1. How many numbers are there, starting with and going through no duplicate digits
  2. How many of these numbers contain the digit
  3. How many numbers have their digits add up to For example: the digits in 783 add up to 18: 7 + 8 + 3 = 18
  4. How many different Sums of Digits are there?
  5. How many different Numbers add up to each of them?