One of a kind (Search result = 1)
Herman Roozen
Netherlands
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When I tried to find a game like Puerto Rico (Categories: Farming, City Building, Economic; Mechanics: Variable Phase Order), I found out that there is only one game with those criteria. Which made me think. There are 76 categories and 43 mechanics in BGG. So there are 3268 possible combinations of 1 category with 1 mechanic. Some combinations will have hundreds of games, some will have none. I am curious which combination of 1 Category with 1 Mechanic has only 1 search result.
I'm sure the admins can cook up a query that gets them all out. Here are the ones (five of them) that I came up with after a brief search. Not systematically (Abstract Strategy x Acting = 8; Abstract Strategy x Action Point Allowance System = 46; etc.), but just 'trial and error'.
Please feel free to add your own "search result = 1".
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Herman Roozen
Netherlands
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Category: Farming
Mechanic: Voting
"Family game based on the British radio drama. Players compete to show their knowledge of the fictional village of Ambridge. Players take on the role of one of six characters and travel around the board gathering information from other players or acting out situations from the show."
One of a kind.
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Herman Roozen
Netherlands
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Category: City Building
Mechanic: Acting
"Western Town is a game based on the West Colonization. It has basics mechanics from Settlers of Catan and Puerto Rico."
But still it is unique.
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Herman Roozen
Netherlands
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Category: Renaissance
Mechanic: Rock-Paper-Scissors
""Rise of Nations" is an empire-building big box game in which players develop their nation from Ancient Age to Modern Age. War, economics, science and diplomacy are to be taken into consideration to successfully win this epic game."
It has a lot more Categories and Mechanics than these two, but the combination of these two makes it special.
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Herman Roozen
Netherlands
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Category: Religious
Mechanics: Secret Unit Deployment
"The players take on the roll of dignitaries in the Temple Order during the Third Crusade to the holy land. They strive to expand the power of their order in order to increase its gold and renown of the Temple Knights and spread belief in the holy land. This choice group in the Temple Order will determine the most capable member under them to become the new grandmaster."
If you are looking for religion and secrecy: look no further.
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Herman Roozen
Netherlands
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Category: Vietnam War
Mechanics: Trick-taking
"The "one hit one kill" sudden death nature of modern combat, makes this game very different than earlier versions of Down In Flames!"
And apparently also very different than any other game.
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The only game about the American Indian Wars, in which Singing is part of the game -> Link
From the description:
"There are NO dismounted/horse-holder RULES and NO rule against the Native player singing War-chants or Death-songs for fallen troops." So singing doesn't seem to be really required to play it... 
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A last one from me. The only game in the Comic book/Strip category with a Line drawing mechanic. -> Link
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Herman Roozen
Netherlands
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Category: Arabian
Mechanics: Role Playing
"Legends of Araby bridges the gap between traditional wargaming and role-playing games."LOA" marks the beginning of the new Role-Playing Lite system where players can create personal characters and travel through the world of Talomir interacting with the people that live there."
Found another "one". This game has 6 more categories and 3 more mechanics, but it is the only one with Arabian Role Playing in it.
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Herman Roozen
Netherlands
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Category: Space Exploration
Mechanics: Rock-Paper-Scissors
"In Rocks for Sale, two to five (best for three to five) players fly their space ships along a pick-up and delivery circuit from the assayer's space station to the asteroid belt and back. Players tow asteroids back from the belt and sell them to the assayer, with the eventual goal of being the first to pay off their ship. But there are additional costs to running a mining ship, such as fuel, repairs and blasting charges. Mining in space can also be dangerous. Fuel leaks, overheating engines and other miners' blasting charges are only a few of the hazards an asteroid minor may face."
That makes sense: a game called "Rocks for Sale" uses the Rock-Paper-Scissors mechanic.
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Herman Roozen
Netherlands
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Category: Negotiation
Mechanic: Route/Network Building
"Eager and hungry to "conquer" more casinos than your opponents in a short space of time, you have various means of transport at your disposal: private jets, sports cars, luxury yachts and the like. Each has particular properties that can help you blaze a trail from Monte Carlo across to Gibraltar round to St Petersburg, back to London and on to Helsinki in time for tea. Whoever has been to the most casinos after each player has been the "dealer" once, wins."
This game has four more Categories and four more Mechanics.
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Posted Wed May 7, 2008 9:16 am
"Secret Unit Deployment"?!? What the, I mean how do you - um - well, you know, deploy your - um - unit secretly? 
Mason
Michigan
Brussels
Edit: yeah, I found some.
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Me too. At least I did it, and it's gone, but I don't remember deleting it. Some pretty weird games were added by others to my list. I think it was 4 pages long.
I've searched thoroughly through the GeekLists on words like "Category", "Mechanics", "One of a kind", "Single", "Unique", etc, before I started this list. A duplicate GeekList with this subject would be embarrasing.
Brooklyn
New York
I love it.
For those who think this is interesting, you might want to check out
http://www.googlewhack.com/.
Nice work!