Disclaimer: (Money JK Rowling gets from Harry Potter) / (Money I get from Harry Potter) = Error: divide by zero.

Parts of this chapter have been quoted from Harry Potter and the Philosopher's Stone.

A/N: Just so there's no confusion here, the Room of Requirement is over in the East Wing. I won't make things quite that easy for her.

Chapter 4

"Professor McGonagall," Hermione asked the next morning after barely finding her way to the Transfiguration classroom on the moving staircases. "Is it possible to get a map of the school somewhere?"

"A map? No, I'm afraid not, Miss Granger," McGonagall answered. "The castle changes too much for any maps to be useful."

"But couldn't you just mark where all the moving staircases go, ma'am? That would make it easier."

"No, it's a little more complicated than that. Everything moves around a bit over time in a place with as much magic as Hogwarts Castle. But not to worry, the classrooms hardly ever change, and I'm sure you'll find your way around in a few days."

Hermione wanted to say that she was interested in a map for more than just finding her way around, and just how could a thousand-year-old stone structure move around even with magic, anyway? But class was starting, so she held her tongue and took her seat. It didn't look like the professors would be that much help with this task. Maybe her fellow Arithmancy students would be able to help at their study session.

"What's a hundred and forty-six times eighty-seven?" Alicia Spinnet said.

"Twelve thousand seven hundred and two." Hermione didn't even hesitate.

Alicia checked the answer. "That's right."

"Wow," said Cedric Diggory.

"I told you she was that fast," Roger Davies replied smugly.

"Well, okay, but can you do bigger numbers?" Cedric asked Hermione.

"Uh huh."

"Alright, then…how about 6,843 times 9,572?" He scribbled down the numbers for himself.

Hermione still didn't hesitate, exactly, but she did have to slow down and sound out answer a bit: "65 million…501 thousand…196."

It took Cedric nearly a minute to check the answer, but he was amazed to find that was also correct. The three third years kept at it, interspersing a few addition and division problems to mix it up. But multiplying large numbers seemed to be the main focus of the questions they were giving her, which wasn't too different than at her secondary school. Wizards, of course, didn't know about other common challenges like finding the thirteenth root of a thirty-nine digit number (which was, in fact, quite easy) because, working with only quill and ink, it would have been nearly impossible for them to find a thirty-nine digit number that was a perfect thirteenth power in the first place.

A small crowd, mostly composed of Ravenclaws, started to gather around as Hermione solved every problem correctly (no easy feat even for her), most of them in her head.

"Hey, I saw somebody do this once in a play," Alicia said. "What day of the week was 14 September, 1194."

It took her only a couple seconds. "Wednesday."

Alicia paused for a moment, then picked up her copy of A History of Magic. After flipping around for a couple minutes and thinking about it, she said, "Yeah, that's right."

"Whoa," several of the spectators said.

"24 March 1603," one of them threw out.

"Which calendar?" Hermione shot back.

"What?"

But she already had the answer: "It was a Thursday on the Julian Calendar, which was in use in Britain at the time, but a Monday on the Gregorian Calendar, which was in use on the Continent." The spectators all looked at each other, having not even thought of that problem.

"Alright, Granger," Roger said with an evil grin. "Try this one." He slid across a piece of parchment to her on which she was expected to multiply two ten-digit numbers. He had been silent and carefully hiding what he was writing for the past five minutes, clearly needing the time to work out the problem for himself.

"Ooh…" several people said.

Hermione got right to work. The bystanders gasped when she started writing out the digits of the answer directly, two by two, without getting into those messy rows of addition that normal people used. It took her a little over a minute, but she put her quill down and confidently crossed her arms.

"There's no way that's right," one of the bystanders said.

"Check it!" said another.

"That's what I'm doing." Roger took the parchment back and checked it against his own work. "No, you got that wrong," he said. There were some murmurs from around the table.

That was possible, but unlikely, Hermione thought. She slid the parchment back over to her side and looked over Roger's work. It took her only a few seconds to spot the problem. "No, you made mistakes here and here," she pointed out.

