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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```

 Submitted by Jer Rating: 3.3333 (3 votes) Solution: (Hide) The minimum of 6 regions is as shown: ```1145 1236 1166 Where 1,3,5 can be one color and 2,4,6 the other. Erase the west border: 1145 1136 1166 With 2 gone, 1&5 can be the same color but 1,3,4 must be different but 6&4 can be the same. Erase one more border: 1144 1136 1166 Now all four regions must be different colors. ``` The map seems to be the smallest possible, using a grid of only 12 squares.

 Subject Author Date A further challenge. Jer 2015-06-06 21:01:25 re: 6 countries solution Steve Herman 2015-06-06 06:23:51 6 countries solution Brian Smith 2015-06-05 22:50:02 Puzzle challenged Steve Herman 2015-06-05 20:23:52 re(3): Drawing Challenged (spoiler?) Steve Herman 2015-06-05 14:00:13 re(2): Drawing Challenged (spoiler?) Jer 2015-06-05 10:51:11 re: Drawing Challenged (spoiler?) Steve Herman 2015-06-05 09:52:09 Drawing Challenged (spoiler?) Steve Herman 2015-06-05 09:40:25

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