The maximum distance between n points in three dimensions can occur no more than 2n - 2 times. Also, there exists a fixed number c such that no distance determined by a set of n points in three-dimensional space occurs more than c n^(5/3) times. The maximum distance can occur no more than ⌊1/4 n^2⌋ times in four dimensions, where ⌊x⌋ is the floor function.
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