Roger quickly snatched the parchment back and looked where she had pointed. "Dammit! You're right."

A few people cheered and others mocked Roger for being shown up by a first year, until Madam Pince shushed them all and forced the gathering to disperse.

"Hermione, that was incredible," Alicia whispered. "How did you do all that?"

"Just a lot of practice," she answered with a shy smile, coming down from her revelry.

"No, there has to be more to it than that," Cedric said. "I've never even heard of anyone that good."

"Not really. It's not…" She smirked a little. "It's not magic or anything like that. I mean, there's some tricks I could teach you, but, honestly, it's probably not worth the trouble for you to learn it. It's mostly for fun, and it doesn't help you all that much on more advanced maths."

"Yeah, but still, how did you get that good?" Alicia pressed.

"Well, a lot of it's just common sense things, like I memorised the multiplication table up to 100 times 100. And that wasn't even from trying so much. I just practised enough that I remembered it. You have to memorise a lot of things: logarithm tables, prime numbers, and there's a bunch of seemingly random multiplications. Like—do you know what thirty-seven times twenty-seven is?"

"Ha, no! You're the human slide rule," Roger said.

"It's nine hundred ninety-nine. And that makes it really easy to multiply things by 37 because it's close to a round number. I've memorised a lot of those kinds of factorisations. Like 499,999 is 3,937 times 127."

"Okay, I can kind of see what you're saying," Cedric said, "but even knowing all that, I don't get how you can do bigger numbers that fast."

"Well, it's a little hard to explain. I can just kind of…see it."

"But…how?"

"It's…uh…well, look, you're all Quidditch players, right?"

"Yeah," they all said.

"I'm sorry, I don't know much about sports, but I assume you have formations and plays, and there are some that are probably standard to the game."

"Of course," said Roger.

"And when you first start playing, it's got to be hard to keep track of fourteen players on the pitch, right?"

"Well, sure, if you're a beginner," Alicia said. "But if you practice, you start to understand the formations."

Cedric and Roger nodded as they started to get the picture.

"Exactly," Hermione said. "If you practice enough, you stop seeing individual players and start seeing formations, and you can react faster. Well, with me, if it's something like…multiplying four-digit numbers, say, after I practised enough, I stopped seeing multiplying the digits and started just seeing the answer."

"That…that is amazing," Alicia exclaimed. "I didn't know you could that with numbers."

"Mm-hmm, I've read that you can do that with almost anything…But we should probably get started on the homework."

"Right," Cedric said, taking out the assignment that reportedly was already mystifying much of the class. "What are the chances that a random pair of socks from this drawer will match…? What does this have to do with making predictions?"

"Oh, you have to think of choosing the two socks as two separate events," Hermione said. "Making predictions is all about tying chains of events together."

"Okay, but what's this probability matrix? I mean, I read about it, but I don't really follow it."

"That just shows what all the different possible outcomes are—it's messier, but it might be easier to start off drawing a probability tree…"

With Hermione helping them to get on their feet mathematically, Alicia, Cedric, and Roger started to make sense of the basic elements of probability and statistics. Meanwhile, Cedric helped Hermione out with the more esoteric and magical aspects of numerology, although she was a very quick study, herself. By dinner time, they had all made great progress on the homework, and the third years were all very glad they had invited the "little firstie witch".

"By the way," Hermione said as they were packing up, "do any of you know if there's anywhere I can find a map of the castle?"

"A map?" Cedric said, confused. "No, the castle changes too much to make a map. Why? You haven't been getting lost, have you?"

"Some. I took a wrong turn on the way to Transfiguration this morning and almost got detention from Mr. Filch because I wound up near the forbidden corridor."

"Ooh, that's not good," Alicia said. "Glad you slipped out of it. But don't worry. You'll get used to this place in a few days."

"Yes, that's what Professor McGonagall said…But it would be nice if I had a map and some pictures so I could show my parents what the castle's like. They'll never get to see it themselves."

