How many different rectangles which are not squares can be found on a chess board?A chess board has 8 rows and?

How many different rectangles which are not squares can be found on a chess board? (A chess board has 8 rows
and 8 columns of squares. A rectangle on the board is a collection of squares that form a rectangular piece of the
whole board. Two rectangles are different if they have different sets of squares. A rectangle with an unequal number
of rows and columns is not square.)

Oh boy, a ton!

Lets see…

2by1 = 7 possible per row x 16 possible (8 horiz and 8 vert) = 112
3by1 = 6 possible per row x 16 possible = 96
4by1 = 5 possible per row x 16 possible = 80
and so on down to…
7by1 = 2 possible per row X 16 possible = 32
8by1 = 1 possible per row x 16 possible = 16

Add those up and get 448

3by2= 6 possible per row x 14 possible rows = 98
repeat for all (4by2, 5by2, 6by2, 7by2…) i get 280

Keep doing this for all combinations. I get 1092.

This entry was posted in squares. Bookmark the permalink.

11 Responses to How many different rectangles which are not squares can be found on a chess board?A chess board has 8 rows and?

  1. BigD says:

    Oh boy, a ton!

    Lets see…

    2by1 = 7 possible per row x 16 possible (8 horiz and 8 vert) = 112
    3by1 = 6 possible per row x 16 possible = 96
    4by1 = 5 possible per row x 16 possible = 80
    and so on down to…
    7by1 = 2 possible per row X 16 possible = 32
    8by1 = 1 possible per row x 16 possible = 16

    Add those up and get 448

    3by2= 6 possible per row x 14 possible rows = 98
    repeat for all (4by2, 5by2, 6by2, 7by2…) i get 280

    Keep doing this for all combinations. I get 1092.
    References :

  2. phxladyphx says:

    i got 1092
    References :

  3. Pingback: TadWinett

  4. Pingback: Eugenie

  5. Pingback: Chantelle

  6. Pingback: Gander

  7. Pingback: Pterker

  8. Pingback: Pehmer

  9. Pingback: Xehmer

  10. Pingback: Erederic

  11. Pingback: Matilde