Mutilated chessboard problem.
The problem is the folkloric one: given a chessboard with two diagonally opposite corners removed, can you tile it with dominoes? A domino is a rectangle which is the size of two adjacent squares. (If you haven't seen it, think about it; the solution is in the article.)
I've known this problem for as long as I can remember, but I didn't realize it had a name. I didn't realize it needed a name. But apparently it's a standard example of a theorem which is hard for automated theorem-proving programs, so that community needed something to call it, because they can't refer to "that one with the dominoes on the chessboard where you get rid of two squares" in the title of their papers.
Harder question, again if you haven't seen it before: when can you remove two squares and have there be a tiling? (I know the answer. If you want to know it, leave a comment.)
Even harder question: when can you remove four squares and have there be a tiling? This might not be that difficult, but I don't know the answer. (It'll give me something to think about on the walk into school this morning, though.)