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I've seen similar questions like this and highly doubt this is a disproof or anything, but I still find solutions to these types of problems very satisfying. Here is the map I developed with my attempt and a black and white one beside it. https://drive.google.com/file/d/1UKUHvCh1EyXS9vh1j2mFC6ljbwSZ0K4b/view?usp=sharing enter image description here

I would like someone to color this image to align with the Four Color Theorem, which states that on any map that contains only contiguous shapes, only four colors are required to color the shapes such that no shape bordering one another shares a color. Corners do not count as borders.

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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – MathGeek
    Jun 2, 2022 at 20:40
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    $\begingroup$ Change the green piece to blue, and change the blue piece in the lower right to white, then only four colours are used. You may be interested in Martin Gardner's 4-colour hoax. $\endgroup$
    – Peter Phipps
    Jun 2, 2022 at 20:45
  • $\begingroup$ @PeterPhipps amazing! Thank you for your quick reply, and yes, I am quite interested in the link you sent. Thank you! $\endgroup$
    – Colby Thompson
    Jun 2, 2022 at 20:51

1 Answer 1

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If you change the green piece to blue, and change the blue piece in the lower right to white you get the picture below which requires only four colours.

four_colours

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  • $\begingroup$ Very nice! This coloring also makes sure that the outer cell can be colored blue which a lot of colorers forget to account for :) $\endgroup$
    – Arkady
    Jun 5, 2022 at 9:36

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