How many rectangles?

Number Theory Level 2

How many rectangles are there on a chessboard?


The answer is 1296.

Anandhu Raj by Anandhu Raj , 23, India

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4 solutions

Aman Kumar
Mar 19, 2014

There are 9 horizontal lines and 9 vertical lines in Chessboard.......TO make a rectangle u have to choose 2 vertical lines and 2 horizontal lines. now total number of ways is 9C2*9C2 =1296......here C stands for combination ...

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Sanyam Goel
Feb 29, 2016

A rectangle is formed by two vertical and two horizontal lines. On an 8x8 chessboard, you can choose two vertical lines in C(9, 2) = 9!/(2! 7!) = 36 different ways. Similarly you can choose two horizontal lines in 36 different ways. So, the answer is 36 36 = 1296..... c= combination :)

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Shubhankar Bhatt
Mar 2, 2014

There are 36 horizontal rectangles(with length=1,2,3,4,5,6,8) and 36 vertical ones....... so total no. of rectangles on-board = 36*36 = 1296

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Aryan Gaikwad
Feb 18, 2014

visit http://bit.ly/RECtANGLE

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