The map in this problem doesn’t need to correspond to real geography—any partitioning of a flat surface into distinct regions qualifies. The question, given any such map, is how many colors are required to fill in each region so that no two adjacent regions have the same shade. Some ground rules: Each distinct region must be contiguous (technically Michigan violates this rule in U.S. maps because Lake Michigan severs the state into two disconnected parts). For two regions to count as adjacent, they must share some length of contiguous border; touching at a single point (or discrete set of points) doesn’t qualify. For example, Utah and New Mexico touch at only one corner and so do not count as neighbors for our purposes.