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[Jimmmmm]

Now for something a bit different.

What is the minimum number of players required for one player to have 12 Provinces by the end of his second turn?

Assume perfect shuffle luck and cooperation by all players.

[hobo386]

I'm not going to hazard a guess at the optimal number of players, but I'm assuming this would require some mix of noble brigand and ambassador, while cards like nomad camp and masquerade would be great facilitators.

[jonts26]

One. Since no one else is around to stop you, just grab the stack of provinces.
Now I'll try to think of a solution that doesn't involve cheating.

[dondon151]

But there's only 8 Provinces in a solitaire game 

[Thisisnotasmile]

But no one else is around to stop you, so you can just get the other four out of the box.

[Titandrake]

Fairly sure this is not optimal, but it works. There may be some empty buys here (i.e. buys that do nothing, and are leftover from previous attempts to solve this).

1st turn

Player 1: Buys Noble Brigand. The rest now have 3 cards left to draw. Players discarded Copper + Estate, players 7-10 discarded 2 estates and gain a copper for it.
Player 2: Buys Embassy, players gain Silver -> Reshuffle, draw Embassy + Silver + Copper + 2 Estates.
Player 3: Buys Embassy, players gain Silver -> Reshuffle, draw Embassy + Silver + Copper + 2 Estates.
Player 4: Buys Masquerade. -> Reshuffle, draw Masquerade + 4 copper
Player 5: Buys Masquerade. -> Reshuffle, draw Masquerade + 4 copper
Player 6: Buys Masquerade. -> Reshuffle, draw Masquerade + 4 copper
Player 7: Buys Embassy -> Reshuffle, draws whatever.
Player 8: Buys Worker's Village. -> Reshuffle, draw Worker's Village + 4 Copper
Player 9: Buys Stables. -> Reshuffle, draw Stables + 3 Copper + Estate
Player 10: Buys Throne Room. -> Reshuffle, draw Throne Room + 4 Copper
Player 11: Buys Jester. ->Reshuffle, draw Jester + 2 copper + 2 estates

2nd turns
Player 1 has 0 cards left to draw and has not reshuffled.
Players 2,3,7 have 8 cards left to draw
Rest have 9 cards left

Player 1: Buys Pawn -> Reshuffle
Player 2: Play Embassy -> Draw 4 Copper, 1 Estate -> Discard 3 estates -> buy KC. After embassy, 3 cards left in draw. so when player 2 draws the next hand -> Reshuffle.
Player 3: Repeat what player 2 did -> buy KC -> Reshuffle
Player 4: Play Masquerade.

8 passes Worker's Village to 9. 9 passes Stables to 10. 10 passes Throne Room to 11. 11 passes an estate to 1. Don't care what the others pass, so let's just say they passed coppers to each other.

Buy Bridge. 2 cards left to draw before the reshuffle after drawing a new hand.

Players 5, 6: Repeat what player 4 did -> buy Bridge

9 passes Worker's to 10, 10 passes Stables to 11, 11 passes estate to 1. Rest pass coppers.
9 passes Estate to 10, 10 passes Worker's to 11, 11 passes Copper to 1. Rest pass coppers.

Player 7: Buys Noble Brigand.
Player 8: Buys Noble Brigand. Players 4,5,6 reshuffle.
Player 9: Buys Noble Brigand. Player 7 reshuffles.
Player 10: Buys Noble Brigand. This totals to discarding 8 cards for player 11, so that player currently has 1 card left to draw and will reshuffle as soon as he/she needs to draw a 2nd card.

Player 11: Play Worker's Village
Play Jester.
Player 1 discards Pawn
Player 2 discards KC
Player 3 discards KC
Player 4 discards Bridge
Player 5 discards Bridge
Player 6 discards Bridge
Players 7-10 discard whatever, and player 11 makes them gain the card instead.

Play TR-Stables. Discard Copper -> Reshuffle -> Draw Pawn, KC, Copper.
2nd Stables -> Draw KC, Bridge, Bridge.
Play Pawn for 1 card, 1 buy. Draw Bridge.
With last action, play KC-KC-Bridge-Bridge-Bridge. Have 12 buys, Provinces cost $0. Buy the 12 Provinces.

[Jimmmmm]

Well done! It's much better (also more complicated) than my solution - exactly what I wanted!
Jester was a great idea that I didn't thought of.

Slight nitpick: Player 2 doesn't have a Silver to draw for his second turn, although it works fine if that Silver is a Copper.

Other than that, good work!

[Titandrake]

Out of curiosity, what was your solution?

Also, on second review, I'm not sure how to optimize my solution, so 11 players might actually be optimal. The only place there might be is in a different starting combo for player 11 that requires less Noble Brigands to cause a reshuffle. Otherwise, every buy from each player is useful. I'm a bit surprised it fit so perfectly.

[Jimmmmm]

Player 1   Buy Noble Brigand
Player 2   Buy Masquerade
Player 3   Buy Masquerade
Player 4   Buy Throne Room
Player 5   Buy Council Room   
Player 6   Buy Masquerade      
Player 7   Buy Ambassador      
Player 8   Buy Council Room   
Player 9   Buy Council Room   
Player 10   Buy Masquerade      
Player 11   Buy Bridge      
Player 12   Buy Bridge      
Player 13   Buy Bridge      
Player 14   Buy Bridge

All players 2-14 shuffle and have their opening buy in hand.

Player 1   -
Player 2   Play Masquerade
Player 3   Play Masquerade; Buy Noble Brigand
Player 4   Buy Noble Brigand
Player 5   Play Council Room; Buy King's Court; Shuffle and draw the King's Court
Player 6   Play Player 4's Throne Room -> Masquerade
Player 7   Play Ambassador -> Player 5's King's Court
Player 8   Play Council Room
Player 9   Play Council Room

After their first turn, players 10-14 each had 6 cards in their draw piles.
After two Noble Brigands were bought, they had 2 in their draw piles.
After three Council Rooms were played, they shuffled their new King's Courts into their draw piles and all drew them.

Player 10   Play King's Court -> Masquerade
Player 11   -
Player 12   -
Player 13   -

Player 14 now has an 8-card hand, which includes 4 Bridges, three of which came from players 11-13, and 3 King's Courts, two of which came from Players 12 and 13.

Player 14   Play King's Court -> King's Court -> King's Court -> Bridge + Bridge + Bridge + Bridge; Buy 12 Provinces

I quite enjoyed coming up with this, but I was certainly hoping and expecting someone to beat it.

[Titandrake]

Slight edit/improvement to my solution:

Edit: Nvm, the improvement didn't work.