A cube-shaped box with an edge of [[$ 20\;\text {cm} $]] is packed in layers of spherical hard candies with a diameter of [[$ 2\;\text {cm} $]]. In this case, the ground floor can hold [[$ 100 $]] caramels and thus a total of [[$ 1,000 $]] in the box. The corresponding filling of the box is repeated using candies with a diameter of [[$ 2/n\;\text {cm} $]] ([[$ n $]] integer). How is the total weight of the candies in the box? (Finnish matriculation exam spring 1990)

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Solution