The following program computes so-called Steiner triplets. The problem is to compute triplets of numbers between 1 and N, such that any two triplets have at most one element in common.

:- lib(ic_sets). :- lib(ic). 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 / |

Running this program yields the following first solution:

?- 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? (;)