How many different squares can be found on a chess board?

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.)

• Answer:

  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.