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[Gveoniz]

Diadem. All of them have non action text that require another action card that is not a copy of itself to work.

Actually, all Prizes, Urchin, Mercenary, Spoils, and all Ruins require an Action not a copy of themselves to work.

Other prize, spoils and ruins don't have non action texts that reference any action card. Urchin can wok with another urchin.

[sudgy]

Diadem. All of them have non action text that require another action card that is not a copy of itself to work.

Actually, all Prizes, Urchin, Mercenary, Spoils, and all Ruins require an Action not a copy of themselves to work.

But there's not a clause on the card itself saying so.

But, Diadem doesn't work because you can always have one action...

[Rubby]

Diadem. All of them have non action text that require another action card that is not a copy of itself to work.

But Tunnel and all Dark Ages cards with on-trash effects also have this trait.

[soulnet]

Other prize, spoils and ruins don't have non action texts that reference any action card. Urchin can wok with another urchin.

I mean Madman, not Urchin, sorry. The rulebook requires other Action cards for those cards to work.

[Gveoniz]

Diadem. All of them have non action text that require another action card that is not a copy of itself to work.

But Tunnel and all Dark Ages cards with on-trash effects also have this trait.

They works with venture and farmland.

[A Drowned Kernel]

Diadem- they all reference a card type that they don't have.

[Rubby]

Diadem. All of them have non action text that require another action card that is not a copy of itself to work.

But Tunnel and all Dark Ages cards with on-trash effects also have this trait.

They works with venture and farmland.

Good point - not sure if I can think of another counterexample! Let's just say the trait is a little more straightforward and not dependent on defining a term such as "non action text" - although that answer is not at all unreasonable, I must say.

EDIT: Actually, I'm not sure how the card you named uniquely has the property that you cited...?
EDIT 2: Because you can't gain it without Tournament? Princess also has "non action text" in the same sense as Lighthouse. Anyway, the answer is more straightforward.

[Rubby]

Diadem- they all reference a card type that they don't have.

Lots of other cards have this property.

[Chaos]

University?

[JW]

Here's another hint. A slightly less restrictive version of the set, which actually might have made for a better puzzle, would also include Quarry and Vineyard.

The amended list -

Beggar
Horse Traders
Lighthouse
Moat
Quarry
Secret Chamber
Squire
Vineyard

is still missing one and only one card.

The problem with puzzles like this is that while it may seem obvious to you that there's one and only one card that completes this set, chances are high that other people could come up with multiple cards that completed the set according to that same reasoning. Therefore, even if someone guesses the reasoning you are using, they won't think they've got the puzzle right because there will be multiple cards that could go along with this set.

University?

This might be the solution if the logic is "cards that have multiple functions, at least one of which is useless in a Kingdom with no action cards in the rest of the Kingdom." But Festival satisfies that logic too (and Vineyard's claim to satisfy that logic is tough, it could power up Silk Roads, for example).

If anyone posts "the common element of the current set is X, and therefore the unique card that completes the set is Y", either A) there's an argument that not all of the current cards have element X, or B) there's an argument that more than one card could be added to the set.

[Rubby]

The problem with puzzles like this is that while it may seem obvious to you that there's one and only one card that completes this set, chances are high that other people could come up with multiple cards that completed the set according to that same reasoning. Therefore, even if someone guesses the reasoning you are using, they won't think they've got the puzzle right because there will be multiple cards that could go along with this set.

Only if I made a factual error, which I was careful not to do.

University?

This might be the solution if the logic is "cards that have multiple functions, at least one of which is useless in a Kingdom with no action cards in the rest of the Kingdom." But Festival satisfies that logic too (and Vineyard's claim to satisfy that logic is tough, it could power up Silk Roads, for example).

Thus that logic is not the solution.

If anyone posts "the common element of the current set is X, and therefore the unique card that completes the set is Y", either A) there's an argument that not all of the current cards have element X, or B) there's an argument that more than one card could be added to the set.

That is not true of this puzzle. The common element is straightforwardly, objectively factual.

[dereeder]

Band of Misfits

Each of them has a property which is useless if the kingdom contains no actions other than that card.  (For vineyard and quarry, "no actions other than that card" means simply "no actions", because those card aren't actions.

[Awaclus]

Band of Misfits

Each of them has a property which is useless if the kingdom contains no actions other than that card.  (For vineyard and quarry, "no actions other than that card" means simply "no actions", because those card aren't actions.

Throne Room.

[A Drowned Kernel]

Band of Misfits

Each of them has a property which is useless if the kingdom contains no actions other than that card.  (For vineyard and quarry, "no actions other than that card" means simply "no actions", because those card aren't actions.

Throne Room.

Throne Room can technically target other throne rooms. Though Procession can't gain an action cards costing exactly one more if it's the only action card...

