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.
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 :
i got 1092
References :
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