- You have 9 dots, labeled A through I.
- You choose a layout (arrangement) for the 9 dots.
- You must connect the 9 dots with straight lines (no curves or extra lines).
- The object is to minimize the "Connect Factor."
- The closest that any 2 dots can be to each other is 1 unit.
There is most likely only one optimal solution, but I do not know what it is (yet).
- There are 36 distinct paths (9 choose 2). Namely, AB, AC, AD, ... , GH, GI, HI
- Consider 2-dimensional and 3-dimensional. Get creative. I have a feeling that the optimal answer is a 3-d layout (maybe 8 points evenly distributed around a dot, 1 unit from it, if that is possible? or some variation of that?)
- Eventually I would like to extend this to other numbers of dots, but for now, let's optimize 9.
Connect Factor Formula:
A = The average of the 36 path lengths
N = Total number of lines used
Connect Factor = A + N
- Add any tags that you think are relevant.
- Should the graph-theory tag be added?