You may find this problem similar.

In a cube of side 4, I pack eight spheres of unit radius.

What is the largest sphere I can place in the center (such that it doesn't overlap any of the other spheres)?

the center sphere would have a radius of:
(suare root of 2)-1
or
.414213562

I came about this by looking at the problem in 2-d. The radii of the circles form a 2 unit square with arcs extending 1 unit into the square from all four corners. the distance between the arcs diagonally will form the diameter of the center circle. useing a^2 + b^2 = C^2, I found the length of the diagonal to be √8. this minus the radii of the two arcs, 1 each, havled is the radius of the center circle.
I think?

Posted by York on 2004-02-09 10:01:16