The others paused and digested that. They clearly weren't used to thinking the way muggle-borns did. "Well, that would be nice," Cedric said, "but I'm afraid you won't find much. You can probably ask Madam Pince to copy some pictures of the castle, though."

"Oh—I guess I can do that, then." But silently, Hermione vowed that she would correct the oversight of the school of failing to produce a map. Seriously, what kind of excuse was "the castle changes too much"?

Hermione succeeded getting in a nap in before trudging up to the top of the Astronomy tower at midnight—more than two hundred feet above the Middle Courtyard and more than four hundred above the Black Lake. The top of the tower was open to the full dome of the heavens, and a clear, moonless sky sparkled with thousands of stars. Hermione was moved to tears by the sight, and she was happy to see she wasn't the only one. She had never got far enough from the cities and towns to see a sky this dark, nor had many of the other students who lived near London.

Professor Sinistra graciously gave them a few minutes to admire the view. Then they viewed the rings of Saturn through their telescopes as it set. (Hermione had always thought Saturn looked a little too perfect through a telescope and was very amused when Ron Weasley insisted his brothers had pranked him and painted it on his lens.) Then, the professor gave them a basic lecture on how to navigate on the sky: the North Star, the Ecliptic, the Milky Way, and how positions were measured on the sky. She was surprisingly knowledgeable about advances in muggle astronomy and even space travel, and she expressed great hopes for the Americans' Hubble Space Telescope, even though it would apparently be two more years before they got the thing working properly. "Imagine a telescope the size of a train car, flying around and around the Earth like the Moon!" she had said. Many of the purebloods refused to believe it, even when Hermione and Sally-Anne insisted it was true.

They climbed back down just after the old crescent Moon peaked over the hills in the east. Hermione managed to wake up in time for breakfast on Thursday and got through the day without incident, aside from getting a bit lost again. Then, she spent that evening reading up for Potions. According to Alicia, she would need to be especially prepared.

She had no idea.

Hermione could tell within the first five minutes of Potions class that Professor Snape would probably be a most unpleasant teacher. It started with singling out Harry Potter during the roll call—and not in a nice way—to the sniggers of the Slytherin students. Then, he raised the bar by calling off of his students a "bunch of dunderheads". You would think a teacher would be above openly insulting his students. Hermione was on the edge of her seat with nervousness. This class might be harder than she thought.

"Potter!" said Snape suddenly. "What would I get if I added powdered root of asphodel to an infusion of wormwood?"

Seeing as she hadn't actually bothered to completely memorise One Thousand Magical Herbs and Fungi, even Hermione's prodigious memory couldn't supply the answer with certainty. She was pretty sure the answer was Draught of the Living Death, just as she was pretty sure that it wasn't anywhere near a first year potion, but she kept her hand down. She wasn't about to give Professor Snape any ammunition to call her a dunderhead.

"I don't know, sir," said Harry.

Snape's lips curled into a sneer.

"Tut, tut—fame clearly isn't everything. Let's try again. Potter, where would you look if I told you to find me a bezoar?"

That one was pretty obvious to most, Hermione thought. Malfoy and even Crabbe and Goyle (who did look like dunderheads, to be honest) were laughing at how easy it was. She could bet that a boy from an old, rich family like Malfoy would know all about poisons and their cures. But Harry was muggle-raised, she recalled. Sure, she had read far enough ahead to know about bezoars, but it wasn't fair of Professor Snape to assume Harry had. She tentatively raised her hand, partly to try to deflect attention away from the boy, but Professor Snape ignored her.

"I don't know, sir."

"Thought you wouldn't open a book before coming, eh, Potter? What is the difference, Potter, between monkshood and wolfsbane?"

To his credit, Harry was still staring straight into Professor Snape's eyes. Hermione raised her hand firmly this time, although she might not have remembered that one, either, except that she had seen references to wolfsbane here and there in other books.

"I don't know," said Harry quietly. "I think Hermione does, though, why don't you try her?"

A few people laughed; Harry caught Seamus's eye, and Seamus winked.

