14. Laboratory + King's Court/Workshop
My first thought was that there were no cards available for Workshop to gain. But that would mean Coppers, Silvers, Estates, Curses, and Workshops were gone, at which point the game would be long over. Then I figured this had to be an attack card, like Thief or Jester, as I saw no other way to gain three cards. But then I remembered the "You may..." clause on King's Court. The Workshop is only played once. Ironworks, gaining an Estate, should do the trick. Another excellent puzzle.15. Laboratory + Hamlet + Bazaar + Black Market + Ironworks
You posted a retraction of this puzzle, but I'd already worked it out far enough to suspect something was wrong. If my idea was what you were going for, you can fix the puzzle merely by adding Peddler.
If adding Peddler does NOT fix it, then DON'T READ WHAT I WROTE BELOW. Instead, consider this a new puzzle for you:
Laboratory + Peddler + Hamlet + Bazaar + Black Market + Ironworks = ?
In any case, here is my thought process on the original puzzle (which didn't have Peddler). I typed it as I was working out, so it's an accurate reflection of the approach I took:
No treasures are played with the Black Market, so that's a clue. Since no other card can buy stuff from the Black Market, nothing could have been purchased unless "Black Market" is the answer. But it can't be, because Bazaar and Ironworks produce other effects that Black Market alone can't replicate. So, to make a short story long, the Black Market is only there for the +$2 coins. Add in Laboratory and Bazaar, and we have 5 cards in hand, 1 action, and +$3. This is starting to smell like Horse Traders, but it's not, because it won't gain a card like Ironworks does. So what provides at least +$3 and gains a card costing up to 4? Baron! With that hypothesis in mind, we can now work backwards from it. Ironworks gains the Estate; since Estate is a victory card, we draw a card. So we're still at a 5 card hand, and have 0 actions. We still need to get rid of a card, and we're short a buy and a coin. That tells us how we should play Hamlet. Discard a single card, not for the action but for the buy. Now everything is right, except we're only up $3, whereas Baron supplies $4. Close, but no cigar. Dare I hope that there's an error in the question? If not, and Baron isn't correct, then a new puzzle with the same cards plus Peddler would be a good one.