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Probability Level 3

Find the number of rectangles in a $10 \times 12$ chessboard.

Note: All squares are rectangles, but not all rectangles are squares.

The answer is 4290.

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Marc Vince Casimiro
Nov 29, 2014

In an a x b board, there are $a+1$ horizontal lines and $b+1$ vertical lines. Since a rectangle has 2 horizontal and 2 vertical lines then the number of rectangles would be: $C\dbinom{11}{2}*C\dbinom{13}{2} = 4290$

Krishna Sharma
Nov 29, 2014

Number of rectangles in

$n \times p$ board is

$\frac{np(n + 1)(p + 1)}{4}$

Here

$n = 10, p = 12$

Final answer = $\boxed{\boxed{4290}}$

Chess boards are always of the dimension 8×8. So your question itself is wrong. But nice solution.

Ashley Shamidha - 6 years, 6 months ago

Maths and physics questions have the weirdest chess boards...

Julian Poon - 6 years, 6 months ago

with all the courtesy, this problem is not about whether it is a chessboard or not.. it is about counting the number of rectangles..

Bhavik Shakrani - 6 years, 6 months ago

not really

Mardokay Mosazghi - 6 years, 6 months ago

But I haven't ever seen a chess board with a dimension other than $8\times 8$ . I may be wrong though. But still, it was a good problem. ;)

Prasun Biswas - 6 years, 6 months ago

@Prasun Biswas – actually... I have played on a chessboard other than $8*8$ . It is a chess for four persons.

Rishabh Tripathi - 6 years, 3 months ago

Mess in Chess Prevails

The answer is 4290.

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