/*
  From  
  Muhammad Zain "Sarwar: People With an IQ of 120+ Can Solve This Missing Number Puzzle"
  https://medium.com/puzzle-sphere/people-with-an-iq-of-120-can-solve-this-missing-number-puzzle-b6a6bbbc2dc9
  """
  Find missing number!

        5       9        13
      2 3 8   4 5 14   6  ?  20
       11      19        27
  """
   Representation
       A 
     B E C
       D

    Manual solutions:

    1)                E  =  A - B
       First figure : 3  =  5 - 2
       Second figure: 5  =  9 - 4
       Third  figre : ?  = 13 - 6 = 7

    2)                E  =  C - A
       First figure : 3  =  8 - 5
       Second figure: 5  = 14 - 9
       Third  figre : ?  = 20 - 13 = 7

    3)                E  =  D - C
       First figure : 3  = 11 - 8
       Second figure: 5  = 19 - 14
       Third  figre : ?  = 27 - 20 = 7

    4)                 E  =  B + 1
       First figure : 3  = 2 + 1
       Second figure: 5  = 4 + 1
       Third  figre : ?  = 6 + 1 = 7


  
   Only + and - (with num_gens=10):

   AllGood:
   [program = A - B, res = 7, count = 35, rank = 5]
   [program = C - A, res = 7, count = 30, rank = 5]
   [program = D - C, res = 7, count = 38, rank = 5]
   [program = C + (C - (B + D)), res = 7, count = 2, rank = 13]
   [program = C + (C - (D + B)), res = 7, count = 3, rank = 13]
   [program = C + (D - (A + D)), res = 7, count = 1, rank = 13]
   [program = C - B + (A - C), res = 7, count = 1, rank = 13]
   [program = D - A + (A - C), res = 7, count = 2, rank = 13]
   [program = A - (A + (C - D)), res = 7, count = 1, rank = 13]
   [program = A - (B - (B - B)), res = 7, count = 1, rank = 13]
   [program = C - (C + (B - A)), res = 7, count = 2, rank = 13]
   [program = C - (A - A + A), res = 7, count = 2, rank = 13]
   [program = C - (B + D - C), res = 7, count = 3, rank = 13]
   [program = C + C - (D + B), res = 7, count = 1, rank = 13]
   [program = C + (B - A) - B, res = 7, count = 5, rank = 13]
   [program = C + (D - D) - A, res = 7, count = 1, rank = 13]
   [program = A - A - (A - C), res = 7, count = 2, rank = 13]
   [program = B - B - (A - C), res = 7, count = 1, rank = 13]
   [program = D - B - (D - A), res = 7, count = 1, rank = 13]

   With +, -, / (num_gens=10):
   AllGood:
   [program = A - B, res = 7, count = 27, rank = 5]
   [program = C - A, res = 7, count = 19, rank = 5]
   [program = D - C, res = 7, count = 16, rank = 5]
   [program = A / A + B, res = 7.00000000000000000, count = 7, rank = 10]
   [program = A - (D + B - D), res = 7, count = 1, rank = 13]

   I.e. B + 1

*/
data(missing_number12,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  Data = [[[5,2,8,11],3],
          [[9,4,14,19],5]
          ],
  % Ops = [+,-,*,/],
  Ops = [+,-],
  Constants = [], % No other values
  Vars = ['A','B','C','D'],
  Unknown = [13,6,20,27],  
  MaxSize = 11,
  Params = new_map([init_size=1000,
                    num_gens=10,
                    sort_by_rank=true
                    % , unique_vars=true
                   ]).  


/*
  Are there cross figure solutions?

  Representation   

        A       B        C
        5       9        13
      2 3 8   4 5 14   6  ?  20
       11      19        27

    C = 2 * B - A

    13 =  9*2 -  5
     6 =  4*2 -  2
    20 = 14*2 -  8
    27 = 19*2 - 11
     ? =  5*2 -  3 = 7


  AllGood:
  [program = B + (B - A), res = 7, count = 9, rank = 9]
  [program = B - A + B, res = 7, count = 9, rank = 9]
  [program = B * 2 - A, res = 7, count = 4, rank = 11]
  [program = B - (A - 1 * B), res = 7, count = 2, rank = 15]
  [program = B - (B + (A - (B + B))), res = 7, count = 8, rank = 17]
  [program = B * 2 - A / 1, res = 7.00000000000000000, count = 3, rank = 17]
  [program = 2 * B - (1 + A) + 1, res = 7, count = 7, rank = 21]

  resultMap = [7 = 6,7.00000000000000000 = 1]

*/
/*
data(missing_number12,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  Data = [[[5,9],13],
          [[2,4],6],
          [[8,14],20],
          [[11,19],27]
          ],
  Ops = [+,-,*,/],
  % Ops = [+,-],
  Constants = 1..2,
  Vars = ['A','B'],
  Unknown = [3,5],  
  MaxSize = 11,
  Params = new_map([init_size=1000,
                    num_gens=10,
                    sort_by_rank=true
                    % , unique_vars=true
                   ]).  
*/