number of rectangles

Probability Level 1

how many rectangles are there in 8 by 8 chess board?


The answer is 1296.

Brian Delatorre by brian delatorre , 21, Philippines

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1 solution

Suresha Hd
Aug 24, 2014

The number of rectangles in a n*n grid is given by (n(n+1)/2)^2

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A more generalised result would be that the number of rectangles in a n × m n\times m grid is given by ( n + 1 ) C 2 ⋅ ( m + 1 ) C 2 (n+1)C_{2} \cdot (m+1)C_{2}

Omkar Kulkarni - 6 years, 4 months ago

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