Subcontests
(4)Arrange 10 sets in a circle
Determine whether there exist ten sets A1, A2, …, A10 such that
(i) each set is of the form {a,b,c}, where a∈{1,2,3}, b∈{4,5,6}, c∈{7,8,9},
(ii) no two sets are the same,
(iii) if the ten sets are arranged in a circle (A1,A2,…,A10), then any two adjacent sets have no common element, but any two non-adjacent sets intersect. (Note: A10 is adjacent to A1.)