For gumballs ( or oranges or cannonballs or any other identical-size spheres ), the densest packing requires laying them in a hexagonal pattern and stacking additional layers on top, each offset so the spheres nestle into the hollows of the layer beneath.
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At each step there are two choices of where to put the next layer, so this natural method of stacking the spheres creates an uncountably infinite number of equally dense packings, the best known of which are called cubic close packing and hexagonal close packing.
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