A Seven Pack?
Eight spheres can be packed into a cubic box as follows:
Is there any way that such spheres can be packed into the same box but with one of its linear dimensions reduced?
Image credit: http://i54.photobucket.com
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1 solution
If you replace two of the top spheres (that share an edge) with one half way in between them, it can "sink down" slightly between the two spheres under it. And, once you have done that, the two other spheres on the top, can be packed in against the third, and also sink down a bit. Therefore, the height of the cubic box can be reduced.
Bonus question : How much can the height be reduced by? :-)