If two neighboring countries merge their border dissolves and they become the same color.
Begin with an island that can be two colored.
One or more pairs of countries merge and now the new map of the island can only be three colored.
Again, one or more countries merge and now the map of the island requires four colors.
Find the smallest number of starting countries for which this is possible as well how they are joined.
A diagram like this example of a 3 color map should be easy enough to read:
1122 1332 1122