/*
  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-c3a3997e1304
  """
  Find the missing number?

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

      A
    B E C 
      D
  """

  Some different solutions:
  * A + E = C: E = 7
    5 + 3 = 8    9+5 = 14   =>  13 + _7_ = 20
 
  * A - B = E: E = 7 
    5 - 2 = 3    9-4 = 5   13 - 6 = 7 
   
  * D - E = C: E = 7
    11 - 3 = 8   19 - 5 = 14   27 - 7 = 20  

  And the differences between the As, Bs, Cs, Ds are also very consistent:
  As: differences are 4 
  Bs: differences are 2
  Cs: differences are 6
  Ds: differences are 8
  Es: assuming same differences:  5-3 = 2 => _7_ - 5 = 2. E is 7 again. 

  There are too many different approaches, so I'm suspicious...
  Are there some other approach?

  There are a huge number of solutions. Here are some with the initial max_size = 1:

  AllGood:
  [program = C - A,res = 7,count = 5840]
  [program = A - B,res = 7,count = 5821]
  [program = D - C,res = 7,count = 5803]
  [program = A - B + (C - C),res = 7,count = 449]
  [program = C - A + (C - C),res = 7,count = 307]
  [program = A - B + (D - D),res = 7,count = 167]
  [program = C - C + (A - B),res = 7,count = 20]
  [program = D - D + (A - B),res = 7,count = 7]
  [program = C - C + (C - A),res = 7,count = 6]
  [program = C - A - (C - C),res = 7,count = 5]
  [program = A - B - (C - C),res = 7,count = 4]
  [program = A - B - (D - D),res = 7,count = 2]
  [program = C - A + (D - D),res = 7,count = 2]
  [program = D - D - (C - D),res = 7,count = 1]
  [program = A - C - (A - D),res = 7,count = 1]
  [program = D + A - (B + D),res = 7,count = 1]

  resultMap = [7 = 16]

  With a larger value of MaxSize (e.g. 11) there are many more solutions.

*/
data(missing_number6,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-

  Data = [ [[5,2,8,11],3],
           [[9,4,14,19],5]
           % [[13,6,20,27],0] % Force another solution
          ],
  Ops = [+,-,*,pow2],
  Unknown = [13,6,20,27],
  Vars = "ABCD",  
  Constants = [], % No constants
  MaxSize = 1,
  Params = new_map([
                     init_size=1000,
                     num_gens=1000,
                     show_only_good=false
                   ]).