//
// 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

import choco.Problem;
import choco.ContradictionException;
import choco.integer.*;
import choco.Solver;
import choco.Solution;

public class MathChallenge {

  
  public static void main(String[] args) {
     Problem pb = new Problem();

     IntDomainVar a  = pb.makeEnumIntVar("a",0,9);
     IntDomainVar b  = pb.makeEnumIntVar("b",0,9);
     IntDomainVar c  = pb.makeEnumIntVar("c",0,9);
     IntDomainVar d  = pb.makeEnumIntVar("d",0,9);
 
     pb.post(pb.allDifferent(new IntVar[]{a,b,c,d}));

     IntDomainVar ab = pb.makeEnumIntVar("ab",0,99);
     IntDomainVar bc = pb.makeEnumIntVar("bc",0,99);
     IntDomainVar cd = pb.makeEnumIntVar("cd",0,99);
     IntDomainVar da = pb.makeEnumIntVar("da",0,99);

     pb.post(pb.eq(ab,pb.plus(pb.mult(10,a),b)));
     pb.post(pb.eq(bc,pb.plus(pb.mult(10,b),c)));
     pb.post(pb.eq(cd,pb.plus(pb.mult(10,c),d)));
     pb.post(pb.eq(da,pb.plus(pb.mult(10,d),a)));

     pb.post(pb.eq(pb.mult(3,ab),cd));     // 3.ab = cd
     pb.post(pb.eq(pb.mult(2,bc),da));     // 2.bc = da

     
     Solver s = pb.getSolver();
     pb.solve(true);
     System.out.println("feasible: " + pb.isFeasible());
     System.out.println("nbSol: " + s.getNbSolutions());
    
     /*
     pb.solve(false); // first solution
     System.out.println(pb.pretty());
     */

  }
}

//
// (unique) solution should be that abcd = 2163
//