Problem of the Fortnight

[MATh...@gmail.com]

(Thanks to Luke for coming up with a more appropriate name for our
problems of every two weeks. ; )

Nine spheres of radius 1 are tightly packed in a cubical box. The
sphere in the middle is tangent to the eight others. Each of the
other eight is tangent to three faces of the box as well. What is the
length of the sides of the box?

There's a pretty picture of this cube and spheres on the handout
provided at the last meeting. I'll *try* to remember to put it up
here later. Otherwise, go find the paper or use your imagination.
q :

Please e-mail your solution (not just the answer, but how you came to
it too) to MATh...@gmail.com by March 9th, 10 AM. Do not post them
here. Good luck and have fun, yo.