MathDB

We are given a coin of diameter

\frac{1}{2}

and a checkerboard of 1\times1 squares of area

2010\times2010

. We toss the coin such that it lands completely on the checkerboard. If the probability that the coin doesn't touch any of the lattice lines is

\frac{a^2}{b^2}

where

\frac{a}{b}

is a reduced fraction, find

a+b

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