/*

  Triangles

  https://puzzles9.com/puzzles/number-sequence-puzzles-with-answers/
  """
  All three triangles are interconnected. Find the answer by deriving a relation between them.


        2           5             3
     4     7     5     9       1     2 
       6  1       11  ?          5  9


  Answer : 10
  Difference of numbers in first two pentagons is in third pentagon at same location.

  difference of
  2,5 = 3
  4,5 = 1
  7,9 = 2
  6,11 = 5
  1,10 = 9

  So, answer is 10.
  """

  * Here's the intended representation of the problem (representation 1) which 
    give the expected solutution (? = 10):
      2,3,5,
      4,1,5
      7,2,9
      6,5,11
      1,9,?
  
    maxCount = 1
    code = (A + B) = [[[2,3],5],[[4,1],5],[[7,2],9],[[6,5],11]] = [[1,9] = 10]
    code = (B + A) = [[[2,3],5],[[4,1],5],[[7,2],9],[[6,5],11]] = [[1,9] = 10]


  * Another representation (which is not the indended one), below called 
    representation 2 finds some alternatives solutions.

        A 
     B     C
       D E

    E is the unknown.

    The program finds a lot of different solutions:

    maxCount = 5
    code = ((1 + (A * A)) - B) = [[[2,4,7,6],1],[[3,1,2,5],9]] = [[5,5,9,11] = 21]
    maxCount = 6
    maxCount = 7
    code = (((D + (A * A)) - C) - A) = [[[2,4,7,6],1],[[3,1,2,5],9]] = [[5,5,9,11] = 22]
    code = (B + ((A * (D - C)) - 1)) = [[[2,4,7,6],1],[[3,1,2,5],9]] = [[5,5,9,11] = 14]
    code = (((A * (A + B)) - C) - B) = [[[2,4,7,6],1],[[3,1,2,5],9]] = [[5,5,9,11] = 36]
    code = (C + (1 + (C * (D - C)))) = [[[2,4,7,6],1],[[3,1,2,5],9]] = [[5,5,9,11] = 28]
    code = (1 + (B * ((A * A) - B))) = [[[2,4,7,6],1],[[3,1,2,5],9]] = [[5,5,9,11] = 101]

    Adding "**" as operator give some other solutions:
    code = ((C - D) ** C) = [[[2,4,7,6],1],[[3,1,2,5],9]] = [[5,5,9,11] = -512]


*/

data(triangles,Data,Vars,Unknown,Ops,Constants,MaxC) :-
  Matrix =   [[2,4,7,6,1],
              [3,1,2,5,9],
              [5,5,9,11,_]
              ],
  member(Representation,1..2),
  Ops = new_map([infix=["+","-","*"]
                ]),
  Constants = 1..1,
  if Representation == 1 then
    nl,
    make_data_matrix(Matrix.transp,Data,Unknown,Vars),
    % Data = [
    % [[2,3],5],
    % [[4,1],5],
    % [[7,2],9],
    % [[6,5],11]
    % ],
    % Unknown = [1,9],
    % Vars = ["A","B"],
    MaxC = 2
  else
    nl,
    make_data_matrix(Matrix,Data,Unknown,Vars),
    % Only show solutions with different values for
    % the unknown
    get_global_map().put("only_first_solution",true),
    % Data =  [
    %          [[2,4,7,6],1],
    %          [[3,1,2,5],9]
    % ],
    % Unknown = [5,5,9,11], 
    % Vars = ["A","B","C","D"],    
    MaxC = 8
  end.