int digital_root(int n) {
  int result;
  int tmp = n;
  do {
    result = sum_digits(tmp);
    tmp = result;
  } while (result >= 10);

  return result;
}

// returns the sum of all digits in n
int sum_digits(int n) {
  if (n / 10 == 0)
  {
    return n;
  }
  else
  {
    return n%10 + digital_root(n/10);
  }
}