1. R.I.P.
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    01 Jun '03 12:19
    Here is an easy one I remember from school.

    How many squares are there on a chess board ?
  2. Joined
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    01 Jun '03 15:56
    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!
  3. Standard memberroyalchicken
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    01 Jun '03 16:39
    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?
  4. Amsterdam
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    01 Jun '03 18:04
    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
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    01 Jun '03 18:14
    A similar thread on this which I thought quite interesting: http://www.redhotpawn.com/board/showthread.php?id=3567
  6. Amsterdam
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    01 Jun '03 20:152 edits
    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...πŸ˜• There can also be squares of 2x2 and 3x3 etc.....don't have time to calculate thatπŸ™‚
  7. Standard memberroyalchicken
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    01 Jun '03 22:38
    We've all come up with 204.
  8. Norway
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    02 Jun '03 14:591 edit
    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
  9. Standard memberroyalchicken
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    02 Jun '03 20:42
    You're right, and we don't even need Acolyte to prove it; it is easily feasible by simple induction....Good job πŸ™‚!
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