[Rubby]

Band of Misfits

Each of them has a property which is useless if the kingdom contains no actions other than that card.  (For vineyard and quarry, "no actions other than that card" means simply "no actions", because those card aren't actions.

Throne Room.

Throne Room can technically target other throne rooms. Though Procession can't gain an action cards costing exactly one more if it's the only action card...

University would also be in the set if that were the trait.

[eHalcyon]

Band of Misfits

Each of them has a property which is useless if the kingdom contains no actions other than that card.  (For vineyard and quarry, "no actions other than that card" means simply "no actions", because those card aren't actions.

Tunnel, Market Square, University, Golem, Feodum, Catacombs, Hunting Grounds

[soulnet]

Any village. Golem.

Ninjaed. Venture can trigger tunnel though.

[DG]

Is this to do with protection against a masquerade pin? The defensive cards will do that and the squire will add a card to a deck when trashed. I can't see how vineyards and quarry fit into that though. So is the extra card the unlikely Sir Vander?

[dereeder]

Band of Misfits

Each of them has a property which is useless if the kingdom contains no actions other than that card.  (For vineyard and quarry, "no actions other than that card" means simply "no actions", because those card aren't actions.

Tunnel, Market Square, University, Golem, Feodum, Catacombs, Hunting Grounds

Venture (as mentioned) can activate Tunnel.  Farmland can activate MS, Feodum, Catacombs, HG.  Golem could play (one) necropolis, which isn't a kingdom card. 

And TR/KC can play more TR and KC.  But Procession and University are solid counterexamples.

I'll try again. 

The first list (Beggar, Horse Traders, Lighthouse, Moat, Secret Chamber, Squire) is a list of Kingdom Action cards that have this property: each card X on the list references a card type (in each case it happens to be Attack) that is not necessarily in the Kingdom when X is in the Kingdom.  The second list (adding Quarry and Vineyards) is a list of Kingdom (not necessarily Action) cards with the same property.

Vagrant (which references Ruins, but does not add Ruins to the Kingdom) completes both lists.  I can't think of another card that has that property.

[Rubby]

I'll try again. 

The first list (Beggar, Horse Traders, Lighthouse, Moat, Secret Chamber, Squire) is a list of Kingdom Action cards that have this property: each card X on the list references a card type (in each case it happens to be Attack) that is not necessarily in the Kingdom when X is in the Kingdom.  The second list (adding Quarry and Vineyards) is a list of Kingdom (not necessarily Action) cards with the same property.

Vagrant (which references Ruins, but does not add Ruins to the Kingdom) completes both lists.  I can't think of another card that has that property.

dereeder wins!

[soulnet]

I'll try again. 

The first list (Beggar, Horse Traders, Lighthouse, Moat, Secret Chamber, Squire) is a list of Kingdom Action cards that have this property: each card X on the list references a card type (in each case it happens to be Attack) that is not necessarily in the Kingdom when X is in the Kingdom.  The second list (adding Quarry and Vineyards) is a list of Kingdom (not necessarily Action) cards with the same property.

Vagrant (which references Ruins, but does not add Ruins to the Kingdom) completes both lists.  I can't think of another card that has that property.

dereeder wins!

I guess type saves it. A Knight or Rats from the Black Market have that property too.

[eHalcyon]

Band of Misfits

Each of them has a property which is useless if the kingdom contains no actions other than that card.  (For vineyard and quarry, "no actions other than that card" means simply "no actions", because those card aren't actions.

Tunnel, Market Square, University, Golem, Feodum, Catacombs, Hunting Grounds

Venture (as mentioned) can activate Tunnel.  Farmland can activate MS, Feodum, Catacombs, HG.  Golem could play (one) necropolis, which isn't a kingdom card. 

Ack, misread your post as saying that it was the only card, not only action card. My bad. And Necropolis is clever.

[soulnet]

Quarry decreases the cost of Necropolis to 0, which matters for Black Market and then TfB. Also, Vineyards does count Necropolis, though it would still be worth 0 VP without Masquerade passing, which implies either Masquerade or Black Market in the Kingdom. You need to word the trait in a way that is really not about the effect but about the text referencing Kingdom cards's types.

[liopoil]

Quarry decreases the cost of Necropolis to 0, which matters for Black Market and then TfB. Also, Vineyards does count Necropolis, though it would still be worth 0 VP without Masquerade passing, which implies either Masquerade or Black Market in the Kingdom. You need to word the trait in a way that is really not about the effect but about the text referencing Kingdom cards's types.

dereeder did.

[JW]

That is not true of this puzzle. The common element is straightforwardly, objectively factual.

I stand corrected. Really interesting puzzle!

One key is that while there are a number of Action cards that refer to Actions, by definition there is always an action card in the Kingdom when such a card is in it.