KGS math club/solution 11 19

{{2}, {2,3}, {2,3,4}, {4}}   giving 1152

{{2,3,4}, {3,4}, {4}}   and   {{2}, {4}, {2,4}, {3}, {2,3}}   also work

The trick is that the elements of a set must be distinct. So { {3,3,3,3,3,3,2} } is not allowed, nor is {{3}, {3}, {3}, {3}, {3}, {3}, {2}}.