Comment on What are the most mindblowing fact in mathematics?

• Afrazzle@sh.itjust.works ⁨11⁩ ⁨months⁩ ago

  I think the four small countries inside would each only have 2 neighbours. So you could take 2 that are diagonal and make them the same colour.

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  • SgtAStrawberry@lemmy.world ⁨11⁩ ⁨months⁩ ago

    Looks to be that way one of the examples given on the wiki page. It is still however an interesting theory, if four countries touching at a corner, are the diagonal countries neighbouring each other or not. It honestly feels like a question that will start a war somewhere at sometime, probably already has.

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    • Vegasimov@reddthat.com ⁨11⁩ ⁨months⁩ ago

      In graph theory there are vertices and edges, two shapes are adjacent if and only if they share an edge, vertices are not relevant to adjacency. As long as all countries subscribe to graph theory we should be safe

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      • SgtAStrawberry@lemmy.world ⁨10⁩ ⁨months⁩ ago

        The only problem with that it that it requires all countries to agree to something, and that seems to become harder and harder nowadays.

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  • Blyfh@lemmy.world ⁨11⁩ ⁨months⁩ ago

    But each small country has three neighbors! Two small ones, and always the big donut country. I attached a picture to my previous comment to make it more clear.

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    • Pronell@lemmy.world ⁨11⁩ ⁨months⁩ ago

      In your example the blue country could be yellow and that leaves the other yellow to be blue. Now no identical colors touch.

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      • wazoobonkerbrain@lemmy.world ⁨11⁩ ⁨months⁩ ago

        You still have two red countries touching each other, what are you talking about?

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    • Afrazzle@sh.itjust.works ⁨11⁩ ⁨months⁩ ago

      Whoops I should’ve been clearer I meant two neighbours within the donut. So the inside ones could be 2 or 3 colours and then the donut is one of the other 2 or the 1 remaining colour.

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      • Blyfh@lemmy.world ⁨10⁩ ⁨months⁩ ago

        You’re right. Bad example from my side. But imagine the four small countries being four parts of another donut that encompass a smaller country. Then it would be impossible.

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  • ikilledlaurapalmer@lemmy.world ⁨10⁩ ⁨months⁩ ago

    Image Ok now do this one. What color is the donut country?

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    • BewilderedBeast@mander.xyz ⁨10⁩ ⁨months⁩ ago

      Image

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    • Afrazzle@sh.itjust.works ⁨10⁩ ⁨months⁩ ago

      Someone beat me to it, so I thought I’d also include the adjacency graph for the countries, it can be easier to see the solution to colouring them. Image

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• BitSound@lemmy.world ⁨10⁩ ⁨months⁩ ago

  In that image, you could color yellow into purple since it’s not touching purple. Then, you could color the red inner piece to yellow, and have no red in the inner pieces.

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