Village problem? Is that even the correct name? Who knows? Here is the puzzle:
There are four villages arranged such that they occupy the 4 corners of a perfect square. What arrangement of roads could you create that would allow access to all the villages but have the shortest total road length?Instead of drawing a picture of the problem, let me just show you this excellent video with the solution. full article
Your diagram with 4 nodes can lose one edge and remain connected (wouldn't work with springs as it would deform the shape), you can afford to subtract the length of one side of the inner square from your path length.
Right, but that misses the idea. I want the program to start in some base manner that doesn't need input from me to tell it what to do. Really, I should have had every node connected to every other node by springs. What should happen would be that the system runs and determines that there should only be two nodes (or the 4 nodes should combine to form 4 nodes)
This is cool, though I noticed that watching the video with the sound off makes it look like an infomercial.
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