/*

  Squares

  https://puzzles9.com/puzzles/number-sequence-puzzles-with-answers/
  Puz1059
  """
  
      13  5    12  4 
       5 20     3  5

      16  4    11  5
      20  4     7  ?


  Answer : 8
  In each rectangle, multiply first row numbers and subtract sum of numbers in second row from it. 
  Result of each rectangle should be 40.

  (13*5)-(5+20) = 40
  (12*4)-(3*5) = 40
  (16*4)-(20+4) = 40
  (11*5)-(7+8)= 40

  So, answer is 8.
  """

  Here we test two different representation from the data matrix
    [[13,5,5,20],
    [12,4,3,5],
    [16,4,20,4],
    [11,5,7,_] ]



  * Representation 1:
    data = [[[13,5,5],20],
            [[12,4,3],5],
            [[16,4,20],4]]
    vars = [A,B,C]
    unknown = [11,5,7]
    ops = (map)[infix = [+,*,-]]
    constants = [1,2,4,8,16,32]

    Some solutions:

    maxCount = 7
    code = ((((A * B) - 32) - 8) - C) = [[[13,5,5],20],[[12,4,3],5],[[16,4,20],4]] = [[11,5,7] = 8]
    code = ((((A * B) - 8) - C) - 32) = [[[13,5,5],20],[[12,4,3],5],[[16,4,20],4]] = [[11,5,7] = 8]


  * Representation 2:
    data = [[[13,12,16],11],
            [[5,4,4],5],
            [[5,3,20],7]]
    vars = [A,B,C]
    unknown = [20,5,4]
    ops = (map)[infix = [+,*,-,mod]]
    constants = [1,2,4,8,16,32]

    With only +,*,- no solution is found, but adding modulo give some other solutions:

    maxCount = 5
    code = (32 mod (C + (A mod 8))) = [[[13,12,16],11],[[5,4,4],5],[[5,3,20],7]] = [[20,5,4] = 0]
    code = (32 mod (C + (1 + 4))) = [[[13,12,16],11],[[5,4,4],5],[[5,3,20],7]] = [[20,5,4] = 5]
    maxCount = 6
    maxCount = 7
    code = (A + (A mod ((8 mod C) - A))) = [[[13,12,16],11],[[5,4,4],5],[[5,3,20],7]] = [[20,5,4] = 20]
    code = (A + (C mod ((2 + 4) - B))) = [[[13,12,16],11],[[5,4,4],5],[[5,3,20],7]] = [[20,5,4] = 20]
    code = (B + (4 - ((C * 32) mod A))) = [[[13,12,16],11],[[5,4,4],5],[[5,3,20],7]] = [[20,5,4] = 1]
    code = (1 + (32 mod (B + (2 + 8)))) = [[[13,12,16],11],[[5,4,4],5],[[5,3,20],7]] = [[20,5,4] = 3]
    code = (4 + (((C + 16) - B) mod A)) = [[[13,12,16],11],[[5,4,4],5],[[5,3,20],7]] = [[20,5,4] = 19]
    code = (4 + ((B - (C * 32)) mod A)) = [[[13,12,16],11],[[5,4,4],5],[[5,3,20],7]] = [[20,5,4] = 21]
    code = (4 + ((16 + (C mod B)) mod A)) = [[[13,12,16],11],[[5,4,4],5],[[5,3,20],7]] = [[20,5,4] = 4]


*/
data(squares,Data,Vars,Unknown,Ops,Constants,MaxC) :-
  Matrix =   [[13,5,5,20],
              [12,4,3,5],
              [16,4,20,4],
              [11,5,7,_]
              ],
  member(Representation,1..2),
  Ops = new_map([infix=["+","*","-"] ]),
  % Ops = new_map([infix=["+","*","-","mod"] ]),  
  Constants = [1,2,4,8,16,32],
  if Representation == 1 then
    nl,
    make_data_matrix(Matrix,Data,Unknown,Vars),
    MaxC = 10
  else
    nl,
    get_global_map().put("only_first_solution"),
    make_data_matrix(Matrix.transp,Data,Unknown,Vars),
    MaxC = 10
  end.