Well after substantial thinking on random topics completely unrelated to the subject, I may have found a solution, however I have yet to actually elucidate the solution -- I just have a hunch that this set of logic applies to the problem I am considering.

First, consider two types of objects (

*o*), objects of size A, and those of size B. Objects of size B are, as a rule, smaller than size A. We also have objects of size C, D, etc. ad infinitum, which all follow the same rule -- the next object in the set is always smaller than the previous object. Now, if we take any arbitrary number of these objects of any arbitrary size (

*l*) (that is, the set of all objects of the mentioned sizes, A, B, C, etc.) and arbitrarily arrange them in a finite space (

*s*), we will usually attain the most amount of objects with the least amount of space taken if we start with the objects of greater size, that is the ratio of objects to space taken up by these objects,

*o/s*, if those objects must vary in size, and those objects cannot move through/into each other. That is, they must collide. Furthermore, if we take two objects of arbitrary size, say, G and V, then there will be a certain ratio in said finite space between the number of objects of size G, and of size V.

This is what I purport: The system of valence electron shells work upon the same logic, save that instead of concerning size, we concern forces (electromagnetic forces)

I just wanted to get these thoughts on paper before I forgot them.