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What is the maximum possible height of the snowman?

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Take a spherical ball of snow of radius 1 and chop off some snow from the bottom, as shown in the diagram. Re-form that snow into a smaller spherical "head" and make a snowman by stacking the head on top of the body. Measure the height of the snowman from the newly-formed flat base to the top of the head.

What is the maximum possible height of the snowman?
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posted Nov 23, 2018 by anonymous

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