A Bewitching Puzzle indeed.
One shot drabble: Sometimes the asker can be more intriguing then the question.

I can't wait to get my hands on the latest Professor Layton game. I was addicted to the Lost Future when it came out and completed it in a total of 17 hours 23 minutes and 3429 Picarats. Not that Miss Hardbroom would be impressed by something as trivial as that. Heck I'd probably get detention scrubbing dried in potion stains off the lab floor if I said I was using my brain.

I own nothing but games and DVDs. I can't take credit for working out any maths problems either as I copied the answer off you guys in the Worst Witch forum. (Yet another thing I'd get detention for!) Enjoy

"Well Flora, it's just an idea I had." Professor Layton smiled secretly tapping the edge of his top hat, "I'll tell you soon. I'm sure you'll both like it but let's wait till Luke arrives then I can tell you together it- ah in fact that sounds like him now. In here my boy," the professor called at the rattle of the front door. "Excellent timing as always!"

Layton's self proclaimed apprentice was more then happy to abandon his homework in favour of a possible puzzle and scampered into the kitchen where Layton was removing a kettle from the hob, his adopted daughter setting out the tea set.

"What is it Professor? A mystery? A case? A client?-"

"Luke, calm yourself. And manners. Never forget to greet a lady when she's present."

"Pardon? Oh er, yes sorry hello Flora." Luke said apologetically taking off his cap and held a kitchen chair out for her. Flora the golden apple giggled and gave him a mock curtsy in return before taking the seat and Layton smiling at the children's antics, joined them at the little round table. "What is it?"
"Now will you tell us?"
"Tell us what?"
"I don't know yet he won't say."
"Professor, don't keep us in suspense!"

"Patience you two," he chided. "Let's discuss this over a cup of tea shall we?"

The pair sulked but did as they where told. Luke offered him one of the scones/Ssc-ownes he'd brought on his way and Flora passed him the milk. Playing mother Layton poured water from the kettle into the three small teapots; each with it's own blend that suited each of it's drinkers,sweetened Oasis berry for Luke, Citrus classic for Flora and as they were out of earl grey, a good old fashioned pot of the finest breakfast tea for the professor himself, and left them to brew.

"Now to business," the professor said finally once this part of the ancient and traditional ceremony had taken place, taking a letter out of his jacket pocket. "Do you remember this letter we received a few days ago?"
"It had a puzzle in it!" Luke beamed then his face fell. "But I still haven't managed to solve it."

"Well don't let it vex you my boy, if you take in to account that it takes four witches twelve hours to train six cats, then it would take four witches two hours to train one cat and then it means then it would take eight hours for one witch to train just a single cat so that means it takes a snail four hours to take one lap around the pond and twelve hours to take three laps and then logically if you assume we're measuring time based on four witches instead of reducing it down to one witch, it would take a snail one hour to go around a pond and three hours for three laps. But anyway that's besides the point-"

Flora who'd been counting on her fingers and Luke who'd been quickly scribbling every word the Professor said, gawpt at him. "It's not the answer I'm after. Look at the question, the letter. What do you make of it?"

Luke took the rather scrupled letter from its envelope and indeed looked it before passing it to Flora. "I can't make out the writing, only Flora could read the writing because it was all swirly and smudged. So was your address on the front which probably post marked from ages ago. The one from a girl, Mildred something, in the country. She said she'd read about you in the papers and was a big fan. I remember that bit- and it had a cat stamp on, I put in my collection." Luke said, listing everything he could think of trying to be impressive. "It was written on paper from an exercise book, because there were notes on the back, doodles, some maths workings out and a list of odd ingredients that would have made a very nasty soup-"

"It didn't sound odd to me, "Flora sniffed. Given her tendency to put fish in cream cakes Flora would probably try making this henbane and toadstool concoction even if she couldn't get hold of any spiders eggs so Luke ignored her and continued.
"But this Mildred mentioned she was at boarding school so that's no mystery she's just pulled it out of a school book."
"And a teacher had set her friend that question about the cats and snails." Flora agreed and read from the page.
"Anyway, Professor, I wondered if you could help me. My friend Charlie wanted to start at Cackles Academy so my tutor set a puzzle for my friend on his entrance exam last week. He changed his mind afterwards for other reasons but he couldn't work it out and neither can anyone in my class not even with,- I can't make out that word, it's scribbled out-
but we all came up with different answer so we thought we'd ask you. I warn you though, she loves catching people out. -Professor I still don't understand."
"Me neither." Luke agreed. "What's going on?"
"Well I merely thought it was interesting." Layton mused sipping his tea. "The fact a letter was addressed here not the university, with a cat stamp? A boy applying at a school named Cackles even though it seems to be a girl's school? An exercise book covered in drawings of stars and broomsticks? And although cats and snails sometimes come up in maths exams, why have witches training cats? As if training cats is just a walk in the park. I find a little curious don't you?" Flora and Luke exchanged blank looks. "No? Oh, well could you read the rest of the letter out to us Flora please."

