Math Curiosity: The Coloring Problem

Objective

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.

Steps

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.

Resources

• The coloring problem maps (PDF)
• The coloring problem maps (Google Slides)