So far I have asked this question in physics, engineering and math sections but have not gotten an answer in three years. If you have 100 identical spheres and group them into A sphere shape, how many will end up on the surface? They can be packed tight or loose in a hexagon pattern or cubicle pattern. They can be symmetrically or evenly spaced. I realize the answer can be off by one or two depending on how you group them, But in general it seems like something that can be answered. Is there a formula that could be applied to any number of spheres? For example what if you have 120 identical spheres, how many will be on the surface then? Imagine an atom with 120 nuclei in the nucleus. Thanks for your help.
EDIT:After seeing some of the responses it reminded me of my thought process a few years ago when I began to think about this. How do you define surface, what type of packing, etc. etc. I too tried the plastic bags and ended up using different colored magnetic balls. Experimenting has worked just fine and I asked the question because I truly thought a simple formula would be available. As for what the surface is I have found another question that actually comes closer to what I'm interested in. No matter how many spheres are accumulated into a spherical shape you can separate them into two categories. Spheres in the (interior) and spheres on the (surface or touching a sphere on the surface). This seems confusing at first but it actually simplifies the surface question by literally filling the gaps. So really the question is how many spheres are not on the surface or touch a sphere on the Surface? Even still it can be difficult counting spheres when you transfer between hexagonal, cubical or symmetrically spherical shaped. That is why I have hoped for quicker solution.