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Squares and Rectangles (Posted on 2004-01-21) Difficulty: 2 of 5
There is a grid of 20 squares by 10 squares. How many different rectangles are possible?
(Note that square is a rectangle).

  Submitted by Ravi Raja    
Rating: 2.0000 (5 votes)
Solution: (Hide)
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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionGeneral Case and Puzzle SolutionK Sengupta2022-06-17 00:18:34
Puzzle AnswerK Sengupta2022-06-17 00:05:58
re: My answerchintan2004-11-14 08:03:12
re(3): One direction at a timeJils2004-01-23 03:34:28
re: My answerRichard2004-01-22 16:59:17
My answerCindy2004-01-22 16:27:32
re(2): One direction at a timeRichard2004-01-22 13:18:40
re: One direction at a timeJils2004-01-22 12:08:15
Hints/TipsOne direction at a timeJils2004-01-22 12:05:49
question of formslothman2004-01-22 00:23:34
re: The real deal: 11,550? Mine was a little smaller than that...Richard2004-01-21 20:56:15
SolutionThe real deal: 11,550? Mine was a little smaller than that...Benjamin J. Ladd2004-01-21 18:03:47
Some Thoughts11,550? Mine was a little bigger than that...Benjamin J. Ladd2004-01-21 17:30:46
solutionDan Porter2004-01-21 15:47:31
No SubjectDan Porter2004-01-21 15:46:59
re(2): NodesSilverKnight2004-01-21 11:46:36
re: NodesSam2004-01-21 11:40:06
re: QuestionSilverKnight2004-01-21 11:26:57
QuestionQuestionPenny2004-01-21 10:47:08
solutionretiarius2004-01-21 09:45:39
re: SolutionSilverKnight2004-01-21 09:35:29
SolutionBrian Smith2004-01-21 09:22:00
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