Given collection of sets S1,...,Sn and a positive number k. Is the problem of selecting some of the sets such that their intersection is of size k NP-hard?
So far, I tend to believe it is so I tried to find a reduction (unsuccessful so far), I have tried is to replace intersection by union (which is equivalent if we take the complementary sets).
I've also tried to dualize the problem and view a values as representing sets where they appear (unfortunately this transformed problem is not equivalent Is this problem NP-hard? select k sets from a collection of sets such that each selected set has an empty intersection with the non selected ones)
I don't know if this problem is of interest for the reduction but it is the closest hard one I've found http://www.ic.unicamp.br/~eduardo/publications/ipl12.pdf