Author: thornmaiden

And we’re off –

I got my first pattern accepted for publication!

Can’t say much about it, but it is a typically weirdy thing (see previous post) and will probably be in print in about a year’s time. I actually submitted two designs, as a matching set, but the second was a garment that had a lot more competition. There, I don’t think I’ve given too much away! I’m exploring where I can publish the second pattern. Possibly with a few mods, possibly not.

So now I’m trying to put together the most comprehensive spreadsheet of sizes in the known universe. I’ve got the Craft Yarn Council’s Standards, used by Knitty amongst others, a spreadsheet by Marnie McLean, who is one of those designers whose pieces I recognise instantly, a chart from a bra company that I can’t find online any more (why didn’t I bookmark it!), and sundry other charts for babies, children, teenagers and adults, covering heads, hands, feet, and anything else I can think of. If you’ve got a body part, I want a measurement chart for it. And no, photos are not acceptable. Yech.

Meanwhile, the head is a-buzz with ideas. As part of an effort to be more organised and logical, I’ve created a set of folders on my laptop for calls, submissions, acceptances, random ideas, useful information, etc. Now I’ll have factor in work times to sit down and do a certain amount of work each day.

One thing the submission process taught me is that I desperately need a decent digital camera. My Fuji FinePix, crapulent thing that it was – one snap and the batteries died – has finally departed this mortal coil, and after selecting a new mobile phone specifically for its high-spec camera, the photos from it are corrupted every. single. time. I had to use the thumbnails for my submission… I do have a great selection of film SLRs, but running off an entire film for each submission, then travelling thirty miles to a developer and paying over the odds for digital copies, just to have a single photo of a sample just doesn’t jib with me. Maybe for Knitty, where I’d need to submit the photography, but otherwise? Nah.

Unfortunately, I don’t really understand digital cameras. Megapixels, CCDs, all wash over me. Apparently, for reasons that I don’t really understand, a digital camera with so many MP will produce much better photos than a camera phone with the same MP, all other things being equal. I’m reasonably good at spotting quality film cameras, but digital is still a bit of a mystery. All I really know is, the higher the MP, the bigger the resulting photo can be without degrading the quality, and digital zoom is way less important than optical zoom.

Okay, ya got me. The teacher will out. Supposing you want to print your photo at a fairly high-quality 300dpi (dots per inch = resolution = clarity), and you need a standard-sized 6″ x 4″ photo to fit in your photo frame. The formula for the minimum number of megapixels you need is

MP >= (height x dpi x length x dpi) / 1,000,000, (or (hl.dpi^2)*10^-6 if you prefer)

(6 x 300 x 4 x 300)/1,000,000

MP >= 2.16

So you need a camera with at least 2.16MP for this size of photo at this resolution. However, if you want an A4 (11.7 x 8.3) size photo – the typical size for graduation photos, for example – then the formula goes

MP >= 11.7 x 300 x 8.3 x 300 / 1,000,000

MP >= 8.7399

So realistically, you’ll need 9MP for that special day. Interestingly (well, for me anyway), if you wanted to announce the event in the newspaper, you’d need an image that’s only at 72dpi. How big an image can you send them from your 9MP camera? Well, we can work the formula backwards to get the area of the photo:

 Area = (MP x 1,000,000) / (dpi x dpi)

(9 x 1,000,000) / (72 x 72)

Area = 1 736.11111…

Now, at this point, I would usually square-root the answer to give me a rough value for the height and length of the image – around 41″ x 41″, if you’re interested (I know I am) – or you could try something a bit more principled, like using paper dimensions. The A0 size (46.8″ x 33.1″) comes in about 8MP. For comparison, that’s 1 square metre, about twice the size of a full spread broadsheet newspaper like the New York Times or the Daily Telegraph. You’d need to be really proud of yourself to pay the publication rates for a pullout centerfold poster in any of those…

Tralalalalalalaaaaaaaaaaaaaaaaaaaaaaaa…..

I’ve been thinking about my ‘voice’. That’s designing voice, what with me doing a bit of designing these days and all. Apparently it’s really important to find your design voice.

Frankly, I don’t think I’ve done enough to have a voice – 4 designs published, and maybe as many again in the creative pipeline. What do they have in common?

