MathDB

Given

n

countries with three representatives each,

m

committees

A(1),A(2), \ldots, 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?

Problem Statement