These 12 pairs of colors can be used to color any-sized map as long as any combination of them follows 4-color theorem such that "1 3 0 1" would be okay, while "1 3 3 0" would not. Also applies to vertical pairs, 1 3 0 2 <-- works.
1 3 0 3 <-- doesn't work.
The computer can randomly pick any pair to fill in more countries following the 4-color theorem.
The 12 pairs can also be used to confirm that the coloring on a map follows the 4-color theorem since any such map would inevitably use the 12 pairs of color ordering shown above, following the horizontal and vertical conditions shown above. I'm sure this is nothing new to anyone here. It was kind of a new insight to me. (no one has hinted at using such a method)
The upside of this is that hundreds or even thousands of colorings on a map may be found depending on the size of a map. The downside is, there's no doubt that even more advanced methods will come along making a method such as this obsolete and archaic in no time.