/*

  Remainder problem 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)
  """

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

*/

import cp.

main => go.

go =>
  writeln(findall(X,$remainder(X,10000))),nl.

go2 =>
  writeln(findall(X,$remainder2(X,10000))),nl.

remainder(X,Max) =>

   [X,A,B,C,D] :: 1..Max,

   X #= A*3 + 1,
   X #= B*4 + 2,
   X #= C*5 + 3,
   X #= D*6 + 4,

   solve([X,A,B,C,D]).


remainder2(X,Max) =>

   [X,A,B,C,D] :: 1..Max,

   foreach({I,K} in zip(1..4,[A,B,C,D])) 
     X #= K*(I+2) + I
   end,
   solve([X,A,B,C,D]).