Hermione blushed. That wasn't exactly the kind of attention she had been going for, and it only got worse when Professor Snape snapped at her, "Put your hand down, you silly girl," before explaining the answers to his questions and taking a point from Harry for his "cheek".

Well, that settled it, Hermione thought. Professor Snape was officially the worst teacher she had ever had. She didn't even have to wait to see how unhelpful he was in the actual lesson (which was very). In the muggle world, any teacher that openly rude and unfair would be sacked in a year. Professor Snape had been here for at least seven, according to the upper year students. She would have to remember to look up if there was a formal complaint process available.

As it happened, Snape—Hermione mentally stopped adding the "Professor" part about halfway through—wasn't much of a lecturer. One could charitably say that he believed in learning by doing, like Professor Sprout, except that Professor Sprout demonstrated most of the things she taught to them first, not to mention that she was actually nice. Snape just told them to brew the Potion to Cure Boils from Chapter 1 of Magical Drafts and Potions and then wandered around the classroom, inspecting their methods. His long, black cloak billowed out behind him as he walked, as if blown by a light breeze, even though the air in the dungeon was stagnant—far more stagnant, in fact, than it had any business being given the fumes they were producing. Hermione suspected there was a spell in play on the first point and could only hope there was a spell for the second as well.

Snape offered both compliments and helpful advice to the Slytherins, especially Malfoy. She was careful to write this down—advice was good any way she could get it—but he seemed to have only condescension for the Gryffindors in general and Harry Potter in particular.

Hermione had been paired with Dean Thomas, who wasn't too bad at potions himself, even though he was also muggle-raised, unlike the unfortunate duo of Neville Longbottom and Seamus Finnigan.

The Potion to Cure Boils wasn't the simplest potion, or the easiest to make (though it scored better than most on both). But it was included in Chapter 1 of Magical Drafts and Potions because it was one of the few potions that required no wand work at all. In principle, even a muggle could brew it if they had the ingredients.

Most potions required at least one spell, and often several, but many of the first-years would not be good enough with a wand to cast them reliably for a few weeks. The most common spell in potion-making was the charm to make the ingredients dissolve properly. After all, snake fangs and porcupine quills would not dissolve very well under any normal circumstances. But here, the Dissolving Charm would not interact well with the ingredients, so it was not used. Instead, concentrated bundimun secretion was added to the water to take care of that. Another common spell was the Sealing Charm that prevented any further dissolution of the ingredients once the potion was finished. Instead, this potion used mashed blueberries to counteract the corrosive effects of the bundimun secretion.

There were other spells, too, used for more advanced potions: spells to add magical energy directly to the mixture, spells to protect any living matter that got into the cauldron, reducing the need for gloves, spells to only dissolve certain ingredients, or to speed up or prevent certain reactions between them. Unfortunately, there were trade-offs in everything, and this potion that required no wand work turned out to be temperamental in other ways, as Neville learnt painfully when he melted down Seamus's cauldron, giving himself severe boils instead of curing them.

Since Snape was so unhelpful, just sending the two of them to the Hospital wing without explanation (or sympathy), it took Hermione a while flipping back and forth through the course books later to figure out what had happened. And to do it, she had to forget almost everything she knew about chemistry, or even cooking for that matter, and start thinking—she couldn't think of any better analogy—like a poet. The bundimun secretion was corrosive and also caused decay. The porcupine quills were barbed and thus scratched things badly (much more than the snake fangs). The fire weakened the soft pewter. The three different types of damage shouldn't have particularly amplified one another, but they did. Any two of them the magically-reinforced cauldron could withstand, but all three together were too much for it. When Neville added the porcupine quills without taking it off the flame, the cauldron melted.

Unfortunately, every ingredient had interactions with every other ingredient that had to be kept track of, which was the most important thing that governed the order they were to be added. No wonder inventing new potions was supposed to be so difficult.

