It is obvious that three colors are inadequate: this applies already to the map with one region surrounded by three other regions (even though with an even number of surrounding countries three colors are enough) and it is not at all difficult to prove that five colors are sufficient to color a map.

The fourcolor theorem was the first major theorem to be proved using a computer, and the proof is not accepted by all mathematicians because it would be infeasible for a human to verify by hand.

The problem on the sphere is equivalent to that on the plane.

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