//
// Maths challenge 2004-2005 J5
// 
//
// My bank card has a 4 digit pin, abcd. I use the following facts to help me
// remember it:
//
// - no two digits are the same
// - the 2-digit number cd is 3 times the 2-digit number ab
// - the 2-digit number da is 2 times the 2-digit number bc
//
// What are the values of a, b, c, and d?
//
import org.chocosolver.solver.Model;
import org.chocosolver.solver.Solver;
import org.chocosolver.solver.variables.IntVar;
import org.chocosolver.solver.constraints.IIntConstraintFactory.*;
import org.chocosolver.solver.search.strategy.Search;
import org.chocosolver.solver.exception.ContradictionException;

public class MathChallenge {

  
  public static void main(String[] args) throws ContradictionException {

      Model model   = new Model("maths challenge");
      Solver solver = model.getSolver();
      
      IntVar a = model.intVar("a",0,9);
      IntVar b = model.intVar("b",0,9);
      IntVar c = model.intVar("c",0,9);
      IntVar d = model.intVar("d",0,9);

      model.allDifferent(new IntVar[]{a,b,c,d}).post();

      IntVar ab = model.intVar("ab",0,99);
      IntVar bc = model.intVar("bc",0,99);
      IntVar cd = model.intVar("cd",0,99);
      IntVar da = model.intVar("da",0,99);

      // ab = 10.a + b
      IntVar a10 = model.intVar("10*a",new int[]{0,10,20,30,40,50,60,70,80,90});
      model.arithm(a10,"=",a,"*",10);
      model.arithm(ab,"=",a10,"+",b).post();

      // bc = 10.b + c
      IntVar b10 = model.intVar("10*b",new int[]{0,10,20,30,40,50,60,70,80,90});
      model.arithm(b10,"=",b,"*",10);
      model.arithm(bc,"=",b10,"+",c).post();

      // cd = 10.c + d
      IntVar c10 = model.intVar("10*c",new int[]{0,10,20,30,40,50,60,70,80,90});
      model.arithm(c10,"=",c,"*",10);
      model.arithm(cd,"=",c10,"+",b).post();

      // da = 10.d + a
      IntVar d10 = model.intVar("10*d",new int[]{0,10,20,30,40,50,60,70,80,90});
      model.arithm(d10,"=",d,"*",10);
      model.arithm(da,"=",d10,"+",a).post();

      // cd = 3.ab
      model.arithm(cd,"=",ab,"*",3).post(); // cd = 3*ab

      // da = 2.cd
      model.arithm(da,"=",bc,"*",2).post(); // da = 2*bc

      //solver.propagate(); // does this solve the problem

      System.out.println(a);
      System.out.println(b);
      System.out.println(c);
      System.out.println(d);
      System.out.println(ab);
      System.out.println(bc);
      System.out.println(cd);
      System.out.println(da);

      
      System.out.println("there is a solution: "+ solver.solve());

      System.out.println(a);
      System.out.println(b);
      System.out.println(c);
      System.out.println(d);
      
  }
}

//
// (unique) solution should be that abcd = 2163
//
// (1) How do I know it is a unique solution?
// (2) How much search effort was involved?
// (3) Have we yet looked at propagate? i.e. is propagate enough?
// (4) Can we make this all a bit simpler? Or is this just java?
//     - see two other versions produced by Charles 
//