  • 3 knit, 1 crochet.
  • 3 free, 1 pay-for.
  • 4 non-brand-name yarns. I do like my yarn, but the muse comes upon me when I only have DK acrylic.
  • 2 child/baby, 1 any age, 1… erm?!
  • 3 fairly quick/small items, one small but tricky.
  • Only 1 pair of gloves and, so far, no hats, even though these are the things I make most often.
  • 2 accessories, 1 garment.
  • 2 with some colourwork, but bizarrely no cables, even though I love ’em.
  • 4 rather odd things. Okay, 1 joke item, 3 moderately quirky.

The planned designs include (1) babywear, (2) accessories, and (3) adult garments. (1) may include some colourwork, and challenging construction. (2) will also include some colourwork, and some lace, but otherwise quite straightforward. (3) will almost definitely be brand-name yarn, and perhaps some challenging construction. Many in categories (1) and (3) may strike some (~cough!~ boring) people as freaky, weird, or mentally unbalanced, and at least one from category (2) as mildly eccentric. But what do I know, I’m on the moon picking whootleberries.

Strange colourwork in bargain bin mystery yarn.

My voice is cracked.

Ahaha hey…

I’ve been selling some patterns, or at least trying to, on eBay. The first one, a Santeenie, just sold, and the cash arrived straightaway. Hoorah!

But.

It’s bought by someone in Spain. A man. Who has no record of purchasing anything knit-related.

And even though the listing states very clearly off the bat that it’s a pattern, not a knitted item, I am concerned. Concerned enough to butcher the listing through Google Translate, which tells me that he may be under the impression that I am auctioning off my nephew, Reilly. Though, to be fair, this guy has no record of buying babies either, not even creepy reborn dollies like Reilly. The bit about the printed out pattern does survive the GT transmogrification, though, so I am hopeful that he’s at least read that bit.

But but but. I’ve a smidge of experience at translating knitting patterns (including those supposedly already translated – ~cough~ DROPS). It’s not easy. Am I going to be getting emails in Spanish about my estupida patruna?

Is Santa Claus even a Spanish thing??

Are the shops going to be full of Hispanic Santeenie knock-offs this Christmas (well, let’s be realistic, by the August Bank Holiday Weekend)???

Well! Time for my annual post!

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And the big news is (1) I’m a qualified teacher – but no job yet because (2) I’ve moved back to Ireland; and (3) I’m re-branding myself as Thorn Maiden Designs, (4) have opened an Etsy shop, and (5) I have finally got a pattern for sale!!! I’ve also (6) begun self-publishing via Kindle Direct Publishing, but only have a couple of test patterns up atm.

The pattern is Santeenie, ab0ve. It’s a fully-featured snowsuit, also known as a onesie or all-in-one, for a 19″ reborn doll. It is constructed as one piece, except for the hood trim which is picked up, with raglan/saddled shoulders. It has the proper babywear pleating and buttoning down the legs, the little pouchy back for the nappy, attached scratch-mitts (which look HUGE, just as they should), and a long hood featuring icord embellished with a pompom. There’s a smidge of intarsia in creating a buckle on the ‘boots’, which are created as toe-up socks with a short-row heel.

I hope to resize it for real babies in time for next Christmas, and I have a range of other outfits planned.

Heck, I’m doing a tension square right now for my next pattern!

More Gloves…

The black gloves are a pair I made for my teaching placement mentor. The pattern is Susie’s Reading Mitts from Dancing Ewe Yarns, and I used one skein of Katia Merino 100%.  Looks great, and can be used for wiping a whiteboard at a pinch.

The Pi Mitts I made for Pi Day – 14th of March, or 3/14 in American. As in 3.14? Because I have a bit of an obsession with π, as the numerati will deduce from the quote under my avatar. Utterly wasted on the little darlings at school, who are largely unaware of the symbol, and the fact that the decimal places continue beyond .14. But I like them. I started with green as the main colour, but found it didn’t quite ‘pop’ enough for my liking, so the second glove uses the red. It’s Teddy DK, wholly acrylic. They’re a little tight on my hands, but I was in a hurry. The pattern is a free Ravelry download.

