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Puzzling

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  • $\begingroup$ I can vouch for the correctness of the calculations, that is, those are indeed the only integer solutions to the system of inequalities and equality. That said, I still think it should be shown whether or not the diophantine solution has a geometric realisation on the plane. $\endgroup$ Commented Apr 11, 2016 at 0:46
  • $\begingroup$ @Fimpellizieri: I added a (semi-trivial) geometric realization of these points in the community wiki answer. $\endgroup$ Commented Apr 13, 2016 at 17:10
  • $\begingroup$ @MichaelSeifert Are they allowed to coincide? That's a bit of a bummer, haha. $\endgroup$ Commented Apr 13, 2016 at 17:49
  • $\begingroup$ @Fimpellizieri: Yeah, it's not terribly interesting. I suspect, however, that this solution could be continuously deformed to another one where the points aren't all degenerate. After all, we have 30 free variables (x and y coords for 15 points) and only 3 constraints, so one would expect the solution space to be 27-dimensional. $\endgroup$ Commented Apr 13, 2016 at 17:52