This is going to be a more informal challenge; because I don't plan on doing a bunch and tracking points, etc. But hopefully people will still be interested in trying it out because it sounds like fun (to me at least.
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1. End the game with 8 Provinces in your deck.
2. After turns 1 and 2, you may not play a Treasure card.
3. You must not have any Treasure in your deck at the end of the game.
Do this in as few turns as possible.
And since I just now realized that all the solutions for "No Buys Allowed" work here as well, we'll go ahead and throw on one more stipulation:
4. You cannot gain any cards other than by buying them.
Feel free to post your answers and thoughts here, since this is an informal puzzle.