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 Map coloring (Posted on 2015-06-05)
Imagine an island composed of several connected countries with no enclaves or exclaves. We are concerned with coloring a map of the island with as few colors as possible.

If two neighboring countries merge their border dissolves and they become the same color.

Begin with an island that can be two colored.

One or more pairs of countries merge and now the new map of the island can only be three colored.

Again, one or more countries merge and now the map of the island requires four colors.

Find the smallest number of starting countries for which this is possible as well how they are joined.

A diagram like this example of a 3 color map should be easy enough to read:

```1122
1332
1122```

 See The Solution Submitted by Jer Rating: 3.3333 (3 votes)

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 6 countries solution | Comment 6 of 8 |

Playing around with this at lunch and found a six country solution:

`AAAAABBACDBAEFAA`
Countries A, D and E are one color and B, C, and F are the second color.

E and F merge - they must become a third color.

Then A and B merge - the remaining four countries all share borders with each other, requiring four colors.

 Posted by Brian Smith on 2015-06-05 22:50:02

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