You know if you've crossed over into the next town over if the style of the street name signs has changed: Cambridge's is green, Somerville blue. How many colors or designs are needed to have a distinctive change at every border?
Answer: 4, by the celebrated four-color map theorem. (See also the NP-complete three-color map problem.)
It can get annoying if a new town is carved out of another one, or towns merge, possibly forcing new street signs all throughout the region.
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