Larry has made several observations that are correct:
1) There are exactly 8 combinations of three numbers 1-9 that add up to 15, which Larry listed.
2) Any combination that adds to 15 has either 1 or 3 odd numbers.
3) It seems like going first would be advantageous -- and it is if the players are not skilled at this game.
4) Test cases ended up with a draw if the players both followed their best strategy.
#4 turns out to be true in general, not just the test cases Larry tried. The remaining challenge (part 2) is to give a demonstration that is closer to a proof than test cases.