Damn, I feel dumb now! Whatcha guys talkin about again? Guess the answer to this thread would be NO!!!!!!!!!

quote:

Originally posted by DigiNut I know we've gotten off-topic, but what is that?

Draw a 2-dimensional map (like countries for example). You need to color them in such a way that no two bordering countries have the same color (to avoid confusing the map viewers!). Is there a bound for the number of colors you must use to do this?

The answer is 4 (?!). That's right, using 4 colors, you can color ANY map so that no two bordering countries have the same color. It was only eventually proven by enumerating equivalence classes by a computer. Nobody's solved it by hand. I think it's the most famous example of a (partially) computer-proven problem.

I guess the rest shall remain forever unsolved :-D

This is quite easy to show on paper really ...

quote:

Originally posted by Flyboy217 I guess the rest shall remain forever unsolved :-D

Well, only 3(b) and 4(b) are unsolved... I just don't have that much time to work on them lately, I'll get to 'em eventually...

___________________
My party schedule:
2009-02-21 - DJ Attention @ I'm So Popular
2009-06-18 - DJ Annoying @ People Need To Know Where I'll Be
2012-11-32 - DJ Insufferable ɸ Or At Least the Stalkers I Complain About
2048-06-66 - Spastic & Whocares ¶ Although I'm Actually Flattered
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quote:

Originally posted by UWM This is quite easy to show on paper really ...

The four-color theorem? Well props to you if you can, but mathematicians have tried (and failed) for decades.

quote:

Originally posted by Flyboy217 The four-color theorem? Well props to you if you can, but mathematicians have tried (and failed) for decades.

Is this any map you could possibly devise, or just our world map?

___________________
My party schedule:
2009-02-21 - DJ Attention @ I'm So Popular
2009-06-18 - DJ Annoying @ People Need To Know Where I'll Be
2012-11-32 - DJ Insufferable ɸ Or At Least the Stalkers I Complain About
2048-06-66 - Spastic & Whocares ¶ Although I'm Actually Flattered
9999-45-81 - Tweaker Gimp ☼ I Probably Won't Even Go To This But I Have To Make Sure I Fill Up All The Available Space Here

quote:

Originally posted by Flyboy217 Draw a 2-dimensional map (like countries for example). You need to color them in such a way that no two bordering countries have the same color (to avoid confusing the map viewers!). Is there a bound for the number of colors you must use to do this? The answer is 4 (?!). That's right, using 4 colors, you can color ANY map so that no two bordering countries have the same color. It was only eventually proven by enumerating equivalence classes by a computer. Nobody's solved it by hand. I think it's the most famous example of a (partially) computer-proven problem.

What about a country with 4 other countries bordering it?

quote:

Originally posted by Flyboy217 The four-color theorem? Well props to you if you can, but mathematicians have tried (and failed) for decades.

Well I don't know if I've necessarily proven it, but I was just toying around with it and came up with what looked to be a solution.

quote:

Originally posted by UWM Well I don't know if I've necessarily proven it, but I was just toying around with it and came up with what looked to be a solution.

i'm piqued. Post a pic and lets see how you did it

quote:

Originally posted by DJ-Fuq What about a country with 4 other countries bordering it?

The center country is colored A and the rest are all B. That's two colors :-)

Yes, this is of course for any possible 2D map, not just our world :-P. That would be a horrible, horrible mathematical theorem.

Four Color Theorem

Last edited by Flyboy217 on Oct-16-2003 at 16:28