# Number of rectangles on a checkerboard

• May 13th 2010, 04:34 AM
oldguynewstudent
Number of rectangles on a checkerboard
How many different rectangles are hiding in a 4 X 7 checkerboard?

Hint: Any rectangle is uniquely specified by the two horizontal and two vertical grid lines that enclose it.

For a two by three checkerboard, I drew 18 different rectangles which seem to correspond to

$\left({4\atop 2}\right)$ * $\left({3\atop 2}\right)$

So I think the answer to the original problem would be

$\left({8\atop 2}\right)$ * $\left({5\atop 2}\right)$

Is this correct reasoning?
• May 13th 2010, 06:25 AM
Plato
Correct.
• October 27th 2012, 08:27 PM
sumittripathi15
Re: Number of rectangles on a checkerboard
ans. will be 280 rectangles.