Because I am a sucker, I made the skully convertible gloves and the Tam of Rassilon for X at Christmas. He has somehow become totally unequipped for winter, no jumpers, coats, gloves, anything to keep warm. I’d always intended to make both for him anyway, but the separation got in the way. The tam had to be blocked on a pizza dish! It is vast – though doesn’t look it worn. It’s now March, and I think he’s probably lost them already, doubtless on a binge. Certainly haven’t seen him wearing or carrying them since January.

I have deleted all the patterns I had favourited for him on Rav. That’s all, folks. I’m done.

On the right is a Drops shawl pattern, a basic garter-stitch domino specifically for long-repeat yarn, somewhat enlarged by m’self. The yarn is Teksrena 4-ply 100% wool, a Lithuanian yarn I got off eBay. The photo doesn’t do justice to the glowy colours. I call this Burning Embers.

It’s not a pretty-pretty shawl, but what I wanted was a big blankie that I could wrap around myself. It’s been very useful in the late and bitter winter weather we’ve had. It’s big enough to wear like a Faroese shawl, tied at the back. People like it a lot: I always get compliments when I wear it.

And finally for this post, Mickey Mouse. The Mighty Offspring has developed a real fondness for Mickey’s Playhouse, to the point where I am actually prepared to take him to Disneyland Paris for a few days this summer. Not going mad and considering a fortnight in Orlando, just 3 or 4 days. I… do not share his enthusiasm. Never have, even as a child. That squeaky voice just infuriates me. At least he’s dumb at Disneyland.

The pattern is Leisure Arts #3293, Disney Home: Mickey and Minnie Dolls, which I scored off eBay. I want to make it in Sirdar Snowflake, but while collecting the necessary colours, I made this in Teddy Vanguard DK, Spectrum Strata, and Robin Bonny Babe which I had to hand. The shorts come off, and I have an order for pyjamas already…
T’ra!

Accessorise This!

Gloves… I love gloves. Since Kim’s Sockotta Fingerless Gloves pattern went viral in my brain while knitting a pair of fingerless gloves, I’ve been able to pick up needles, wool and produce them with no trouble. In fact, that’s pretty much what I did one day when a friend’s daughter admired a pair my son was wearing – I even did an impromptu cable down the back. Unfortunately, I didn’t get a picture, but I was very pleased with them. I also have a pair of Cotillion Half Gloves to finish off, using some Twilleys of Stamford Freedom Spirit yarn that I received in a swap.

Last summer, we went on our first (and as it transpires, last) family holiday. I had been pushing this for – well, ever, but there was either not enough money, holiday time, or something, and it never happened. However, Summer 2009 I decreed to be the year we would finally go to Sweden. X’s friend emigrated there – well, I told him to go. Sounds good, yes? I scare X’s best friend into leaving the country! But in reality, his girlfriend lived there and their long distance relationship was wearing on them. On his way home from one visit, he bemoaned that he couldn’t just stay there – so I pointed out that he had every right, as an EU citizen, to move to another EU country and sent him some websites on the issue. Six months later… The relationship has since foundered, but he has friends there, a job, and he speaks the language and is even going to university now. All good.

Naturally, I wanted to take some knitting with me to Sweden. We flew out from Stansted at silly o’clock in the morning, necessitating taking a train down the previous evening, and sleeping in the airport until check-in. Then the flight, the bus to Göteborg, the holiday itself, and the return journey – lots of knitting time. Because I can never seem to get any sensible information about flying with needles, and had a steel crochet hook in my check-in luggage confiscated by airport security/customs on another flight before the current terrorist panic, I decided not take anything I would care about losing. So I made a couple of sets of dpns out of bamboo skewers!   There was another motivation: I’d been seeing short dpns mentioned around and about – 5″ and 6″. Never having used anything shorter than 8″, I wondered if these would be useful – after all, I’m fine with circs, and the needle part of them is about 4″-6″. However, I didn’t want to spend money on what might turn out to be nothing more than a multi-pack of cable needles. Like I don’t have enough of them!

