STUMPER #1.3: FROM HERE TO THERE
(Did you solve something differently? There's almost always more than one way to solve
a math problem. Sometimes there's even more than one correct solution!)
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3. Mapping Mathematica
You are the ruler of the country of Mathematica. It has 10 states. Draw a map of Mathematica using these three rules:
(1) States can be any shape and in any position, but together they have to form one single country with no holes or gaps in it.
(2) Each state must be a single color, and no adjacent states can share the same color. Note: if states touch only at a single point, they’re not considered "adjacent" for this problem.
(3) Use exactly 4 colors in your map.
If you can do that, can you design another map with the same rules but with just three colors? How about two? Although it took them more than a century to prove it, mathematicians say that there is no map you could possibly draw that would require more than 4 colors. Experiment and see.