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?
Oooh, good one
if celecstia comes Wednesday AFTER twilight goes to bed, or Thursday b4 she gets up, then its possible, twilight logic says the day is over when she goes to bed
Twilight’s logical deduction method eliminated all of the days in the week for Celestia to visit, but since Celestia said she would be coming over, clearly one of Twilight’s guesses was wrong. The scientific community refers to this as false positives or false negatives, depending on what you are looking for. My science teacher did something like this once, where he talked about how the correct answer to a multiple choice question usually wasn’t A, because otherwise lazy students could be assured of a good grade by just by guessing A for the entire test. The very next test, for at least ten questions in a row, the correct answer was A.
On a side note, logic tests such as this are probably why Twilight acts the way she does in the show. Twilight does know teleport and therefore, if Celestia feels she needs to banish Twilight, placing Twilight in a dungeon in the place she was banished to is one of the few non-lethal options available. Learning where Luna was for the past thousand years probably didn’t help.
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...wrong, but close enough.
Oh-h-h, I read this one once in Wikipedia! It is called "the unexpected hanging paradox", or "the hangman paradox". According to that, Twilight expects Celestia not to show up, because that would be no surprise, since she can be sure she'll know by the end of the week, that Celestia will visit her. How? She trusts her former mentor, so, if she said "the next week", it shall happen on one of the seven days. But by the end of the week it's going to be just one day. So she may expect Celestia to show up. Therefore Celestia will not visit on the seventh day (otherwise Celestia would have lied!). So on which day out of the remaining six will Celestia visit? Well, applying the same logic, as to the seven days, the sixth day would be the only day. By that time Twilight could expect Her Majesty. In order to come unexpectedly, Celestia will surely NOT come on the sixth day!
As described, Twilight narrowed it down to just one day. Now that would mean, Celestia should definitely not visit her on that day, for Twilight will surely have expected her! Therefore, concludes Twilight, Celestia shall NEVER pay her a visit!
Now Twilight expects Celestia not to show up, so, when Celestia does show up anyway, Twilight is surprised. She should not have convinced herself in Celestia not coming, but rather expected her everyday . For example, when she said to herself, that Celestia wouldn't come on the seventh day, she might have stopped there. Convinced, that she wouldn't come, she would expect her on every other day. Celestia would come on the seventh day. And that would be unexpected .