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[pitythefool]

At the start of my turn, I have no cards and my opponent has 10 cards. At the end of the turn, I have 10 cards and my opponent has no cards. What happened?

One can assume that before trashing your deck, you have managed to accumulate many coin tokens.
So by using Traveling Fair, buy two King's Courts, a Thief, a (1st edition) Masquerade, and Mission.
Play KC-KC-Thief-Masquerade.
Opponent has all 10 Scepters; five in hand, five in deck.
The Thief trashes 3 Scepters and gains them.
The Masquerade draws the Scepters and exchanges them with the opponent, without trashing any.
Now play two Scepters to replay the Thief twice and trash the rest of the opponent's deck.  Do not gain the Scepters.
Play the remaining Scepter to replay the Masquerade.  Receive a Scepter from the opponent.  Repeat four times.
Buy Bonfire to trash two cards and you're left with ten cards.

The drawback is that this does not work with 2nd edition rules for Masquerade.  But there are many variations that can be substituted.
KC-KC-Thief-Torturer.  Torturer will draw the first three Scepters and force the opponent to discard his hand.  Replay Thief and Torturer as needed to gain/draw the remaining Scepters.

I particularly like a variant that forces him to trash all of his Scepters, then you play a Treasurer which can gain one to your hand.  Rinse and repeat.

[crj]

I'd argue that things you do during a Mission turn don't happen before the end of "the" turn, and therefore don't satisfy the challenge.

[pitythefool]

I'd argue that things you do during a Mission turn don't happen before the end of "the" turn, and therefore don't satisfy the challenge.

Fair enough.  I'll do it in the first turn.
Setup:  purchase Innovation, accrue many coin tokens, trash all of your deck (perhaps Donate).
Turn:  Buy many Travelling Fairs for extra buys.  Buy a Sculptor, play it with Innovation, gain a Watchtower to your hand.
Still in buy phase:  Buy 2 King's Courts, a Thief, a Torturer.  Buy two Cultists, use the Watchtower to trash them thus drawing your deck.
Buy a Villa, return to action phase.
Proceed as before:  KC-KC-Thief-Torturer, gaining and using opponent's Scepters.

[majiponi]

A new puzzle.

Create a kingdom where you can play an Action card any number of times in a single Buy phase.

[hhelibebcnofnena]

A new puzzle.

Create a kingdom where you can play an Action card any number of times in a single Buy phase.

Scepter, Captain, Quarry.
Play Captain in Action phase. Buy phase: play Quarry, play Scepter, replaying Captain. Captain now costs $4, so you can play Captain with Captain recursively.

[majiponi]

A new puzzle.

Create a kingdom where you can play an Action card any number of times in a single Buy phase.

Scepter, Captain, Quarry.
Play Captain in Action phase. Buy phase: play Quarry, play Scepter, replaying Captain. Captain now costs $4, so you can play Captain with Captain recursively.

No. Captain cannot play a Duration card.

[hhelibebcnofnena]

A new puzzle.

Create a kingdom where you can play an Action card any number of times in a single Buy phase.

Scepter, Captain, Quarry.
Play Captain in Action phase. Buy phase: play Quarry, play Scepter, replaying Captain. Captain now costs $4, so you can play Captain with Captain recursively.

No. Captain cannot play a Duration card.

Ah, right. Okay, then:
Scepter, Captain, Quarry, Inheritance
Slight change to the first answer. Play Quarry on some setup turn to allow Inheriting Captains. Then, later, play Scepter to play Captain or Estate. Each Estate plays a Captain, which plays an Estate.

I think someone else came up with this idea on a different thread (probably the Rules Tweaks/Errata thread), but I don't remember who.

[majiponi]

A new puzzle.

Create a kingdom where you can play an Action card any number of times in a single Buy phase.

Scepter, Captain, Quarry.
Play Captain in Action phase. Buy phase: play Quarry, play Scepter, replaying Captain. Captain now costs $4, so you can play Captain with Captain recursively.

No. Captain cannot play a Duration card.

Ah, right. Okay, then:
Scepter, Captain, Quarry, Inheritance
Slight change to the first answer. Play Quarry on some setup turn to allow Inheriting Captains. Then, later, play Scepter to play Captain or Estate. Each Estate plays a Captain, which plays an Estate.

I think someone else came up with this idea on a different thread (probably the Rules Tweaks/Errata thread), but I don't remember who.

Nice. How about this?

... play  a Tactician any number of times in a single Buy phase.

[hhelibebcnofnena]

Does the Tactician have to have something to discard each time? Or can they be dead Tacticians?

[majiponi]

Does the Tactician have to have something to discard each time? Or can they be dead Tacticians?

