MathDB
SMT 2010 General #24

Source:

February 11, 2012
geometryprobability

Problem Statement

We are given a coin of diameter 12\frac{1}{2} and a checkerboard of 1\times1 squares of area 2010×20102010\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 a2b2\frac{a^2}{b^2} where ab\frac{a}{b} is a reduced fraction, fi nd a+ba+b
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