/*
  https://puzzles9.com/puzzles/number-sequence-puzzles-with-answers/
  Puz253
  """
      5  _  4        7  _  1
      _  2  _        _  5  _
     11  _  4       13  _  3

          ??  _  4
          _   4  _
         20   _  4 

  """

  Encoded as 
      E  _   A
      _  B   _ 
      C _    D

  * Representation 1:

    All these solutions are probably not correct since all values are not used: 

    [program = B - 1 + (D + (1 - 1)),res = 7,count = 9]
    [program = B - 1 + D,res = 7,count = 8]
    [program = D - (1 - B),res = 7,count = 7]
    [program = B - (1 - D),res = 7,count = 7]
    [program = D - 1 + B,res = 7,count = 7]
    [program = B - 1 * 1 + D,res = 7,count = 7]
    [program = B + (D - 1),res = 7,count = 7]
    [program = 1 + D - (1 + (1 - B)),res = 7,count = 6]
    [program = 1 * (B + D - 1),res = 7,count = 6]
    [program = 1 * D + (B - 1 * 1),res = 7,count = 5]
    [program = B + D - 1,res = 7,count = 4]
    [program = B + (D - 1 * 1),res = 7,count = 4]
    [program = D * 1 + B - 1,res = 7,count = 3]
    [program = (B + D - 1) * 1,res = 7,count = 3]
    [program = 1 * 1 * 1 * (B + D - 1),res = 7,count = 3]
    [program = (1 - 1) * 1 + (B + D - 1),res = 7,count = 2]
    [program = C - B - A,res = 12,count = 1]
    [program = C - A - 1 * B,res = 12,count = 1]
    [program = D + B * 1 - 1,res = 7,count = 1]
    [program = D + B - 1,res = 7,count = 1]
    [program = (B + D) * 1 - 1,res = 7,count = 1]

    resultMap = [7 = 19,12 = 2]

    Another run, adding to_num2/2 and to_num3/3:
    [program = D + (B - 1),res = 7,count = 29]
    [program = B + (D - 1),res = 7,count = 26]
    [program = D - to_num3(1,1,1) + to_num3(1,1 * 1,B),res = 7,count = 23]
    [program = B + (D * 1 - 1),res = 7,count = 22]
    [program = D - 1 + 1 * B,res = 7,count = 21]
    [program = D - 1 + B,res = 7,count = 13]
    [program = C - (B + A),res = 12,count = 11]
    [program = B - (1 - D),res = 7,count = 9]
    [program = B / 1 + (D * 1 - 1),res = 7.0,count = 6]
    [program = 1 + B / 1 + (D - 1 - 1),res = 7.0,count = 6]
    [program = D - 1 + B * 1,res = 7,count = 5]
    [program = B + D - 1,res = 7,count = 1]
    [program = D - (1 - 1 * B),res = 7,count = 1]

    resultMap = [7 = 10,7.0 = 2,12 = 1]


  * Representation 2 (transposed data matrix)
    No solution.

  The intended solution:
  """
  Answer  :   12
  In each box, sum of numbers in first column divided by sum of numbers in third column 
  gives middle number in second column.

  (5+11)   ÷   (4+4)   =  2
  (7+13)   ÷   (1+3)   =  5
  (20+12)  ÷   (4+4)   =  4

  So, answer is 12.
  """

*/
data(puz253,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  Matrix = [
            [4,2,11,4,5],
            [1,5,13,3,7],
            [4,4,20,4,_]
          ],
  Ops = [+,-,*,/,to_num2,to_num3],
  Constants = [1], % ++ [random(-10,10) : _ in 1..10],
  make_data_matrix(Matrix,Data,Unknown,Vars),
  % make_data_matrix(Matrix.transp,Data,Unknown,Vars),
  MaxSize = 21,
  Params = new_map([num_gens=30]).