Ducklings in a Lake

2016 small ducklings are resting in a large circular lake; each duckling can be at any point in the lake with equal probability. What is the probability \(P\) that a diameter can be drawn so that all 2016 ducklings are in the same half of the lake?

Because \(P\) is small, evaluate and submit \(\log_2\dfrac{63}{P}\) as your answer.


Inspiration.

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