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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