But it all made sense in a poetic, medieval sort of way if you thought about how you might expect things to work if you'd never been taught actual science. Some of the ingredients were used the way you would expect anyway: bundimun secretion was a solvent; nettles had known medicinal properties; horned slugs were a thickening agent. Yet on another level, the ingredients seemed to be almost metaphorical: live horned slugs didn't do much; therefore stewed ones didn't interact much with other ingredients. Porcupine quills and snake fangs were best known for penetrating the skin; therefore, even crushed, they would help the skin absorb the final product. Blueberries grew in acidic soil; therefore they could counteract the corrosive effects of the bundimun secretion. This metaphorical dimension also probably had something to do with why some ingredients had to be prepared at a certain time of year or phase of the Moon in more advanced potions.

Hermione thought that Magical Drafts and Potions did a really poor job at explaining all of this because it treated all the ingredient properties and interactions the same. That would be fine for a catalogue or reference book, but to teach the conceptual principles on potion demanded more discussion on the multiple ways in which one needed to think about the same ingredients.

One other good thing about the Potion to Cure Boils, setting it apart even from the other recipes in Chapter 1, was that it was easy to see how well it turned out from the final colour. Brewed properly, it was supposed to be a soft, soothing light blue. This allowed Snape to grade the potions on the spot when they turned in samples at the end of class—a nice touch for the the first class, Hermione thought, although she suspected Snape really did it so he could get in a few more digs at them. Sure enough, Draco Malfoy and Gregory Goyle (whom Malfoy didn't allow to do any difficult work) got an Outstanding grade. Harry and Ron were graded Poor. Hermione and Dean received (grudgingly, she thought) an Exceeds Expectations, while poor Neville and Seamus got a zero for the day.

Hermione woke on Saturday morning to the excited chatter of her roommates who were happy to have a free day. "Free" was a relative term, of course, since they still had homework, but Lavender and Parvati seemed to be in the mood to put that off until tomorrow. Hermione, on the other hand, had got as much as she could done in the free period yesterday afternoon and last evening. She was looking to take a break from schoolwork herself today, but for a different reason.

"What about you, Hermione, what are you doing today?" Parvati asked her.

"Me? Oh, I just thought I'd explore the castle for a while," she said innocently.

"Oh, well be careful with that. You don't want to get lost," Lavender said. "I heard the unused parts of the castle can shift around and trap you so you can't find your way out."

"What? Where did you hear that?" Hermione said.

"The Weasley Twins told me. I mean, sure they might have made it up, but I'm not about to risk it."

Parvati rolled her eyes at Lavender. "Anyway, we were going to check out the grounds this afternoon. You should come along."

"Well, maybe," Hermione said noncommittally. "I'll see how the morning goes."

Later, when she came back up from breakfast, Hermione dug out her small drafting kit and a book of graph paper. She didn't use them all that much, but they were great for geometry and would be even better for map-making. She would show everyone who said she couldn't make a map of the castle. She would just need to measure everything out.

"Sally-Anne, I was going to try to map out the castle. Do you want to, you know, come along?" she asked, before getting started.

"No, sorry, I've got a lot of homework," her fellow muggle-born said. "I don't know how you get through it so fast. It's hard not having the magical background."

"Oh…okay," she said, a little disappointed. But she wrote it off and got to work. Starting with her own dormitory, she stepped off the bedroom, the lavatory, and the spiral staircase outside the door. She was pretty sure the boys' dorm was a mirror image and that the other floors were the same, so a small, quick sketch was sufficient to describe the eighth through fourteenth floors of Gryffindor Tower. She followed this up by heading down and stepping off the Common Room, prompting a few funny looks, but she quickly got that done, too, and climbed through the portrait hole into the corridor, her graph paper in hand.

The first order of business was to step off the West Wing. She looked down the long corridor that led to Ravenclaw Tower, picked one of the seams between the stones on the floor and walked along it, stepping it off heel to toe from one end to the other. It took her about five minutes to cover the whole length, but she got the measurement she wanted. Hermione's size two and a half trainers were nine and three-quarters inches long, so the one hundred seventy-two steps she marked in the corridor equalled one hundred forty feet. (Okay, a hundred thirty-nine feet and nine inches.) The second corridor, from Ravenclaw Tower to the Grand Staircase, was one hundred thirty-eight steps, or about one hundred twelve feet. So far so good.

