Of course, since you use three dimensional space. I believe the Four Color Theorem assumes a single plane. If you could create a map in two dimensions then I'd be impressed.

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- 05-14-2004jlou
Of course, since you use three dimensional space. I believe the Four Color Theorem assumes a single plane. If you could create a map in two dimensions then I'd be impressed.

- 05-15-2004Zach L.
That was my point. It is easy if you change the assumptions, and

*probably*impossible if you don't. :) - 05-15-2004Perspective
alright, ill take a shot at it.

*note: black region counts as a region that needs to be coloured. I guess i could have used orange or something :rolleyes: - 05-15-2004anonytmouse
Change the inner black to blue and the outer black to yellow.

According to this page:

Quote:

*http://www.math.gatech.edu/~thomas/FC/fourcolor.html*

The next major contribution came from Birkhoff whose work allowed Franklin in 1922 to prove that the four color conjecture is true for maps with at most 25 regions.

- 05-15-2004scrappy
hmm.. how about this?

- 05-15-2004Glirk Dient
color red gree and and the middle and outside red.

- 05-15-2004anonytmouse
Back to kindergarten.

- 05-15-2004ZerOrDieQuote:

Originally Posted by**axon**

1). Parts are done on computers and cannot be verified by hand.

2). No one has been able to check the rest of the proof in it's entirety. - 05-15-2004Glirk Dient
Can anyone link to a site that says in the theorem the regions cannot touch at a point? I searched and didnt find anything about that.

If no one can I will continue to think I am the winner so I feel special. - 05-15-2004XSquaredQuote:

The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary**(other than a single point)**do not share the same color.

- 05-16-2004Glirk Dient
Awwww....

- 05-16-2004Dissata
What about this one? (find the black one) :confused:

- 05-16-2004XSquared
Change all of the dark green ones to light green and then you can colour the black part dark green.

- 05-16-2004Xterria
what about this one?

- 05-16-2004grib
Exchange either yellow and red vertically and color the square yellow or red.