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Old 06-02-2013, 09:04 PM   #1
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Default Colors on a map

We wish to publish a world map. Each color on the map requires a pass through the press. In order to reduce costs, we will use the minimum number of colors required.

What is the minimum number of colors required to make a political map, such that no two adjacent countries are the same color?

(Disregard colors for labels, boundary lines and water, we will not count those)
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Old 06-03-2013, 12:30 AM   #2
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This is one of the oldest problems in topology, and the attempt to prove an answer occupied many mathematicians for whole careers.

Interestingly, the answer doesn't depend upon whether we intend to publish a flat map or a globe. But if the world were donut-shaped the answer would change.
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Old 06-03-2013, 08:01 AM   #3
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The counties have change borders and names, so what is the purpose?

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Old 06-03-2013, 09:39 AM   #4
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I'm going with seven colors.

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Old 06-03-2013, 05:29 PM   #5
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Quote:
Originally Posted by TXiceman View Post
The counties have change borders and names, so what is the purpose?

Ken
Well, we could have a black and white map, with just the borders and labels in black. Of course, all the white countries would be adjacent to white countries.

HINT: I have an ARRL Great Circle Map and they have "X" number of colors. No more than that are required.
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Old 06-03-2013, 07:09 PM   #6
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4 color print.
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Old 06-03-2013, 09:59 PM   #7
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Quote:
Originally Posted by Radio View Post
Each color on the map requires a pass through the press.
Man, that's gotta be a really old press. Modern rotary web-fed presses -- that is, from late 19th century onward -- require only one pass, and only three or four inks to make a whole spectrum of colors.
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Old 06-04-2013, 09:31 AM   #8
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Zambia is bordered by 8 countries, but some of them can have the same color since they border few countries. Hungary is bordered by 7 counties, but southern europe is a mess.

Let me change my number to 6 colors.

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Old 06-04-2013, 05:07 PM   #9
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Quote:
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Disregard colors for labels, boundary lines and water, we will not count those)
Actually, of course, the inclusion of water would not change the answer.
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Old 06-05-2013, 02:50 PM   #10
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And the answer is .... four!

Try it. Get a pencil and paper and try to make a "map" where more than 4 colors are required to prevent adjacent (not corner to corner) countries (or states) from having the same color.

Been working on it for years... never got past 4. Have fun trying though!
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Old 06-05-2013, 02:51 PM   #11
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Quote:
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Man, that's gotta be a really old press.
It's a really old puzzle.
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Old 06-05-2013, 04:10 PM   #12
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Definitely a really old puzzle, from 1852.

The four-color theorem wasn't proven until 1976, when it was 124 years old. It applies strictly only when each area to be colored is contiguous. Thus it strictly doesn't apply to maps of Earth's countries, for some countries aren't contiguous. The USA, for example, isn't contiguous if you include Hawaii or Alaska or both. Pakistan wasn't contiguous until East Pakistan split off and became a separate country (Bangladesh) in 1971. Brunei isn't contiguous, and I'd bet there are many more that I never learned of.

But none of my examples requires a fifth color, and maybe no country does.
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Old 06-05-2013, 06:59 PM   #13
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With 4 colors you can make any color you want during the print process.
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