I cut the skewers to size and started off using a pencil sharpener to create the points, but this just caused splitting no matter how careful I was. An emery board turned out to be just perfect. Afterwards, I painted them with nail varnish as a quickie way of smoothing the surface. As it happens, the skewers are exactly 2.5mm, spot on. The first set, the 6″ dpns, I painted in gloss colours which only afterwards I realised were Rastafarian. The 5″ set were in more subdued frosted purple, gold and white varnishes. As an aside, the gloss lacquer held up well at first, and stitches passed smoothly over it. However, over time, it seemed to get sticky, and wore away on the points, leading to splits. The frosted varnish, initially grabby because, you know, it’s got slivers of glitter in it, has held up better, and did not wear as badly.

After this, I was on the hunt for a pattern that I could use them on, and decided I deserved some gloves. The yarn is Teddy Picasso Colour-keyed, a DK acrylic: I’ve used the chunky version before for a much-loved jacket.  Due to the colours of the 6″ dpns and the DIY nature of their construction, I dubbed the gloves Jamaica? Why, yes I did! Go on, laugh. I know you want to. The Mighty Offspring noticed me making the gloves and demanded a pair as well, just like mine. This is my own free pattern, the Mitts-to-Mittens – linky on the right.  It took some fiddling to get my own pair to match (sorry about the swirling on the right-hand pic, I think it’s because of shrinking down too much), but you can imagine what it was like with his. The single ball could have made a few more pairs, but not after I’d hacked it to bits. It was worth it. They are Ben 10 gloves. They are Humungasaur hands. He can shoot lasers out of them, and absorb sunlight that turns in to BLOOD. Good value for 69p.

The next pair I made from some Teddy Vanguard chunky in a green so light it is practically fluorescent. I think I got it with the intention of teaching someone to knit. It just happens to be nephew Ben’s favourite colour, and he was thrilled to receive these an hour or so after admiring the MO’s pair. These, naturally, were knit with 8″ 8mm plastic dpns from under the counter in a charity shop, where such shameful items are kept. Why? Don’t be daft. Chunky on 2.5mm? As handy as the DIYdpns were at the time, I’ll be sticking with 8″ plus in future. The 6″ set were okay, but doing the MO’s gloves on the 5″ set nearly ruined me. It might have been the 10 days of knitting with shorter needles, or just the 5″ set, but for the first time ever I got hand pain. I was not knitting much more than usual, possibly slightly less, but my hands, both of them, felt like someone had taken a hatchet to the palms. Varying my hold didn’t help, and even now, over a year later, I still get twinges.

Never again…

T’ra fn

K

Dive In!

Well, let’s pile through this, starting with …socks!

Top left is a self-striping yarn from LIDL, Zettl Sockenwolle Cortina. Just after I finished them, the word on Rav was that Cortina was being pulled and buyers refunded because the stuff felted! These are about a year old, getting tight, and have felted slightly through wear, not washing – so I’m happy enough. Another pair, recently finished, will appear soon. Well, soon for me…

The blue pair is in Katia Merino Baby, a wonderfully soft yarn I picked up in Christine’s of Bournville (a wee treasure house – go there if you can). I did a slipstitch pattern on them, but the wool is so soft and fuzzy that the definition has all but vanished. I also picked up Katia Merino DK for socks for myself – haven’t got round to trying it though. The remaining socks are with the good old Teddy sock yarn from the Bull Ring. The one with the cabled ankles (Ankle of Green Cables, ho ho ho!) has never been on the offspring – the cables draw in too much to fit over his chunky wee limbs – nonetheless, they make a fetching phone sock. The others are my usual negative stripe and Fibonacci in what I poshly call my Crab Apple colours.

Heading north, to Hats!

The pink cloche, Big Belle, is a last-minute, no-pattern knit for Pink Day at school – a fundraiser for breast cancer. I don’t have much pink, apart from a too-small PVC jacket, so I cast on top-down in my one remaining ball of Sirdar Bigga, increasing and trying on as I went. The last few rows were done ‘flat’ in reverse stocking stitch, with a couple of stitches cast on to make the tab that the button is sewn to. It’s a tight fit and maybe a bit too pointy, but looks okay.

