All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 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)

Comments: ( Back to comment list | You must be logged in to post comments.)
 A further challenge. Comment 8 of 8 |
I enjoyed creating this problem and seeing how has progressed.  So... now that a six region solution has been found:

Brian's solution is on a 4x4 square grid, requiring an island of 16 squares.

Can you minimize the number of squares required?

 Posted by Jer on 2015-06-06 21:01:25

 Search: Search body:
Forums (0)