Let's Play Chess on Other Planet

Probability Level 4

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

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

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

Details and Assumptions

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