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The 3 dimensional version of this problem relates to the mathematics of sphere packing--how to most efficiently pack spheres into a confining space (e.g. packing oranges into a crate). The most efficient configurations attain about 74% efficiency, ie. if you pack the oranges just right, about 74% of the crate's volume is occupied by the oranges...the other 26% is just air.

Mathematicians have extended the notion of sphere packing to hypersphere packing in higher dimensions.

https://en.wikipedia.org/wiki/Sphere_packing
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