Just to check her results, she paced off the other two corridors, up to the North Tower and back to Gryffindor Tower. But as she grew nearer to the North Tower, she grew more and more uneasy. Something didn't look right, and as she crossed the last few feet, it was obvious. This corridor was only a hundred and fifty-nine steps long. She tried the fourth corridor. One hundred forty-seven. Clearly, the West Wing wasn't a perfect rectangle.

It sure did look like it, though. She looked down at the stone floors of the corridors. The seams between the stones were perfectly straight. She took her protractor to a few of them. All the corners were right angles, or at least close enough that the lengths wouldn't be off by that much. It looked like a rectangle, but the lengths of the opposite sides were about ten feet different.

She tried measuring the entire floor again, this time pressing as close as she could to against the outer wall, all the way around the seventh floor of the West Wing. She was extra careful now to place her feet exactly in front of each other in a straight line. She got all the same numbers to within three steps.

She tried a third time, this time along the inner walls of the corridors. With the extra care she took on the last two measurements, she got the same numbers again to within one step.

It took only a few seconds of mental math to figure out that that was physically impossible. If the castle weren't a perfect rectangle, there should have been a larger difference than that between one side of the corridors and the other, no matter what the angles were. The only explanation—and because she had dabbled in the works of Lovecraft, she shuddered a little as she thought it—was that Hogwarts Castle was not built on Euclidean geometry.

Hermione Granger wasn't about to give up, though. That would certainly make mapping the castle a pain, but the differences were only about ten percent. She could just take an average length to draw it as a rectangle and then write in the actual measurements. At least she wouldn't have to be quite so careful about doing it exactly right. Within a couple feet would be good enough since the castle didn't seem to want to cooperate on exact measurements anyway.

By now, almost two hours had gone by, but she figured she might as well keep on going until lunch time. She went down to the sixth floor to pace that off as well and see if it was any different. And it was a good thing she did because when she got to the south corridor, the one that had been one hundred thirty-eight steps long on the seventh floor, she found it was one hundred forty-five steps on the sixth floor. This was going to be harder than she thought.

She was pacing off the north corridor on the sixth floor when she heard more footsteps behind her.

"Well, what have we here, Fred?"

"A little firstie wandering off by herself, George. I do hope she's not lost. Good morning, Miss Granger," Fred said, as both Weasley twins stepped in front of her and started walking backwards to face her.

Hermione looked up from her feet to glance at each of them. "Hello, Fred, George," she said, trying to hide her discomfort around the notorious pranksters.

"And what are you up to on this fine morning?" George asked.

"Well…" Oh, what could it hurt? "I was trying to make a map of the castle. I'm trying to measure the corridors." She considered asking what they were up to, but quickly decided she didn't want to know.

"A map of the castle, Fred." The twins shared a knowing look and started laughing.

"What? What's so funny?"

"Oh nothing," said Fred. "It's just we've never heard of anyone making a map while we've been here."

"And measuring the corridors with your feet," George added. "I'd say that takes quite some dedication, wouldn't you, Fred?"

"That I would, George."

"Are you even counting your steps, Miss Granger?"

"Of course," she said. "One-twenty-one, one-twenty-two, one-twenty-three—"

"Through this entire conversation?" George asked.

"Yes."

"Without losing count?" Fred added.

She smirked in spite of herself. This proved to be a bad idea, since they took it as a challenge.

"Oh, so you wouldn't mind if we called out random numbers like—"

"One-sixty-two!"

"One-oh-five!"

"One-thirty-nine!"

"Seventy-seven!"

But she didn't even slow her pace. Hermione Granger did not lose count. "One-thirty-five, one-thirty-six, one-thirty-seven…"

"I think we've been had, Gred."

"Well, Forge, we did hear Alicia talking about this one. We'll have to keep on our toes around her."

"She's certainly a clever one…"

"One hundred forty-seven," she said, reaching the end of the corridor. "Hmm…that one was the same," she mused as she marked the measurement on her map.

