All Distances on a 2D Grid

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For a one-dimensional set of integer marks on a ruler, a Golomb ruler like {0, 1, 4, 9, 11} has no repeated distances but misses some, whereas a sparse ruler like {0, 1, 2, 6, 9} misses no distances but repeats some.


The Demonstration No Repeated Distances covers the equivalent Golomb case in two dimensions on an integer grid. In this Demonstration, a minimal set of points can cover all distances found within the given grid.

Intriguingly, for grids of size from 5 to 10, the minimal solution needs points. But a grid of size 11 needs 14 points.


Contributed by: Ed Pegg Jr (August 25)
Open content licensed under CC BY-NC-SA


Many thanks to Tom Sirgedas and Victor Miller for solving the six larger cases here.


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