There's a 10-digit number, ABCDEFGHIJ, whose digits are all different, and that has an interesting property: if you take the first N digits from left to right, the resulting number is exactly divisible by N. What's the number? To clarify: A is divisible by 1, AB is divisible by 2, ABC is divisible by 3, etc., up to ABCDEFGHIJ that is divisible b…

[Puzzle] Find the number.java

  @Test
  public void findNumber() {
    int[] CD = new int[]{12,16,24,28,32,36,48,64,68,72,76,84,92,96};
    int[] B = new int[]{2,4,6,8};
    int[] F = new int[]{2,4,6,8};
    int[] FGH = new int[]{216, 248, 264, 296, 416, 432, 472, 496, 624, 632, 648, 672, 816, 824, 832, 864, 872, 896};

    int[] valid = new int[]{1,2,3,4,6,7,8,9};

    validate(CD, B, F, FGH, valid);
  }

  private void validate(int[] CD, int[] B, int[] F, int[] FGH, int[] valid) {
    for(int i=0; i < FGH.length; i++) {
      int fgh = FGH[i];
      int[] CDExtracted = extract(fgh, CD);

      for (int j=0; j < CDExtracted.length; j++) {
        String n = fgh + "" + CDExtracted[j];
        int[] BExtracted = extract(Integer.valueOf(n), B);
        for (int k=0; k < BExtracted.length; k++) {
          String l = n + "" + BExtracted[k];
          int[] validExtracted = extract(Integer.valueOf(l), valid);
          
          int preNumber = validExtracted[0];
          int lastNumber = validExtracted[1];

          String number = "" + preNumber + BExtracted[k] + CDExtracted[j] + "5" + fgh + lastNumber + "0";
          if (isValidNumber(number)) {
            System.out.println(number);
          }
        }
      }

    }
  }

  private int[] extract(int fgh, int[] cd) {
    String _fgh = fgh + "";
    List<Integer> result = new ArrayList<>();
    for(int i=0; i < cd.length; i++) {
      boolean exists = false;
      String n = cd[i] + "";
      for (int j=0; j < _fgh.length(); j++) {
        if (n.contains(_fgh.charAt(j) + "")) {
          exists = true;
        }
      }
      if (!exists) {
        result.add(cd[i]);
      }
    }
    return result.stream().mapToInt(i->i).toArray();
  }

  private boolean isValidNumber(String number) {
    boolean result = true;
    String n = "";
    for (int i=1; i <= number.length(); i++) {
      n += "" + number.charAt(i - 1);
      long division = Long.valueOf(n) % i;
      if (division != 0) {
        result = false;
      }
    }
    return result;
  }

3816547290

The number has the format ABCD5FGHI0