/* 

  Hardy's 1729 problem in Picat.

  From Hardy "A Mathematician's Apology"
  """
  I had ridden in taxi cab 1729 and remarked that the number seemed to
  be rather a dull one. I hoped it was not an unfavorable omen.
  "No", he replied, "it is a very integresting number: it is the smallest
  number expressed as the sum of two cubes in two different ways.
  """
  

  Solution:
   X1:  1
   X2: 12
   Y1:  9
   Y2: 10
    Z: 1729 


  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.


main => go.

go ?=>
  L = [X1,X2,Y1,Y2,Z],
  L :: 0..10000,
  
  X1 #<= X2, Y1 #<= Y2,  % symmetry breaking
  X1 #!= Y1, X1 #!= Y2,
  X1*X1*X1 + X2*X2*X2 #= Z,
  Y1*Y1*Y1 + Y2*Y2*Y2 #= Z,

  % symmetry breaking
  X1 #<= Y1,

  solve($[inout],L),
  println(L),
  fail,

  nl.

go => true.