Coloring Maps (Critical Thinking, Four Color Theorem)

Question

When coloring a map of countries, we want to give countries different colors if they are touching each other. (If they are only touching at a single point, that doesn’t count.)

• Draw a map that requires three colors. Draw a map that requires four colors. Draw a map that requires five colors.

• What is the fewest number of colors needed to fill in the United States map? (Of course, here states are playing the role of countries.)

• One reason a map will need more than 2 colors is if there are 3 countries that are all touching each other - for example, look at Washington, Oregon, and Idaho in the NW corner of the US. However, that’s not the only reason. Draw a map that doesn’t have three countries all touching each other, but still requires 3 or more colors to draw.

• Find a criterion that will determine without fail when a map will require at least 3 colors to draw.

Answer 1

The four-color theorem was proved in 1976.

It states that no more than four colors are required to color a map so that two adjacent areas do not have the same color.