Puzzle – quick sum extension

Using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 exactly once each, the sum of any list of 1- and 2- digit numbers we create will be a multiple of 9. Several commenters demonstrated this convincingly here.

“Pseudonym” (probably not his real name), suggested several extensions, and I added a few of my own:

1. What are the maximum and minimum sums, using only 1- and 2- digit numbers?
2. Can every multiple of 9 between those 2 numbers be created?
3. If we waive the limit on the number of digits in each addend, verify that all possible sums are still multiples of 9.
4. Now, having waived the limits on the number of digits, what are the maximum and minimum sums?
5. How many of the multiples of 9 between that max and that min can be created?
6. Can we play the same set of games in base n, using the digits 0, 1, 2, … , n-2, n-1 ? Eg, in base 6, using the digits 0 through 5, can we make a list of one and two digit numbers that add to 100 (base 6) ?

Submit comments by clicking “comments,” above, but if you want to submit answers, click right here –> “Answers.”