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Posers and Puzzles

Posers and Puzzles

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

    How many squares are there on a chess board ?
  2. Standard member Toe
    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 member royalchicken
    CHAOS GHOST!!!
    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. 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
  5. 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. 01 Jun '03 20:15 / 2 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... There can also be squares of 2x2 and 3x3 etc.....don't have time to calculate that
  7. Standard member royalchicken
    CHAOS GHOST!!!
    01 Jun '03 22:38
    We've all come up with 204.
  8. 02 Jun '03 14:59 / 1 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 member royalchicken
    CHAOS GHOST!!!
    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 !