In Oddtown with $n$ citizens, $m$ clubs are formed. Every club has an odd number of members and also each two clubs have an odd number of members in common. Given that no two clubs have exactly the same members, find the largest possible value of $m$.
As mavropnevma said Here, The other three cases, "odd clubs with even pairwise intersections", "even clubs with even pairwise intersections", and "even clubs with odd pairwise intersections are discussed in Bollobas's book, The Art of Mathematics, but not this one, so I'm intrested to see it's answer.
P.S: The topic in AoPS got no answers, so I'm posting it here.....