"The same as what?" one the twins asked—she'd lost track of which now.

"The seventh floor."

They stared at her in confusion.

"The south and west corridors are different lengths on the seventh floor," she explained.

"What?" the twins said at once.

"And all four sides are different from each other, even though the Quad is a rectangle."

"Is that even possible?" One of them snatched her map out of her hand and started looking over her measurements. "This can't be right. We would have noticed it on—" He stopped as the other twin coughed. "Now I really think we're being set up, George."

"Indeed, Fred," George said with an evil grin. "If you're looking for a prank war, Miss Granger, we'd be happy to oblige."

"I-i-it's not a prank," Hermione said nervously, taking a step back. "Y-you can step it off for yourselves."

Fred and George looked at each other, no longer mischievously, but with genuine curiosity.

"I think this calls for investigation, brother," said Fred.

"I quite agree. If Miss Granger can discover something about the castle in a week that we haven't in two years—"

"She could be a valuable ally."

"Well, I'm not looking to prank anyone, if that's what you mean." Fred and George looked unconvinced. "May I have my map back, please? I want to try to pace off a couple more floors before lunch."

"Of course." Fred handed back her graph book.

"And good luck with your…mapping."

"Thanks…" Hermione backed away, not wanting take her eyes off the pair until she reached the staircase to go down to the fifth floor. She kept working.

The small windows that lined the Quad had no sills to speak of. She was able to poke her head out one of them and run her eye down the sheer wall. It was perfectly straight. She tied an eraser from her drafting kit to a string to make a plumb bob to check the walls. She tried it on both the fifth floor and back up on the seventh floor. All the walls were vertical. From those two facts, every floor of the West Wing should have been exactly the same shape and size. And yet, not only were the measurements different on each floor, but the perimeter of each floor she paced off was about ten feet larger than the floor above.

It was while she was stepping off the fourth floor, trying to get around it quickly to avoid going too far into the lunch hour, that another unwanted attendant spotted her. Hermione tried to ignore the scraggly-looking tabby as it meowed menacingly at her. She momentarily thought she had dodged a bullet when Mrs. Norris ran away, but, somehow, just a few seconds later, Argus Filch came around the corner. Hermione's only direct run-in with the Caretaker, at the third-floor corridor on Wednesday, had not been pleasant, and most of what she'd heard from the other students was worse.

"You, there, what are you doing?" Filch wheezed.

The direct approach was probably best here. "I'm measuring the corridors, sir."

"I can see that. What are you up to? Aiming fireworks? Spreading Slipping Solution? Planting those infernal Ricochet Balls?"

"N-no, sir, I'm just trying to map the castle." And she held up her graph paper to show him.

"Mapping the castle? Mapping the castle?" Filch said suspiciously. "Oh no you don't. I found the Weasley Twins doing the same thing up on the sixth floor. You're definitely up to something. What is it? Searching for more secret passages? I won't allow it."

"Please, Mr. Filch, I'm not breaking any rules. I'm just trying to learn to find my way around. I only told Fred and George that the measurements are different on every floor. I didn't ask what they were doing."

"Measurements are different—" Filch's mind apparently needed a moment to switch gears on that one. "Well of course they are!" he complained. "What did you expect with as much magic as there is around this place?"

"Please, sir, I've only known about magic for a few weeks."

"Well, best learn to stay away from those two," Filch said. "Nothing but trouble from the start. Deserve a few days strung up by their ankles if you ask me…Well, then, go on. Finish what you're doing and get on to lunch," he said, apparently conceding that he had nothing on her.

"Um…yes, sir."

Filch walked away, muttering to himself, "Students wandering about like they own the place. Ought to stay in their Common Rooms where they belong…"

Hermione finished pacing off the fourth floor as quickly as she could and dashed down the stairs to the Great Hall, barely remembering to jump the vanishing step. That was a health and safety hazard, alright. She didn't understand why they couldn't patch it up. In any case, Filch may have had nothing on her, but he certainly wasn't nice to talk to. She felt much better when she was out of his sight.