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Squares and Rectangles (Posted on 2004-01-21) |
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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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Submitted by Ravi Raja
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Rating: 2.0000 (5 votes)
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Solution:
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(Hide)
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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. |
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