Question 2
(CAN 1) 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 $i=1,2,\ldots,m$, committee $A(i)$ and committee $A(i+1)$ have no member in common, where $A(m+1)$ denotes $A(1)$;
(iv) if $1\lt |i-j|\lt m-1$, 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?
(i) each committee has $n$ members, one from each country;
(ii) no two committees have the same membership;
(iii) for $i=1,2,\ldots,m$, committee $A(i)$ and committee $A(i+1)$ have no member in common, where $A(m+1)$ denotes $A(1)$;
(iv) if $1\lt |i-j|\lt m-1$, 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?