Lick, Lick, Lick...

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How many licks does it take take to get the the tootsie center of a tootsie pop?

Note: The tootsie center has a radius of 1 mm and the whole lollipop has a radius of 3 mm. Each licks takes away \( \frac {1}{20} \) of a millimeter of the entire outside layer. Every layer is a perfect sphere.

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