/*
  https://puzzles9.com/puzzles/number-sequence-puzzles-with-answers/
  Puz254
  """
  5 6 7 4 9
  2 4 8 1 6
  7 5 4 7 1
  6 1 3 5 8
  4 2 6 ? 6

  Answer  :   3
  In the above puzzle, in each row , treat first two digits as one number and also last 
  two digits as one number. subtract last number from first number to get middle number.

  56  –  49  =  7
  24  –  16  =  8
  75  –  71  =  4
  61  –  58  =  3
  42  –  36  =  6

  So, answer is 3.
  """

  We rearrange to get the unknown last:
    5 6 7 9 4
    2 4 8 6 1
    7 5 4 1 7
    6 1 3 8 5
    4 2 6 6 ?

  Nope, this is too hard to find.
  Adding to_num/2 does not help.

*/

/*
data(puz254,Data,Vars,Unknown,Ops,Constants,MaxC) :-
  Matrix = [
            [5,6,7,9,4],
            [2,4,8,6,1],
            [7,5,4,1,7],
            [6,1,3,8,5],
            [4,2,6,6,_]
  ],
  Ops = new_map([infix=["+","-"],
                 user=["to_num"]
                 ]),
  Constants = 1..1,
  MaxC = 7,
  (
    nl,
    make_data_matrix(Matrix,Data,Unknown,Vars)
   % ;
   % nl,
   % make_data_matrix(Matrix.transp,Data,Unknown,Vars)  
  ).
*/

/*
  A simpler variant.

  Let's simplify the problem a little and make the mid column
  the unknown instead:

    5 6 4 9  7
    2 4 1 6  8
    7 5 7 1  4
    6 1 5 8  3
    4 2 3 6  ?

  For this simple version we find the solution:
  maxCount = 4
  code = (B - to_num((C - A),D)) = [[[5,6,4,9],7],[[2,4,1,6],8],[[7,5,7,1],4],[[6,1,5,8],3]] = [[4,2,3,6] = 6]
  code = (to_num((A - C),B) - D) = [[[5,6,4,9],7],[[2,4,1,6],8],[[7,5,7,1],4],[[6,1,5,8],3]] = [[4,2,3,6] = 6]

  Without to_num/2, the following is also found:
  maxCount = 7
  code = (B + ((10 * (A - C)) - D)) = [[[5,6,4,9],7],[[2,4,1,6],8],[[7,5,7,1],4],[[6,1,5,8],3]] = [[4,2,3,6] = 6]

*/
data(puz254,Data,Vars,Unknown,Ops,Constants,MaxC) :-
  Data = [ [[5,6,4,9],7],
           [[2,4,1,6],8],
           [[7,5,7,1],4],
           [[6,1,5,8],3]
        ],
  Unknown = [4,2,3,6],
  Vars = ["A","B","C","D"],
  Ops = new_map([infix=["+","-","*"]
                 % , user=["to_num"]
                 ]),
  Constants = [1,10],
  MaxC = 7.