Flora did so right the way though to the end; "Thank you for reading and I hope you like the puzzle. Yours sincerely, Mildred Hubble. Oh and there's a PS. I didn't see that last time, it's all squashed at the bottom It think it's...PS If you'd ever like to visit the school to give a lecture or something I sure you'd be more then welcome to as we'd love fore you to come I'm sure you'd find it very interesting."

There was a moment's pause that Luke broke. "So, we're going to their school?"
"It would be rude to ignore the girl and her friends. Well? Would you like to?" Layton smiled. "A day out in the countryside?"
"I wouldn't mind. But you don't normally accept an invitation unless someone needs help urgently." Flora said. "You said we can't accept every invitation or else we'd be over run. What's so special about this place?"
"Maybe it's a school for wiiiicked witches! WOowooOOo!" Luke grinned and wailed, "Granny Riddleton will get yooOoO-"

"Luke." His apprentice stopped mucking about and drank his tea like a good little boy. "Witches or no witches, its young Mildred's school that interests me. Not only the curious manner but I did a little research and after a lot of digging I came up with the background history for the place. It seems the site Cackle's Academy for young girls is found formally known as Overblow Castle, once home to a notorious cavier baron who is said to have hidden his treasure somewhere in the walls of his keep."
"Wow!"
"Wow indeed. It get's better as Hermione Cackle the founder of the school is also said to have lived an extraordinary life as a high wayman. Well, lady. Now local legend or not, I've always preferred learning the history of a place first hand and I am in need of new topic for my next paper." Layton took in the now rather excited faces of the pair.
"I'll write to the current Miss Cackle, explaining what had occurred and offering a talk on what ever subject she deems fit for her students. It sounds a good place as any to start a new line of research, let's see what her reply brings..."

A few days later and not a million miles away, the worst witch was in hot water again. Not bad considering it wasn't even lunchtime. Mildred Hubble was stood in front of her headmistress as Miss Cackle discussed the reply from the professor that had arrived that morning but the young witch was paying more attention to the scary faced deputy. For a change she'd been summoned to the staff room rather then the Miss Cackle's office but the routine was the same. She was told to explain herself and then would be told off. She'd had much worse tellings off to be fair, barely registering a one on the rictor rage scale so it was practically HB's equivalent a grumble. Mildred didn't quite see why she'd been summoned and would have thought it a little unfair if it hadn't been for the rather exciting news Miss Cackle had just told her. And was then told to stop grinning like a fool. Again, this was merely a formality as after being lectured at she was dismissed.
"It'll be all around the school by the end of break."
"She hasn't really done anything against school rules." Amelia sighed as Constance took a seat.
"Aside from cheating, pulling exercise books apart and going out of bounds to the post box." Constance said in clipped tones. "And I hardly think we ort to encourage the girls to seek out side help on what should have been a test paper or use magic to find a person's home address."

"Well true. But that's quite a grey area and it'll be rude to take back Mildred's offer of hospitality."
"And we are to extend it to all three of them? His foster daughter and this boy-"
"Luke." Amelia clarified popping her glasses on the end of her nose and tapped the letter where in blue biro someone had scribed the title in the margin. "His apprentice."
"This schoolboy that would be coming with him? It's bad enough when Mr Blossom's nephew distracting and bothering the girls!"

"You never know, Professor Layton's presence here might do wonders for our reputation. It would be for the good of the school."
"Or it's damnation. Miss Cackle I must protest, if the man's as clever as they say he is he'll take one look at us and realise we're a witch school. If he hasn't done so already."

"Yes but don't forget he is offering a talk on any subject Constance." Amelia sighed in exasperation. "Imagine what good what a boost to the girls' education that will be. And it might make a change from the Chief Wizard's assemblies."

"And what if he does put two and two together and gets the correct answer that we are a school for not young girls but young witches teaching magic and potions despite us our cover up stories? " Constance continued ignoring the last comment. "Do you really think you can make him keep quiet about the magic and its history that he may discover?"

"Well…" Amelia sighed, gazing in to her mug the contents of which had tragically now gone from piping hot to cold and stewed. "No. Not unless we can bribe him with of tea..."