/*
  
  Curious set of integers problem in ECLiPSe..
  
  Martin Gardner (February 1967):
  """
  The integers 1,4,9, and 120 form a set with a remarkable priperty:
  the product of any two integers is one less than a perfect square. 
  Find a fifth number that can be added to the set without destroying 
  this property.
  """
  
  Solution: The number is 0.
 
  There are however other sets of five numbers with this property.
  Here are the one in the range of 0.10000:
  [0, 1, 3, 8, 120]
  [0, 1, 3, 120, 1680]
  [0, 1, 8, 15, 528]
  [0, 1, 8, 120, 4095]
  [0, 1, 15, 24, 1520]
  [0, 1, 24, 35, 3480]
  [0, 1, 35, 48, 6888]
  [0, 2, 4, 12, 420]
  [0, 2, 12, 24, 2380]
  [0, 2, 24, 40, 7812]
  [0, 3, 5, 16, 1008]
  [0, 3, 8, 21, 2080]
  [0, 3, 16, 33, 6440]
  [0, 4, 6, 20, 1980]
  [0, 4, 12, 30, 5852]
  [0, 5, 7, 24, 3432]
  [0, 6, 8, 28, 5460]
  [0, 7, 9, 32, 8160]

  Compare with the MiniZinc: 
  http://www.hakank.org/minizinc/curious_set_of_integers.mzn


  Model created by Hakan Kjellerstrand, hakank@bonetmail.com
  See also my ECLiPSe page: http://www.hakank.org/eclipse/

*/

:-lib(ic).
:-lib(ic_global).
:-lib(ic_search).


go :-
        N = 5, 
        dim(X, [N]),
        X :: 0..10000,

        ic_global:alldifferent(X),
        ordered(<, X),

        (multifor([I,J],1,N), param(X) do
             I\=J ->
             P :: 0..1000,
             P*P-1 #= (X[I]*X[J])
        ; 
             true
        ),

        search(X,0, occurrence, indomain_min, complete, []),
        writeln(X), fail.