Given n countries with three representatives each, m committees A(1),A(2),…,A(m) are called a cycle if
(i) each committee has n members, one from each country;
(ii) no two committees have the same membership;
(iii) for i \equal{} 1, 2, \ldots,m, committee A(i) and committee A(i \plus{} 1) have no member in common, where A(m \plus{} 1) denotes A(1);
(iv) if 1 < |i \minus{} j| < m \minus{} 1, then committees A(i) and A(j) have at least one member in common.
Is it possible to have a cycle of 1990 committees with 11 countries? combinatoricsSet systemsgraph theoryExtremal combinatoricsIMO Shortlist