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Think of a hypothetical earth:

1.The poles was each their own country with a color on the map

2. Every country stretch all the way from south to north

Every country in 2. then only need two colors. Because the “same” color can never meet in any point.

The fourth color comes into play if you have a new country that bridge the south (or north) and both of the countries in step 2. at the same time.

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