The jester’s hat (Borg Queen) is Fool’s Gold, but in gold Hjertegarn Natur Uld that I picked up on hols in Gothenburg, and some leftover Sirdar Big Softie from Begotha. There were some mods for using superbulky. Also, I didn’t bother knitting the 5-stitch hat band. Instead, I picked up stitches afterwards, 2×2 rib for 5 rows, and then did a knitted Picot edging, which l think looks better… I then crocheted chains and sewed them in place on the opposing colours of the crown (no pun intended). I love this hat, though it really only sits on my head. I may have to make another, maybe with more tentacley peaks.

The Spiderman balaclava (Peter Parker Picked a Perfect Period to Press for this Present) is my 100th project!

The Mighty Offspring asked me to tell Santa to buy him a Spiderman mask for Christmas – on 22nd December! I had no idea where to buy one now that Woolies is gone, and no desire to spend time trekking through the shops in the run-up to Christmas, so I decided to cobble something together. The pattern is based loosely on Jackyll and Hide and We Call Him Spidey.  It was finished with a couple of hours to spare – HANDS LIKE CLAWS!!! I went off-chart with exhaustion, eye-fuddle and any other excuse about the eyehole area, but it looks okay for all that. It IS too big, though it would be probably be fine if I sewed some shirring elastic into the collar. MO was speechless when he saw it hanging on the Christmas tree! On recovering the power of speech though, he put in a request for a Venom mask… He’s making do with his father’s BSJ hat in the meantime, pulled down over his face.

The remaining two are a Drops pattern, made with the recommended yarn, Drops Eskimo! I must have come over peculiar to actually use the yarn for the pattern, it’s just not like me at all. I even bought the yarn (from Scandinavian Knitting Design, good value and fast delivery) with the pattern in mind! However, I saved myself by not using the recommended Drops Puddel for the trim. Instead I used some Patons Lush fancy yarn that I picked up on eBay a couple of years ago. It’s a little sparkly and adds some girliness to the hats, which do get compliments. There was only just enough yarn in the balls to complete them, but they do run a bit large – even with my tight knitting. I lightly felted them a few weeks ago and the fit is much better.  The jumper I’m wearing in the photos is a handknit that I liberated from a charity shop. It’s a chunky yarn, 100% wool, with big hairy guard hairs through it. Itchy as all get out, but I don’t mind. £4! I also liberated an off-white fishermans rib crewneck and a blue and white marl 4×4 rib turtleneck, both too large for me so given to X, and a soft and fuzzy Shetland wool jumper with an Aztec-look Fair-Isle design, all for similar prices.

So, lowering the tone to the neck region – scarves!

The first two were last Christmas’s gifts to Mum and Ma-In-Law – Debbie Bliss Cashmerino Aran and DK respectively. The pattern is a Rav-only download, Anthro-Inspired Scarflet. I got lucky and picked up exactly the right brooch the church Christmas Fayre for Mum’s pink scarf, but couldn’t find anything for the lavendar one, so instead I crocheted a rose using the same pattern I used for the Mighty Offspring’s Christening Shawl. Looks effective, no? My own version is an iron grey yarn from eBay, Knitwitz Camel – 30% camel, 30% alpaca, 40% wool. Very resistant to blocking, as you can see. The brooch is a vintage bone daisy, picked up at the same Fayre along with a matching necklace.

The scarf on the left is Ragged Robin, a reverse-engineering of Annie Modesitt’s Ruffled Roses which is available only through LYS in the US, hence the reverse engineering. The green is Teddy 4ply, but the ‘rose’ is Jaeger Fur, a super-chunky wool-mohair blend that I stumbled across in Northfield’s Pins & Needles. The yardage is tiny – 22yds – but I still have about half the ball left! It’s a bit pouffy and OTT, but livens up a dull suit and is surprisingly warm.

The bobbly purple scarf below left is not a triumph of Aran bobbles, but a very simple scarf made with Teddy Pom-Tiddly-Om-Pom. At £2 in the Bullring, it was 75% off – you couldn’t be bad to it. The yarn came in a great tangled mass, and I wound up cutting it 4 times – yes, me, the master untangler of mohair and laceweight, defeated by novelty yarn. While knitting I just tied the ends together, cutting off any inconvenient bobbles on the way. The bobbles are big enough to hide the ends of the knots! I cast on 5 stitches, one between each bobble. On the second row, I knit into the front and back of each stitch (10sts). Then continued till I ran out of yarn. It really looks like it’s going horribly wrong for the first 6 rows or so, when the bobbles lie down and start behaving themselves. Be patient.

