Blogs, Fun and Games

Coloring game!

I really enjoy coloring. Some of my favorite lectures are the ones I’ve planned out in such a way that I can use all types of fun colors in my lecture. I still prefer a chalkboard, as the feeling of writing with chalk is just more pleasing to me than using a dry erase board, but both are fun.

My wife also enjoys coloring, and she likes to get adult coloring books so that she can relax at home and fill out a picture with as much color as she can. The process is really calming, and I would suggest trying it if you haven’t.

Even though I enjoy coloring, it is difficult since I am color blind. I can see colors, but differentiating different colors can be very difficult. As such, I do have to plan out my color choices so that they are distinct enough that I don’t get confused as to which color I’m using. This does limit the number of colors I get to use, and since I don’t like to have things next to each other be the same color, I’m left with the problem of, how do I color this in with a limited number of colors?

Now, I would like to pause there to point that this question was naturally occurring to me. Therefore, when I found out that this was a problem posed in the 1852 with the conjecture that at most four colors were needed, it was exhilarating. Now, to prove this conjecture took over 100 years with a lot of the work being done exhaustively by a computer for the proof1.

What this means to me though, is that, I know that it is always possible to color in any picture with four colors in such a way that parts that share any boundary beyond a single point can be colored using different colors. However, there is no condensed algorithmic form of explaining how you would actually do this for an arbitrary example (there are algorithms, but the many cases introduced make it difficult to follow without the aid of a computer). Therefore, whenever I do some coloring with my wife, I get to play this game over and over. I know I can win, but I don’t know exactly how to do so, which makes it all the more fun.

For more information on references on the four-color theorem, see

  1. Weisstein, Eric W. “Four-Color Theorem.” From MathWorld–A Wolfram Web Resource.

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