code: public class LogicPuzzle
  {
      boolean S[] = new boolean[13];
      int Count = 0;
  
      public boolean check2 ()
      {
          int count = 0;
          for (int k = 7; k <= 12; k++)
              if (S[k]) count++;
          return S[2] == (count == 3);
      }
  
      public boolean check3 ()
      {
          int count = 0;
          for (int k = 2; k <= 12; k += 2)
              if (S[k]) count++;
          return S[3] == (count == 2);
      }
  
      public boolean check4 ()
      {
          return S[4] == ( !S[5] || S[6] && S[7]);
      }
  
      public boolean check5 ()
      {
          return S[5] == ( !S[2] && !S[3] && !S[4]);
      }
  
      public boolean check6 ()
      {
          int count = 0;
          for (int k = 1; k <= 11; k += 2)
              if (S[k]) count++;
          return S[6] == (count == 4);
      }
  
      public boolean check7 ()
      {
          return S[7] == ((S[2] || S[3]) && !(S[2] && S[3]));
      }
  
      public boolean check8 ()
      {
          return S[8] == ( !S[7] || S[5] && S[6]);
      }
  
      public boolean check9 ()
      {
          int count = 0;
          for (int k = 1; k <= 6; k++)
              if (S[k]) count++;
          return S[9] == (count == 3);
      }
  
      public boolean check10 ()
      {
          return S[10] == (S[11] && S[12]);
      }
  
      public boolean check11 ()
      {
          int count = 0;
          for (int k = 7; k <= 9; k++)
              if (S[k]) count++;
          return S[11] == (count == 1);
      }
  
      public boolean check12 ()
      {
          int count = 0;
          for (int k = 1; k <= 11; k++)
              if (S[k]) count++;
          return S[12] == (count == 4);
      }
  
      public void check ()
      {
          if (check2() && check3() && check4() && check5() && check6()
              && check7() && check8() && check9() && check10() && check11()
              && check12())
          {
              for (int k = 1; k <= 12; k++)
                  if (S[k]) System.out.print(k + " ");
              System.out.println();
              Count++;
          }
      }
  
      public void recurseAll (int k)
      {
          if (k == 13)
              check();
          else
          {
              S[k] = false;
              recurseAll(k + 1);
              S[k] = true;
              recurseAll(k + 1);
          }
      }
  
      public static void main (String args[])
      {
          LogicPuzzle P = new LogicPuzzle();
          P.S[1] = true;
          P.recurseAll(2);
          System.out.println();
          System.out.println(P.Count + " Solutions found.");
      }
  }
  