The lacy little number is another Christine’s of Bournville find, Katia Tobago. The colours really are that vivid. Okay maybe not – the camera was playing up at the time. The pattern is Queen Anne’s Lace, which, though really quite simple, manages to be oddly tricky. You need to do EXACTLY what the pattern says, even if it seems a bit odd at first. I made this for Ma-In-Law for what I thought might possibly her birthday – I only have a rough idea of when this is, as X had no idea of the date at all. Unfortunately, this was around the time things came to a head between us, so I have no idea what she thinks of it, or indeed if she even received it.

I think that will do for now. I do have a few more scarves to include, but they are either not quite finished or I have no photos as yet. Only the finished product will appear, m’dears.

T’ra fn!

K

New blog, new life!

I’ve moved to WordPress!

My old blog is still there – I may move stuff, or not. Unfortunately Blogger was making me crazy over image handling, and the blog itself was too full of old memories, as a quick look at the last couple of updates will prove.

So here is what I’ve been up to for the last year:

What a difference a year makes.

AKA Tiny Husband is getting the chop…

It’s been almost exactly a year since my last post – more than that if we go back to my last crafting post. And life has changed.

For a start, I’m now half way through my teacher training, and a single mother. TH and I separated in July, initially to give ourselves a break while he sorted out some issues. Now, however, it looks like we won’t be getting back together, as TH – must find a more suitable acronym – has decided, in effect, that his problems are actually personality flaws on my part. But he doesn’t want a divorce, unless one of us wants to remarry.

We’ll be getting a divorce. It’s either over, or it’s not. I’m not having this hanging over me. I’m already pissed that I’m in this halfway house of being ‘unofficially’ separated. There is no way that I could put up with having to explain my whacko living arrangements and non-divorcee status for the rest of my life. And while we’re at it, I’ll be going back to my maiden name.

And so to our normal schedule: the remaining creations from 2009 –

And 2010 so far:

More later…

A detailed mathematical and historical analysis of four of the challenges encountered in the game L – A Mathemagical Adventure

Introduction

L – A Mathemagical Adventure (hereinafter referred to as L) is a text-based single-player role-play computer game produced in 1984 by the Association of Teachers of Mathematics (ATM, no date), aimed at Key Stages 2 to 4. Originally designed to run on the BBC platform then more or less common in schools, the game is similar in format to other text-based games, such as Zork (Barton, 2007): the player has a quest – in this instance, to rescue a fair maiden named Runia; to achieve this objective, the player must overcome obstacles, defeat fearsome enemies, solve puzzles, and so forth; and the play is controlled by means of a set of relatively simple commands. Despite its single-player setup, there are opportunities for shared gameplay, discussion and co-operation in solving the puzzles presented.

The scenario contains references throughout to the literary works of Lewis Carroll, who – as Charles Dodgson – was an eminent Victorian mathematician with a predilection for games and puzzles. The puzzles are, naturally, mathematical. Some are relatively easy, others less so; and a few seemingly innocent tasks conceal problems of considerable depth and antiquity.  This paper will explore the solution and pertinent history of four of the tasks: the telephone; the bat room; the code room; and baking a cake.

My route through the palace was fairly systematic. In each room or area, I initially travelled east, then explored other routes in an anticlockwise direction. Having selected a direction, I explored it as far as possible, retracing my path backwards in stages to the first room after attempting all the tasks.


The Telephone

The telephone room is at the north end of a corridor to the west of the workshop. The possible phone numbers run from 000 to 999 (see Figure 1). The telephone itself is a red herring in the quest: no useful information is revealed in solving this puzzle. It is the chest on which the telephone sits that is important. Due to the route taken, this was one of the last places I looked: I was laden with objects and it is only thanks to a friendly games guru that I realised I had to drop them all to move the chest. I initially tried a few likely numbers (000, 111, etc.) to no effect. I then tried prime numbers, and got messages for 002, 003 and 005. When 007 yielded nothing, I tried 008, the next Fibonacci number, and on its success I tried the remaining Fibonacci numbers below 999 – 16 in all (see Appendix 1).

