/* 

  Remainder puzzle (Kordemsky) in Picat.

  """
  11.  Is there a number which when divided by 3 gives a remainder of 1;
  when divided by 4, gives a remainder of 2; when divided by 5, gives a
  remainder of 3; and when divided by 6, gives a remainder of 4?
  (Kordemsky)
  """

  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 ?=>

  puzzle(5),
  fail,
  nl.

go => true.

go2 ?=>

  puzzle2,
  fail,
  nl.

go2 => true.


puzzle(N) =>  
  N = 5,
  X = new_list(N),
  
  X[1] #> 0,
  foreach(I in 2..N)
    X[1] #= X[I]*(I+1) + I-1
  end,

  solve([ff], X),

  println(X),
  println(x1=X[1]),
  
  nl.


% another approach
puzzle2 =>  
  X = new_list(4),
  N = new_dvar(),

  N #> 0,  
  -3*X[1] + N #= 1,
  -4*X[2] + N #= 2,
  -5*X[3] + N #= 3,
  -6*X[4] + N #= 4,

  solve([ff], X++[N]),

  println(x=X),
  println(n=N),
  
  nl.