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 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)