Other correct solutions were sent in by Nathan Pauli, Carl Westine, Jake Krippelz, Lori Niquette, Brandon Schwoerer, Scott Baker. Further solutions were submitted by alumnus Brian Laughlin ('81), and from Burkart Venzke, Mike Lynch, Dane Brook, Lou Cairoli, Philippe Fondanaiche, Al Zimmermann, Skip Kuzel, Steve Prowse, Alexey Vorobyov, Shekhar Joglekar.  There were many incorrect solutions submitted.

Consider a line going along one of the long diagonals of the box.  This line will traverse the centers of three tangent spheres, covering 4 units of distance along the way.  For the remaining bits, draw a cube with side length 1 from the center of a corner sphere to the nearest corner of the box.  The edges of this small box have length 1 and diagonal of length Ö3.  The diagonal of the entire box then has length 4 + 2Ö3, and edges of length 2 + 4/Ö3.

Al Zimmerman points out that this is one step in an infinite chain of such problems.  He observed that in n-dimensional space you can pack 2ⁿ +1 unit spheres tightly into a box.  The case above is n = 3.  He then determined, in general, the length of the side of the box.  Can you?

(Hint:  Work out the case n = 2 and observe the pattern.)

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