# Let's Play Chess on Other Planet

Consider a $$n\times n$$ chess board. Let the total number of possible rectangles and squares be $${ R }_{ n }$$ and $${ S }_{ n }$$ respectively.

$\displaystyle{\lim _{ n\rightarrow \infty }{ \cfrac { { R }_{ n } }{ { n \ S }_{ n } } }}$

If the limit above is in the form of $$\frac a b$$ for coprime positive integers $$a,b$$, find $$a+b$$.

Details and Assumptions

• All squares are rectangles, but not all rectangles are squares.
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