The Fibonacci sequence is named after Leonardo of Pisa [1] (O’Connor & Robertson, 1998) -nbsp;undoubtedly the 13th century Italian mentioned in one of the telephone messages. It appears in his Liber Abaci, in which he also introduces place-value decimal numbers. Fibonacci came to the attention of the Holy Roman Emperor, Frederick II, and his court. He was set a series of problems, including a problem regarding rabbit populations (see Figure 2). Starting with a pair of rabbits, and assuming they mature at one month old and produce young at two months old, how many pairs of rabbits would there be at the end of any given month? Fibonacci determined that the number of pairs in any one month was equal to the sum of the pairs in the previous two months: 1, 1, 2, 3, 5, 8 being the number of pairs in each of the first six months.

Had the sequence remained in the sphere of population dynamics, it would have been of limited use: none of Fibonacci’s rabbits ever die, for example, and continue to breed unabated by considerations of food supply, or, indeed, the walls surrounding their habitat as described in the original problem. However, the sequence has found applications in such a wide arena that there is a scholarly journal, the Fibonacci Quarterly, is devoted to its academic study. An examination of the L telephone messages reveals some of the areas in which the Fibonacci sequence has been applied:

001, 377:  meteorology (Swinbank & Purser, 2006);
013:          botany and biology (Knott, date unknown);
089:          economics (Frost & Prechter, 1998);
114:          sports and betting (O’Connell, 2008).

An unusual property of the Fibonacci sequence is that, when each number in turn is divided by its predecessor, the results converge on a curious number known as ϕ (phi), or the Golden Ratio. This number is found in nature, in architecture, art, music, geometry, and visual perception; it appears to underlie our notions of beauty; and has even inspired authors such as Dan Brown. Its pervasiveness is such that some see it written by the hand of God (Meisner, date unknown).

Surprisingly then, under the circumstances, I have been unable to establish a link between Lewis Carroll’s Alice and the Fibonacci sequence, except for the rather trivial coincidence that both began with rabbits.

[1]: Leonardo was a member of the Bonacci family: Fibonacci may be a contraction of figlio Bonacci – son of Bonacci.


The Bat Room

The Bat Room occurs towards the end of the game. The solution to this puzzle, any triangular number between 20 and 90, is one of the most clearly signalled in the game: the room has a triangular floor and walls. If this were an insufficient clue, any mistake causes the large bat to write out a triangular list of numbers, declaring that he hates anything that is not triangular (see Figure 3). This hint is repeated every time an error is made; any attempt to leave without completing the task causes the bats to swarm around the door, making escape impossible.

The triangular numbers are one of a class of numbers known as ‘figurate’, meaning that each term can be represented as a figure: graphically as a pattern of dots, or physically using counters, bottle tops, etc., where they can be used to teach younger students about the relationships between numbers, patterns and graphical representation. Such figures are regular geometric shapes – triangles, squares, pentagons, and so forth (Weisstein, date unknown–a). The figurate numbers are widely studied in number theory, but the triangular numbers attract considerable interest as they pop up in a variety of different equations, such as the sum of consecutive integers, square numbers, Pascal’s Triangle, and even integrals (Weisstein, date unknown – b). The most famous triangle number is the infamous 666, the so-called Number of the Beast. Sadly, the true Number of the Beast according to modern Biblical scholarship is the rather less inspiring 616.

The link to Lewis Carroll’s work in this task is again somewhat tenuous. The Bat was the nickname for Bartholomew Price, a professor of mathematics at Oxford known to both Lewis Carroll and Alice Liddell, the model for Alice, and Carroll parodies a well-known nursery rhyme through the voice of the Mad Hatter:

Twinkle, twinkle, little bat
How I wonder what you’re at!
Up above the world you fly
Like a tea-tray in the sky.
Twinkle, twinkle, little bat
How I wonder what you’re at!

The Code Room

The code room is located to the south of the billiards room, through an anteroom, and was thus located at an early point in my quest. In the code room, the screen fills with apparently random letters, digits and punctuation marks (see Figure 4). I solved this by making a codebook: typing each line of keys on the keyboard, and writing down the resulting text (see Appendix 2). Fortunately, it turned out to be a simple substitution code. Despite my lack of gaming knowledge, I knew that there should be a device in the room which would return its appearance to normal, and this turned out to be the case. I kept the glasses with me for the rest of the quest: this was not necessary for all the tasks, but a few did turn into code if I had to set the glasses down.

