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Problem of the Day #95: A cube in a sphere in a cube June 22, 2011

Posted by Sreenath in : potd , trackback

A sphere is inscribed within a cube. A cube is then inscribed within the sphere such that the faces of the inner cube are all parallel to the corresponding faces on the outer cube. Let $S$ be the set of the distances from the center of one face of the larger cube to the vertices of the smaller cube. If the side length of the smaller cube is $1$, compute the sum of the squares of the elements in $S$.


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