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The Four Color Map Problem
Suppose you have a map.
You want to color all the countries, states or counties on it,
so that they are easy to distinguish.
In particular, you want to color neighboring countries with different colors.
Two countries are " neighboring" if they share a border
segment that consists of more than one point.
How many colors do you need at most?
Apparently four colors are always sufficient.
Since mapmakers began making maps that show
distinct regions (such as countries or states),
it has been known that if you plan well enough, you will never need
more than four colors to color the maps that you make.
This four color map theorem was proven in 1976
by Kenneth Appel and Wolfgang Haken.
It was the first major theorem to be proven using a computer.
