Magic Hexagon

Construct a hexagon of the form

  A B C
 L M N D
K R S O E
 J Q P F
  I H G

hexagon:-
  R19=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],
  remove(A, R19, R18),         
  choose1(C, B, A, R18, R16),
  A > C, % Avoid rotations
  choose1(E, D, C, R16, R14),
  A > E, % Avoid rotations
  choose1(G, F, E, R14, R12),
  A > G, % Avoid rotations
  choose1(I, H, G, R12, R10),
  A > I, % Avoid rotations
  choose1(K, J, I, R10,  R8),
  A > K, % Avoid rotations
  C > K, % Avoid reflections
  calc2(L, A, K, R8, R7),    
  choose2(N, O, B, F, R7, R5),
  calc3(M, D, N, L, R5, R4),  
  calc3(P, D, O, H, R4, R3),  
  calc3(R, J, M, B, R3, R2),  
  calc3(Q, J, P, F, R2, [S]),  
  tab(4),  writes([A,B,C]),
  tab(2), writes([L,M,N,D]),
         writes([K,R,S,O,E]),
  tab(2), writes([J,Q,P,F]),
  tab(4),  writes([I,H,G]), nl,
  fail.
hexagon.

choose1(X, Y, I, P, Q):-remove(X, P, R), Y is 38-X-I, remove(Y, R, Q).

choose2(X, Y, I, J, P, Q):-remove(X, P, R), Y is 38-X-I-J, remove(Y, R, Q).

calc2(X, I, J, P, Q):-X is 38-I-J, remove(X, P, Q).

calc3(X, I, J, K, P, Q):-X is 38-I-J-K, remove(X, P, Q).

writes([]):-nl.
writes([X|Xs]):-fwrite(i, 3, 0, X), tab(1), writes(Xs).

LPA Index     Home Page