The maximum distance in 3-D can occur no more than times. Also, there exists a fixed number such that no distance determined by a set of points in 3-D space occurs more than times. The maximum distance can occur no more than times in 4-D, where is the Floor Function.

**References**

Honsberger, R. *Mathematical Gems II.* Washington, DC: Math. Assoc. Amer., pp. 122-123, 1976.

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1999-05-26