Whichever is ok. I have both answers.

Setup: trash Mandarin

play Storyteller to play Scepter for +$2
play Necromancer to play Zombie Apprentice to trash Tactician
play Rogue to gain Tactician, revealing Watchtower to trash it

you have 4 Scepters and a Watchtower in hand

play Scepter to replay Storyteller
play Scepter to replay Rogue to gain Tactician, revealing Watchtower to trash it
play Scepter to replay Rogue to gain Mandarin, revealing Watchtower to trash it
play Scepter to replay Necromancer to play Tactician to discard Watchtower

you have 4 Scepters and a Watchtower in hand
repeat

[hhelibebcnofnena]

Does the Tactician have to have something to discard each time? Or can they be dead Tacticians?

Whichever is ok. I have both answers.

Setup: trash Mandarin

play Storyteller to play Scepter for +$2
play Necromancer to play Zombie Apprentice to trash Tactician
play Rogue to gain Tactician, revealing Watchtower to trash it

you have 4 Scepters and a Watchtower in hand

play Scepter to replay Storyteller
play Scepter to replay Rogue to gain Tactician, revealing Watchtower to trash it
play Scepter to replay Rogue to gain Mandarin, revealing Watchtower to trash it
play Scepter to replay Necromancer to play Tactician to discard Watchtower

you have 4 Scepters and a Watchtower in hand
repeat

How is this in the buy phase?

[markusin]

Necromancer cannot play durations. It's an explicit restriction on the card.

Edit: the fix would be to replace the Tactician in the trash with Band of Misfits and put the Ferry token on Tactician.

[majiponi]

Necromancer cannot play durations. It's an explicit restriction on the card.

Edit: the fix would be to replace the Tactician in the trash with Band of Misfits and put the Ferry token on Tactician.

Oops. Replay Overlord to play Rogue and Tactician instead.

[markusin]

Necromancer cannot play durations. It's an explicit restriction on the card.

Edit: the fix would be to replace the Tactician in the trash with Band of Misfits and put the Ferry token on Tactician.

Oops. Replay Overlord to play Rogue and Tactician instead.

Overlord cannot be gained from the trash by Rogue, which is why I gave BoM as an example to make sure the solution wasn't broken.

Edit: nevermind, I understand what you mean now.

[dghunter79]

Several Monument cards start the game with 12 VP chips on them, to be gained under certain circumstances. However, in some kingdoms it is impossible to gain any. 

Across all possible Kingdoms, what is the smallest non-zero maximum number of VP chips it is possible to gain off of one of these cards?

[FrenziedHavoc]

Several Monument cards start the game with 12 VP chips on them, to be gained under certain circumstances. However, in some kingdoms it is impossible to gain anys. 

Across all possible Kingdoms, what is the smallest non-zero maximum number of VP chips it is possible to gain off of one of these cards?

Well it's no more than 8. Colonnade + Gladiator + 9 non-action kingdom cards

[markusin]

Several Monument cards start the game with 12 VP chips on them, to be gained under certain circumstances. However, in some kingdoms it is impossible to gain anys. 

Across all possible Kingdoms, what is the smallest non-zero maximum number of VP chips it is possible to gain off of one of these cards?

I'll give this a shot.

In 2-player, 12VP on the landmark, I can get it down to 6VP max:
The kingdom has Labyrinth and Blessed Village, and the rest of the kingdom does not provide any extra source of +buy/gain. The only source of Labyrithn points are the 10 Boons that can be received from gaining Blessed Village. There are 5 Boons that give +buy/gain: Earth, Forest, Mountain, Sky, and Swamp. If two of those five boons are the bottom two cards of the 12-card boon deck, then one can only gain an extra card on their turn up to three times, yielding 6 VP total across the game.

Concerning 3+ player games:
If we go to 3+ players, then the minimum number goes down to at least 4VP:
The Kingdom is Castles, Collonade, and the rest of the kingdom consists of non-actions. The only source of Collonade points becomes buying Small Castle when having the other Small Castle in play and Opulent Castle when the other Opulent Castle is in play.

[markusin]

Several Monument cards start the game with 12 VP chips on them, to be gained under certain circumstances. However, in some kingdoms it is impossible to gain anys. 

Across all possible Kingdoms, what is the smallest non-zero maximum number of VP chips it is possible to gain off of one of these cards?

I'll give this a shot.

In 2-player, 12VP on the landmark, I can get it down to 6VP max:
The kingdom has Labyrinth and Blessed Village, and the rest of the kingdom does not provide any extra source of +buy/gain. The only source of Labyrithn points are the 10 Boons that can be received from gaining Blessed Village. There are 5 Boons that give +buy/gain: Earth, Forest, Mountain, Sky, and Swamp. If two of those five boons are the bottom two cards of the 12-card boon deck, then one can only gain an extra card on their turn up to three times, yielding 6 VP total across the game.

