/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Magic Hexagon of order 3, solved with CLP(Z) constraints Written 2006 by Markus Triska triska@metalevel.at Public domain code. Place the integers 1,...,19 in the following grid so that the sum of all numbers in a straight line (there are lines of length 3, 4 and 5) is equal to 38: A B C D E F G H I J K L M N O P Q R S - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ :- use_module(library(clpz)). :- use_module(library(lists)). sum38(Vs) :- sum(Vs, #=, 38). magic_hexagon(Vs) :- Vs = [A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S], Vs ins 1..19, all_different(Vs), maplist(sum38, [[A,B,C], [D,E,F,G], [H,I,J,K,L], [M,N,O,P], [Q,R,S], [H,D,A], [M,I,E,B], [Q,N,J,F,C], [R,O,K,G], [S,P,L], [C,G,L], [B,F,K,P], [A,E,J,O,S], [D,I,N,R], [H,M,Q]]). %?- magic_hexagon(Vs), labeling([ff], Vs). %@ Vs = [3,17,18,19,7,1,11,16,2,5,6,9,12,4,8,14,10,13,15] %@ ; Vs = [3,19,16,17,7,2,12,18,1,5,4,10,11,6,8,13,9,14,15] %@ ; ...