Codes have a history beyond the scope of this paper, ranging from military ciphers to Victorian flower language. Much ingenuity has gone into producing unbreakable codes for military and political uses, where a variety of techniques and devices have been employed – once-only codes, and the Enigma machine are examples. While many early codes were simple substitution codes such as found in the code room, there has been a progressive move toward mathematically-based codes and ciphers – and the use of mathematical techniques in cracking them. Naturally, as codes became more complex, computers are needed: it is arguable that computers would not be the household item they are today, if they had not been necessary for code breaking in the Second World War. Today, encryption is a major area in computer and internet security.

Dodgson was greatly interested in cryptography both recreationally and academically, and is known to have produced several ciphers, including a matrix cipher (Abeles, 2005). Some of these ciphers cunningly included nulls – non-code characters, or code characters used randomly – to disguise the meaning further. He used these codes to write letters to friends, and to remember dates.


Baking a Cake

The new kitchen is situated on the east of the palace, almost opposite the old kitchen near the game entrance. A cook needs to bake a cake at least 25cm high, using three ingredients, TOLT, FIMA and MUOT, in grams. The scenario glosses the soup-making episode in Alice in Wonderland, substituting a salty cake for the over-peppered soup.

Initially, I attempted to use the codebook on the ingredient names. I tried to find another code or language that might convert the letters into digits, sums, four-letter number names, ingredients with four letters (e.g., eggs or soda), or even four-letter acronyms. Finally, I tried simply putting in random numbers. More than 100g was declared ‘wasteful’ by the cook. By systematically changing one number at a time, I found a rough relationship similar to a Bell curve between the ingredients and the cake: that is, up to a point, increasing the ingredients increased the size of the cake, but beyond that, the cake decreasing in size. However, I was unable to find any distinct mathematical relationship, such as Pythagorean Triples.

Then I had a happy accident. Having found that 6g TOLT, 10g FIMA and 8g MUOT produced a 25cm cake, I decided to leave the game but forgot to save my position. When I went back in, I accidentally typed 10g MUOT instead of 8g – and it worked. After another 20 or 30 tries, I determined that 5, 6 or 7g of TOLT, 10-18g inclusive of FIMA, and 1-100g inclusive of MUOT, in any combination, produced a cake of the desired height.

It would be disappointing if this task, which must on average take players more time to complete than any other, were merely some kind of trial and error problem. I searched for more possibilities, but with little success. However, amongst the extra pieces of information I gleaned was that Dodgson had done some research on matrices, or ‘blocks’ as he called them, and had produced a method for finding determinants, known as Dodgson’s Condensation, which remains one of the most efficient to date (Dodgson, 1867). I also discovered, quite incidentally, that a contemporary of his, Sylvester, worked on the determinants of rectangular matrices (Weisstein, date unknown-c). It then occurred to me that the ingredients could be arranged into a rectangular 3 x 4 matrix of letters, with 25 perhaps representing a determinant. Unfortunately, I could go no further forward with this idea – partly because the mathematics is currently beyond me, and partly because there is still a crucial element missing: the key to the matrix. I was unsuccessful in finding a copy of Dodgson’s matrix cipher, which may be the key – assuming, of course, that I am not seeing patterns where none exist.

Conclusion

As a disclaimer, I should say that I have an intense dislike of computer games. This dates back to my early experience of programming in the mid to late 1980s, when running silly games on a computer was irresponsible and wasteful. However, I do acknowledge that some games can be educational, and therefore worthwhile. L – A Mathemagical Adventure has thus been an interesting look at the possibilities of such games. I found there is plenty of food for more advanced thought – up to A Level and beyond in some tasks. The literary allusions are amusing, and could be useful in broadening students’ views on mathematics, too.

When drawing the map, I noticed that the palace is missing much of its ground floor. Perhaps it is a fully-working evaluation copy, missing some additional ‘levels’: some objects are of no use; some tasks are unconnected to the quest; and there are unresolved issues at the end of the game. If so, then I would love to play a full version – which is high praise indeed.