Problem of the Week 1216

Distances in Sequence

Is there a set of points in the plane so that the set of squared distances between all pairs of the points, ignoring duplicates, is {0, 1, 2, 3, 4}?

Source: Michael Elgersma and Stan Wagon, inspired by the more difficult problem in 3-space that Ed Pegg (Wolfram Research) told me about and solved — namely, find points in 3-space such that the set of squared distances (ignoring duplicates) is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. There is a quite surprising answer to this 3D version.

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