/*

  From https://www.themathdoctors.org/pattern-and-sequence-puzzles/
  """
  How do I figure out the next 2 numbers in the pattern 1, 8, 27, 64, ____, ____?
  ""

  * Just +,-,*,/:"
    [program = A * (A * A),res = 125,count = 11]
    [program = A * A * A,res = 125,count = 10]
    [program = A / 1 * (A * A) * (3 - 2),res = 125.0,count = 8]
    [program = A / 1 * (A * A) * 1,res = 125.0,count = 4]
    [program = A * (A * A) + (3 - 3) * 2,res = 125,count = 3]
    [program = A * (A * A) / 1,res = 125.0,count = 1]
    [program = (A * 2 - A) * (A * A),res = 125,count = 1]
    [program = A * A * 1 * (1 * A),res = 125,count = 1]
    [program = A * A * (A * 1),res = 125,count = 1]
    [program = 1 * 1 * (A / 1 * (A * A)),res = 125.0,count = 1]

    resultMap = [125 = 6,125.0 = 4]

  * Using ** (which blows up after a while):
    [found_function = A ** 3,check = 125]
    [found_function = A * A ** 2,check = 125]

  * Also pow2 and pow3 (no **)
    [program = pow3(A),res = 125,count = 230]
    [program = pow2(A) * A,res = 125,count = 9]
    [program = A * pow2(A),res = 125,count = 8]
    [program = 1 * pow3(A),res = 125,count = 6]
    [program = pow3(A) * 1,res = 125,count = 5]
    [program = A * (A * A),res = 125,count = 4]
    [program = pow3(pow2(A) / A),res = 125.0,count = 4]
    [program = 1 * A * A * A,res = 125,count = 3]
    ...

*/
data(puzzle4,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  Seq = [1, 8, 27, 64],
  Ops = [+,-,*],
  % Ops = [+,-,*,/,**],    
  % Ops = [+,-,*,/,pow2,pow3],
  Constants = 1..3,
  MaxSize = 5,
  make_point_seq(Seq,Data,Unknown,Vars),
  % make_seq(Seq,1,Data,Unknown,Vars),
  % make_seq(Seq,2,Data,Unknown,Vars),
  Params = new_map().