Math Curiosity: The Coloring Problem

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How few colors do you need to color in any map so that no two neighboring regions are the same color?

Note: "neighboring" means that the regions share a side, not just a point. So New Mexico and Utah could be the same color on the US map as they only share a corner.


  1. First, we introduce the idea of coloring in regions on a map with a very simple example that needs only three colors.
  2. Then, we increase the challenge a bit with a second map that still only needs three colors.
  3. Next, we present an even more challenging map.
  4. We reveal the coloring problem's true solution: no map needs more than four colors.


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