Four Color Theorem

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20KB, 926x481px

only took 3 colors

>-You cannot have the same color on both sides of a border.
go re-read the statement of the theorem, it doesn't say this

it says two regions sharing a border can't have the same colour, the green part here >>8968673
is only one region

>>8968668
equations and symbols and shit

>>8968679
Thank you, this was the explanation I was looking for.

>>8968668
That line in your circle is not a border. it is just a line. I'm not clear on weather you meant for it to be the fourth shape or if the circle in the centre is actually connected to the outside and the line represents an infinitesimally small gap.

>>8968703
right, there are 4 options for that line, using the colors from this post >>8968673

1) The line is part of the red territory
->every territory is a neighbor and there are 3 territories
2) the line is part of the green territory
->red is surrounded by and neighbors with green, green is neighbors with blue and red
3)the line is part of the blue territory
->same outcome as 1
4) the line is its own territory, lets call it black
->black is neighbors with green/blue/red, red inherits the relationship in 2), and blue gains a neighbor in black

If you really want to understand these problems though OP, break them down as a series of dots and lines. Try constructing graphs which break the four color theorem. The first proof of this theorem that was accepted was basically a computer doing this millions of times and concluding that it holds (don't get triggered, its a summary)