/* 

  One off digit problem in Picat.

  From Richard Wiseman
  http://richardwiseman.wordpress.com/2012/10/19/its-the-friday-puzzle-182/
  """
  in the equation:
  
     43 + 57 = 207
  
  every digit is precisely one way from its true value.  What is the correct sum?
  """

  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 = 2+2+3,

  % The incorrect numbers: 43, 57, and 207
  G = [4,3, 5,7, 2,0,7],

  % decision variables
  X = new_list(N),
  X :: 0..9,

  X12 #= X[1]*10+X[2],
  X34 #= X[3]*10+X[4],
  X58 #= X[5]*100+X[6]*10+X[7],

  X12 + X34  #= X58,

  % one off
  foreach(I in 1..N) 
    abs(G[I]-X[I]) #= 1
  end,

  solve(X),
  println("orig: 43 + 57 = 207"),
  printf("sol : %d + %d = %d\n",X12, X34, X58),
  println(sum=X58),
  fail,
  
  nl.

go => true.