Final answer:
To print every region without any two adjacent ones being the same color, it takes a maximum of four colors.
Step-by-step explanation:
To print every region without any two adjacent ones being the same color, we can use the concept of graph coloring. In graph theory, the minimum number of colors required to color the vertices of a graph without any adjacent vertices having the same color is called the chromatic number. In this case, each region can be represented as a vertex, and two vertices (regions) are connected if they share a border.
By using the four-color theorem, which states that any map on a plane can be colored using at most four colors, we can conclude that it takes a maximum of four colors to print every region without any two adjacent ones being the same color. This theorem holds true for any map, whether it is a national flag or other graphical representation of regions.
Therefore, when printing every region without any two adjacent ones being the same color, it takes a maximum of four colors.