Although Princess Twilight Sparkle is no longer Princess Celestia's student, but a fully-fledged Princess with her own responsibilities, Celestia does admit to herself that Twilight does on occasion need to be kept on her hooves to avoid complacency. A prankster at heart, Celestia decides to pull the mother of all pranks on Twilight.
She sends a letter through Spike straight to Twilight, announcing that she'll be visiting Ponyville just to oversee how the School of Friendship and how Ponyville in general is getting on, and just to mess around with Twilight's neurosis and fear of tardiness still further, she won't announce exactly when she'll appear, nor will there be any sign: she won't even use the Royal Chariot for official visits, she'll just teleport straight to Twilight's Castle. All she says in the letter is that it'll be on a weekday the following week after receiving the letter.
After Twilight has gone through enough breathing exercises and paper bags, Spike reminds her that Celestia's probably pulling her hoof, if her pet phoenix Philomena is anything to go by, and the phrase 'pets take after their owners' is any indication.
Twilight then calms down, and decides to think about it logically. Using recursive reasoning, she deduces that Celestia won't be visiting her on a Friday, because after Thursday has passed, if there is no sign of her, she can expect Celestia to visit on Friday, thus ruining the surprise. She then reasons that by the same token, Thursday is out as well, because she'd know by Wednesday if this is the case, and can expect her that day too. She then deduces, going backwards, that there IS no day Princess Celestia can visit her without it ruining the surprise, and she pens a letter back explaining this. She then sets out to perform her duties as head-teacher of the School of Friendship.
Sadly, she's forced to swallow her words (and her ink bottle) when she turns around to the kitchen to eat breakfast the following Thursday morning, only to find the white alicorn munching down on a bowl of bran flakes. HER bran flakes.
Celestia, to her credit, is very patient, and after listening to Twilight fire off several complaints about how she totally went back on her word and all logic (and for finishing off an unopened box of bran flakes in one sitting, seriously, too much fibre can't be good for a pony), she calmly explains that she never lied in the letter she sent once. It was because of a flaw in Twilight's reasoning that led to her total surprise, just as she said.
She then sits Twilight down and asks her to work out what that was, before they set out for the inspection. What was it?