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There is a grid of 20 squares by 10 squares. How many
different rectangles are possible?
Note that square is a rectangle.
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Answer Posted / guest
11550
The Generic solution to this is:
Total number of rectangles = (Summation of row numbers) *
(Summation of column numbers)
Here there are 20 rows and 10 columns or vice versa. Hence,
total possible rectangles
= ( 20 + 19 + 18 + 17 + 16 + .... + 3 + 2 + 1 ) * ( 10 + 9
+8 + 7 + .... + 3 + 2 + 1)
= ( 210 ) * (55)
= 11550
Hence, total 11,550 different rectangles are possible.
If you don't believe it, try formula on some smaller grids
like 4x2, 3x2, 3x3 etc...
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