Concerning 3+ player games:
If we go to 3+ players, then the minimum number goes down to at least 4VP:
The Kingdom is Castles, Collonade, and the rest of the kingdom consists of non-actions. The only source of Collonade points becomes buying Small Castle when having the other Small Castle in play and Opulent Castle when the other Opulent Castle is in play.

Oh, for the 2p, 12VP puzzle, I can get it down to2VP by replacing Blessed Village with Cursed Village and putting two of Plague, Locusts, and Greed on the bottom of the Hex deck.

[dghunter79]

Several Monument cards start the game with 12 VP chips on them, to be gained under certain circumstances. However, in some kingdoms it is impossible to gain anys. 

Across all possible Kingdoms, what is the smallest non-zero maximum number of VP chips it is possible to gain off of one of these cards?

Several Monument cards start the game with 12 VP chips on them, to be gained under certain circumstances. However, in some kingdoms it is impossible to gain any. 

Across all possible Kingdoms, what is the smallest non-zero maximum number of VP chips it is possible to gain off of one of these cards?

Oh, for the 2p, 12VP puzzle, I can get it down to2VP by replacing Blessed Village with Cursed Village and putting two of Plague, Locusts, and Greed on the bottom of the Hex deck.

I'm still trying to find a solution to this that doesn't involve stacking the Boons or Hexes deck, but that only allows a single player a single gain of 2 VP off of Colonnade or Labyrinth. Why? I don't know.

One thing that Menagerie has opened up is a solution where only one "player" can gain all the chips, while the other is locked out.

Can anyone find that solution? Or come up with an alternate one that only permits a single gain of 2 VP and no more?

[bitwise]

I think this is another 2VP solution: with Cemetery and no gainers/buys, the only time you can gain multiple cards in a turn is to trash Haunted Mirror to gain Ghost.

[dghunter79]

I think this is another 2VP solution: with Cemetery and no gainers/buys, the only time you can gain multiple cards in a turn is to trash Haunted Mirror to gain Ghost.

Totally. In that case each player can gain 2VP. I'm also looking for one where there are 2 or more players but only one player can gain 2VP.

[LaLight]

I think this is another 2VP solution: with Cemetery and no gainers/buys, the only time you can gain multiple cards in a turn is to trash Haunted Mirror to gain Ghost.

Totally. In that case each player can gain 2VP. I'm also looking for one where there are 2 or more players but only one player can gain 2VP.

feast in a black market?

[hhelibebcnofnena]

I think this is another 2VP solution: with Cemetery and no gainers/buys, the only time you can gain multiple cards in a turn is to trash Haunted Mirror to gain Ghost.

Totally. In that case each player can gain 2VP. I'm also looking for one where there are 2 or more players but only one player can gain 2VP.

feast in a black market?

No, that wouldn't work. You can gain the feast in the same turn as another card, and then use the feast to gain two cards in a turn.

However, any card that doesn't gain, if it is the only card in the black market deck (although I don't know if that's allowed) would work

[bitwise]

Several Monument cards start the game with 12 VP chips on them, to be gained under certain circumstances. However, in some kingdoms it is impossible to gain anys. 

Across all possible Kingdoms, what is the smallest non-zero maximum number of VP chips it is possible to gain off of one of these cards?

I'll give this a shot.

In 2-player, 12VP on the landmark, I can get it down to 6VP max:
The kingdom has Labyrinth and Blessed Village, and the rest of the kingdom does not provide any extra source of +buy/gain. The only source of Labyrithn points are the 10 Boons that can be received from gaining Blessed Village. There are 5 Boons that give +buy/gain: Earth, Forest, Mountain, Sky, and Swamp. If two of those five boons are the bottom two cards of the 12-card boon deck, then one can only gain an extra card on their turn up to three times, yielding 6 VP total across the game.

Concerning 3+ player games:
If we go to 3+ players, then the minimum number goes down to at least 4VP:
The Kingdom is Castles, Collonade, and the rest of the kingdom consists of non-actions. The only source of Collonade points becomes buying Small Castle when having the other Small Castle in play and Opulent Castle when the other Opulent Castle is in play.

For the 3+ player games, I don't believe that it's possible to have Small Castle in play and have the other copy available to buy. So this should actually count as 2VP.

[dghunter79]

Small Castle is “trash this or a Castle in your hand.” So I believe there are 4VP up for grabs.

Putting a single card in the Black Market deck is like stacking the boons deck. The true solution should be implicit in the kingdom.