that🙂

We've all come up with 204.

Originally posted by royalchicken
Right on...of course there must be 64+49+36+25+16+9+4+1=204 squares . incidentally, when summing consecutive square number like this, there is a simple formula. Can anyone figure it out?

I don't have the time to give a proof to this, but I'm sure Acolyte will.

As you've figured out, the number of squares on a 8x8 chess board is:
1^2 + 2^2 + 3^2 + ... + 8^2 = 204

For a nxn chess board, it would be:
1^2 + 2^2 + ... + (n-1)^2 + n^2 = 1/6*n*(2n+1)*(n+1)


- Johan

You're right, and we don't even need Acolyte to prove it; it is easily feasible by simple induction....Good job 🙂!