"This mathematical theory that has been proven is bunk"
Right... Either you're misunderstanding what the theory says or your crazy concentric countries idea doesn't work (hard to tell from your description).
Right... Either you're misunderstanding what the theory says or your crazy concentric countries idea doesn't work (hard to tell from your description).
The third and fifth rings (counting from the inside) don’t touch each other so, you can give them the same color.
Again, as mentioned in my earlier comment, I would suggest thinking of things / describing things in terms of plane graphs rather than "maps". It'll make everything easier.
I might also suggest learning some of the relevant graph theory? It sounds like you're trying and failing to embed a K_5, or perhaps an arbitrary K_n, into the plane. That can't be done, and the proof that this is impossible is much easier than the full 4-color theorem. (There are also the 5-color and 6-color theorems, which again have much easier proofs than the 4-color theorem, and which are another reason you can't embed an arbitrary K_n in the plane.)