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Coco

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What a colourful world

A little problem to kill time on the subway, the bus or whatever... You need a pen and a piece of paper.
What is the minimum number of colors needed to color a (political) world map ? Well, naturally two countries which touch each other must be of different colors :

An easy way to model that problem is to draw « potatoes » :

Now try to draw 4 potatoes. Then 5, then 6... Every potato must touch all the other potatoes.

Careful : the contact must be in an indeterminate number of points

indeterminate number of points

determinate number of points (Impossible ! you can't find this kind of configuration on the world map )

Last edited by Coco (2014-10-09 23:01:42)

Coco

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Re: What a colourful world

Well, I've still got some work to do if I wanna make my exercices fun !

Here we are for 4 :

A touch B,C, D
B touch A, C, D
C touch A, B, D
D touch A, B, C

If someone manage to draw 5, I'll send him a case of champagne.

Coco

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Re: What a colourful world

Yes, I will cover my costs selling your address to BF1942 police

without using singularities

The contact surface between the shapes must be more than one point

Coco

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Re: What a colourful world

Go for a case of red cabbage

Coco

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Re: What a colourful world

The earth isn't a torus. It's flat.

Heretic !

tuia

BFSoldier

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Re: What a colourful world

I think it is not possible with 5 surfaces, unless 4 touch each other at a single point.
I guess you can paint world map with just 3 colors.

Coco

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Re: What a colourful world

I guess you can paint world map with just 3 colors.

France/Belgium/Luxemburg/Germany need 4, for instance.

I think it is not possible with 5 surfaces, unless 4 touch each other at a single point.

Yes. So there is no need for more than 4 colors. But, actually, my model is wrong : I assume that the countries are in one piece, which is not always the case (Alaska, Kaliningrad...)

Let us pretend that it's the year 1939. Hitler and Staline are going to divvy Poland up... and twisting time is here : Poland invades Romania !

5 colors. So all we can say is, there's only a very small chance that we need more than 4 colors.

Vojislav

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Re: What a colourful world

Fake map

Timmos

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Re: What a colourful world

what the fuck lol

tuia

BFSoldier

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Re: What a colourful world

Nice explanation.