Had you any idea that brainery is a real word?!
Neither did I, and actually, I'm still not sure. It's here, but not in the dictionary, and the Scrabble dictionary is down so I can't tell you if it's legal on the big board, but I'm gonna guess no. (Have you ever read that book, Word Freak? Highly recommended.)
Across the internet, there are 66,700 search results for "brainery" but the only one that seems remotely interesting is The General George Squier Brainery, a conference named after the founder of Muzak (they're a company?). They even had a performance by The Constellations, a band that once recorded a song with Asher Roth, of all people. I could not have made any of that up if I had tried.
In case the above wasn't educational enough for you, here's a couple of random, entirely unrelated facts I've been telling everyone lately:
Bangladesh is the world's 7th most populous country!
Phoenix is the 5th largest city in the US!
If your friends are anything like mine, they will only be mildly impressed by these facts, but it's a start.