# Four-colors on a map thing

**URL:** <https://boards.straightdope.com/t/four-colors-on-a-map-thing/168763>\
**Category:** Cecil's Columns/Staff Reports\
**Created:** [April 15, 2003, 12:06am UTC](https://boards.straightdope.com/t/four-colors-on-a-map-thing/168763 "2003-04-15T00:06:57Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![maralinn](https://avatars.discourse-cdn.com/v4/letter/m/d9b06d/32.png) [@maralinn](https://boards.straightdope.com/u/maralinn)\
**Post date:** [April 15, 2003, 12:06am UTC](https://boards.straightdope.com/t/four-colors-on-a-map-thing/168763/1 "2003-04-15T00:06:57Z")

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I read Cecil’s answer at [http://www.straightdope.com/classics/a1\_126b.html](http://www.straightdope.com/classics/a1_126b.html), but I’m still confused.

Is the four-color map problem about the _actual_ countries of the world – real maps? Or is about theoretical maps?

Because if it’s about theoretical maps, it seems quite easy to envision a map that needs five colors.

There must be something I’m missing.

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**Author:** ![maralinn](https://avatars.discourse-cdn.com/v4/letter/m/d9b06d/32.png) [@maralinn](https://boards.straightdope.com/u/maralinn)\
**Post date:** [April 15, 2003, 12:08am UTC](https://boards.straightdope.com/t/four-colors-on-a-map-thing/168763/2 "2003-04-15T00:08:59Z")

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Sorry, the URL works if you remove the comma.

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**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\
**Post date:** [April 15, 2003, 12:10am UTC](https://boards.straightdope.com/t/four-colors-on-a-map-thing/168763/3 "2003-04-15T00:10:21Z")

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Nope, it’s theoretical maps, and the thing you’re missing is that your intuition plays tricks on you. Go ahead and try it. Draw out a map. Then color it in as best you can.

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**Author:** ![maralinn](https://avatars.discourse-cdn.com/v4/letter/m/d9b06d/32.png) [@maralinn](https://boards.straightdope.com/u/maralinn)\
**Post date:** [April 15, 2003, 12:21am UTC](https://boards.straightdope.com/t/four-colors-on-a-map-thing/168763/4 "2003-04-15T00:21:06Z")

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LOL! Since Cecil was of no help, I found other sites that explained two things to me. One, theoretical maps count. Two, my efforts at creating maps requiring five colors were futile, and when I thought I had one it was because I was using a color unnecessarily. 🙂

Thanks anyway!

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**Author:** ![Jabba](https://avatars.discourse-cdn.com/v4/letter/j/b5e925/32.png) [@Jabba](https://boards.straightdope.com/u/Jabba)\
**Post date:** [April 15, 2003, 12:23am UTC](https://boards.straightdope.com/t/four-colors-on-a-map-thing/168763/5 "2003-04-15T00:23:53Z")

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Two points to remember:  
(i) In real maps, the sea is painted blue and no land masses can be coloured that shade. These restrictions do not apply in the 4-colour theorem.  
(ii) In real maps, separate parts of one country must be the same colour. Again, this does not apply in the theorem.

With these restrictions, I would recommend **Achernar’s** advice. Try and construct a counterexample.

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**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\
**Post date:** [April 15, 2003, 11:36am UTC](https://boards.straightdope.com/t/four-colors-on-a-map-thing/168763/6 "2003-04-15T11:36:05Z")

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An excellent introduction to the four color theorem may be found [here](http://www.mathpages.com/home/kmath266/kmath266.htm). It’s got lots of pretty pictures.