All Touch Map

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All Touch Map

Postby dabrink05 » Wed Jan 11, 2012 2:39 pm

This may not be the right place, but can't find a better one. Has anyone created or played on a map where all of the territories are touching one another? I'm trying to work on one, but haven't gotten very far. Want to see if anyone else has had the idea/already done it.
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Re: All Touch Map

Postby BetaGen » Wed Jan 11, 2012 6:17 pm

As in: every single territory has borders with all the other territories? I don't think it's possible for more than 5 territories due to the hexagon shape of the editor. Just try putting 4 single dots next to each other and then a bigger one surrounding all of them - that's the best I could do = 5
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Re: All Touch Map

Postby magves » Wed Jan 11, 2012 6:23 pm

can´t you do like more cake slices form, where everyone touches eachother in the middle??
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Re: All Touch Map

Postby BetaGen » Wed Jan 11, 2012 7:43 pm

Single hex symmetry is impossible while touching all regions with each other, the sliced pie analogy illustrates that well
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Re: All Touch Map

Postby Lopdo » Wed Jan 11, 2012 7:54 pm

BetaGen wrote:As in: every single territory has borders with all the other territories? I don't think it's possible for more than 5 territories due to the hexagon shape of the editor. Just try putting 4 single dots next to each other and then a bigger one surrounding all of them - that's the best I could do = 5
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and even there you are wrong, top quarter doesn't touch bottom one
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Re: All Touch Map

Postby BetaGen » Wed Jan 11, 2012 8:17 pm

My bad a silly mistake :roll: then It's like to be max 4
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Re: All Touch Map

Postby techgump » Wed Jan 11, 2012 10:50 pm

It's 4.
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Re: All Touch Map

Postby Ratburntro44 » Wed Jan 11, 2012 11:37 pm

Wikipedia wrote:In mathematics, the four color theorem, or the four color map theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. Two regions are called adjacent if they share a common boundary that is not a corner, where corners are the points shared by three or more regions.[1] For example, Utah and Arizona are adjacent, but Utah and New Mexico, which only share a point that also belongs to Arizona and Colorado, are not.


That's why you can't get 5.
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Re: All Touch Map

Postby Robomajor » Thu Jan 12, 2012 10:38 am

Challenge accepted.
This too shall pass.
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