In high school I played this game a lot with my friend Daniel, and we wrote down some of the more memorable puzzles that came up. All the ones I'm posting are from that collection, so I know they're all possible
Next puzzle:
351100, 75, 5, 8, 2, 9
(Pooty: I'm sure that's just a typo, should read 5 x 2 + 3, comes to (74 x 13) + 1 which is indeed 963.)