Ok, let's try a new version of the same puzzle.
You have 5 cards in hand, no cards in play, set aside, or on the Tavern mat, no accumulated money (or actions or buys other than the one you started your turn with). You may specify the kingdom, your hand, and the contents and order of your draw deck and discard pile. No Empires stuff, though. You play a card. When that card finishes resolving, you have at least 10 cards in hand.
How many possibilities are there for that card?
Hard mode: how many of those do not require Adventures tokens already placed and are independent on the order and/or contents or your draw deck or discard pile?
I make it 30; hard mode: 15 but I wouldn't be surprised if I've missed one or two.