Abstract
1. Statement of results. Let Sn denote the set of (closed) n-spheres with radii of length (n1I2)/2 and centers on the lattice points of a rectangular Cartesian coordinate system in En (Euclidean n-space). Since (n1l2)/2 is half the largest diagonal of the unit n-cube, every point of En falls on or within some of the spheres of S,. For n = 1, 2, 3, if an n-sphere is removed from S., then certain points of En are not covered by the remaining spheres. However, for n > 3, proper subsets of Sn cover En completely. Let [x ] denote the greatest integer less than or equal to x. We prove the following theorem:
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