/* 

  Divisible by 7 in Picat.

  (Attributed to Sam Loyd)
  """
  Three numbers (6, 3 and 1) are drawn on the sides of three cubes - a number 
  per cube. Can you arrange the three cubes in a line so that to create a 
  3-digit number divisible by 7? Each cube must be employed.
  """


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

*/

import cp.


main => go.

go ?=>
  N = 3,
  % The trick is - of course - that the 6 cube could be 9 as well
  X = new_list(N),
  X :: [1,3,6,9],
  
  Z #= 100*X[1] + 10*X[2] + X[3],

  all_different(X),
  Z mod 7 #= 0,
  
  % cannot have both a 6 and 9
  count(6,X,#=,1) #<=> count(9,X,#=,0),

  Vars = X ++ [Z],
  solve(Vars),
  println(x=X),
  println(z=Z),
  nl,

  fail,
  
  nl.

go => true.