It’s been a week since Commencement now, and about two weeks since I had my last philosophy final. I can tell that I’m finally fully recovered, because I’ve started thinking about philosophy in the shower again. This morning, I remembered that someone at NYU had mentioned the surprise test puzzle to me several weeks ago but not the solution he’d come up with. So I thought I’d do the same to you: I’ll describe the puzzle, and then forget about it for a couple of weeks, and then bring up the solution I came up with. (There are several solutions on the web, of course, but it’s more fun if you think about it on the subway or while doing dishes or something.)

Here’s someone else’s formulation of the surprise test puzzle: Suppose a teacher announces to her class one Friday afternoon that she will give a surprise quiz sometime during the following week. Her class meets five days a week (poor class), so the test could be on Monday, Tuesday, Wednesday, Thursday, or Friday. But it can’t be on Friday - by Thursday night, the class will know that the test is on Friday, and then it won’t be a surprise. And if it can’t be on Friday, then it can’t be on Thursday, because by Wednesday night the class will know it has to be on Thursday (since it can’t be on Friday), and so on. So, does this show that surprise tests are impossible?