The following program computes so-called Steiner triplets. These are triplets of numbers from 1 to N such that any two triplets have at most one element in common.
:- lib(fd_sets). :- lib(fd). steiner(N, Sets) :- NB is N * (N-1) // 6, % compute number of triplets intsets(Sets, NB, 1, N), % initialise the set variables ( foreach(S,Sets) do #(S,3) % constrain their cardinality ), ( fromto(Sets,[S1|Ss],Ss,[]) do ( foreach(S2,Ss), param(S1) do #(S1 /\ S2, C), % constrain the cardinality C #<= 1 % of pairwise intersections ) ), label_sets(Sets). % search label_sets([]). label_sets([S|Ss]) :- insetdomain(S,_,_,_), label_sets(Ss).
Here is an example of running this program
?- steiner(9,X). X = [[1, 2, 3], [1, 4, 5], [1, 6, 7], [1, 8, 9], [2, 4, 6], [2, 5, 8], [2, 7, 9], [3, 4, 9], [3, 5, 7], [3, 6, 8], [4, 7, 8], [5, 6, 9]] More? (;)