There are two parts to the proof:
- Some map requires at least four colors.
- No map requires more than four colors.
But part 1 is easy. Here is one such map.
One of the assumptions of this theorem is that the map is on a flat plane. But what if we have a map on a donut's surface? It turns out that we need seven colors. Can you find a map on a donut that requires at least seven colors?
You can send solutions to skepticsplay at gmail dot com. A tip: you can represent a donut with a flat square in which each edge wraps around to the opposite edge.