# 2015 Countdown Problem #21: Buffon's Clean Tile Game Revisited

A rectangular tile has area $$2015$$ $$cm^2$$ and perimeter $$192$$ $$cm$$. A coin of diameter $$2$$ $$cm$$ is randomly tossed onto a floor laid with such rectangular tiles which tessellated in the following arrangement as shown (checkerboard arrangement).

Let $$P$$ be the probability of the coin landing on exactly 2 tiles (i.e. such that when it lands it covers part of exactly two tiles, as shown). Find $$2015P$$.

This problem is part of the set 2015 Countdown Problems.

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