# Number of rectangles on a checkerboard

#### oldguynewstudent

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

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

So I think the answer to the original problem would be

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

Is this correct reasoning?

MHF Helper
Correct.

oldguynewstudent

#### sumittripathi15

ans. will be 280 rectangles.

Last edited: