If it's an open problem, according to mathoverflow.net/help/on-topic it should apparently be tagged as such and sent to the community wiki (whatever that is). In fact, the question was a literature search. So what to do now?

I wondered whether my mildly cheeky remark would provoke someone to actually respond. I have of course removed this clause immediately. Please can you exercise similar enthusiasm to lobby to actually fix the incorrect classification of this question.

See chess.stackexchange.com/questions/33347/… where 4 necessary & sufficient inequalities are given for a collection to be achievable

This answer comes from a purely chess-playing perspective, not a mathematical perspective, and should never have been marked as correct. The question (at least in its current form) is capable of a proper mathematical response