/* 

  Octagon product in Picat.

  From Chris Smith Math Newsletter #592
  """
  Use the numbers 1-9 in the octagons so that the products
  of the octagons that touch each square give the total in
  the square!
   
      A    B    C 

        90    84

      D    E    F

        80    72

      G    H    I

  [E = 1]

  """


  This model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.

main => go.

go ?=>
  L = [A,B,C,D,E,F,G,H,I],
  L :: 1..9,

  all_different(L),

  A*B*D*E #= 90,
  B*C*E*F #= 84,
  D*E*G*H #= 80,
  E*F*H*I #= 72,

  % E #= 1, % This is not needed

  solve(L),
  println(L),

  printf("  %d    %d    %d\n\n",A, B, C),
  printf("    %d    %d\n\n", 90, 84),
  printf("  %d    %d    %d\n\n",D,E,F),
  printf("    %d    %d\n\n",80,72),
  printf("  %d    %d    %d\n",G,H,I),
  nl,
  fail,
  
  
  nl.
go => true.