Final answer:
In mathematics, the four-color theorem indicates that a minimum of four colors is required to color a map like Japan, ensuring no two adjacent areas have the same color.
Step-by-step explanation:
The question pertains to a problem known as the four-color theorem in Mathematics, which states that you can color any map with only four colors such that no two adjacent areas share the same color. When applied to Japan, you would need a minimum of four colors to ensure that no two areas that share a common boundary are colored the same. This theorem simplifies the complex task of color planning in cartography and also finds relevance in various other fields where distinguishing adjacent entities is crucial.