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Balls in Space (Posted on 2005-12-09) Difficulty: 4 of 5
What is the maximum proportion of space that can be filled with an infinite number of identical spheres?

No Solution Yet Submitted by Andre    
Rating: 4.4000 (5 votes)

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Solution (on a technicality) Comment 12 of 12 |
I just thought of something. The answer is zero. The definition of a sphere is (correct me if I'm wrong) the set of points in a three-dimentional space that are equidistant to a single point (the center of the sphere). So, spheres don't actually fill any space; they define spherical regions. This is just a technicality, and if you replaced the word "spheres" with "spherical regions" you would probably have the problem Andre intended.
  Posted by hal on 2007-04-20 01:39:56
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