Sunday 28 June 2020

Where's My Hammer?

Where's My Hammer? by Dee Dixon
No! I have not taken leave of my senses and decided to use forbidden tools on a wooden puzzle! Today we have a surprise guest blog post from a new friend who I have met at a couple of the recent Midlands Puzzle Parties - Michael Quigley seems to have gotten sucked into the hobby hook, line and sinker and not only has he spent a fortune on lots of new and expensive toys, he's joined us at puzzle meetups, but he has also managed to get himself cajoled into writing something for my silly little piece of Internet! I am very grateful to him for writing up on a puzzle that I don't own and technically cannot justify buying because (horror) it's a box and we all know that I don't collect boxes!

My Covid-19 infection has begun to settle, thank goodness. Last Tuesday, I finally felt like this damn thing was not going to kill me! My progress is slow - mainly now my symptoms are just being very quickly fatigued and with minimal effort. I'm back to work tomorrow which is going to be rather interesting (especially as my first day is doing emergency surgery) - here's hoping that it's not as bad as I'm expecting. Thank you everyone for your support and thank you to Michael for helping me with a blog post. Over to you, mate...

Like Pavlovian dogs, there are certain trigger words that have many a puzzler salivating on command: puzzle box (Ed - nope, not my thing!), sequential discovery and exotic woods to name just a few (Ed - drooool!). So when Dee Dixon released Where’s My Hammer? – a sequential discovery puzzle box, handcrafted from exotic woods, the frothing mouths of the marauding metagrobologists caused a spike in humidity that was lucky not to ruin the very boxes they coveted.

Beautiful wood!
Professionally known as DedWoodCrafts, Dee Dixon has been producing decorative boxes and puzzle boxes for many years in his spare time.  Often tested on friends and family it was the production of a prototype box that led the tester, who was unable to open the box, to exclaim “where’s my hammer?” and the box’s name was born (Ed - was he an orthopaedic surgeon?).
Dee has started to mass-produce a few designs and selling via Cubic Dissection, Where’s My Hammer? was the first of these to be released on there.  The release didn’t last long however with all copies selling out rapidly and leading to Dee’s Blinded II box set for their Cubic Dissection release at the end of June. (Ed - after a little "mishap, this is due to go on sale on Monday 29th June).

The box itself is a hefty piece of wood, which has a weight and sturdiness to it that makes you feel like it is up for a fight. That is not to say it is an ugly box, far from it, it is a lovely crafted box adorned with a plethora of fancy wooden panels, many of which I can’t identify.  It is a tactile puzzle, which is lucky owing to the amount of time I had to handle it. On to the solving experience…

Now I don’t have lots of experience solving sequential discovery puzzle boxes but I thought long and hard and realised that there must be a thing or two to do before the lid comes off.  Instantly disregarding this I try and open the lid to feel that it has some give but nothing much else.  There are a few rattles from within and I start tilting the box from side-to-side trying to uncover its secrets.
At this point my other (much better I’m told) half looks at me.  Usually this means “your toy is making too much noise, go and play in the other room” but this time she asked if she could “have a go” (Ed - gasp! A wife that puzzles? Maybe some wife-swapping is in order? Whack! Ouch!). Here I was stuck in a conundrum, whilst I want to show willing and involve my NPSO (non-puzzling significant other) in my hobby I don’t think she really understands the unwritten rule (someone should really write a long list of rules down somewhere – say on a Facebook page) of the puzzling communities “no spoilers”.  Meaning that the second she found anything I was going to be told.  Luckily after 5 minutes of her playing she was no further along the solve process than when I had handed her the box. Relief!

Any tools here?
My first few minutes were a little more fruitful and without too much trouble I was able to gather together a collection of tools and pieces (at this point I wasn’t sure which was which) before grinding to a halt. A long halt. I tried everything I could think of using everything I had found. I even tried putting the box all back together and going through the solve process thus far in the hope that I would have enough momentum to propel me to the next stage of the solve… but to no avail.  I once read that thinking© helps, so put the box away for the night and tried this approach the following night and the night after that until finally I made my breakthrough.  At this point I should mention that one of the things I was trying was correct, I just wasn’t trying that thing correctly! The final steps came quickly to leave me joyful, relieved and amazed at this wonderful box. I’d say there was only one step towards the end that I wasn’t a great fan of but everything else about the solve was a joy.

In total, and depending on how you count these things, there are probably between 7 and 10 steps for the total solve. There is nothing hugely revolutionary in the construction of the puzzle or mechanics used but the build quality, design and aha moments of this puzzle mean it is a great one to try.  I’m certainly looking forward to sharing this box at the next puzzle party I go to and if my patience wears much thinner I’ll be sharing via the good old Royal Mail before then.  A super box from a new designer that is definitely worth getting hold of.

Thank you Dee for the production of this box.

Thank you Michael,  for sharing this with the "group" - I am very grateful for the effort you put in and a new voice on the blog! Hopefully we will hear from you again before long!

I am back to puzzling and have even managed to solve a few things whilst I have been off work - I am looking forward to regaling you all with tales of acquisition and utter stupidity over the next few weeks and maybe even a puzzle success or two!

Do take care of yourselves in these trying times! I have noticed that the virus has been very much on the upsurge again in parts of Europe and is close to being out of control in much of the USA - be careful, keep socially distant - there is absolutely no need to congregate just now. Masks (and other face coverings) may help protect others from you and certainly don't do you any harm. Your "freedom" should not be significantly impinged by wearing a face covering - think of others!

Sunday 21 June 2020

Too Stupid For a Life Lesson

Rhombic Tuttminx from Leslie Le's VeryPuzzle
I do apologise for missing a week! I am incredibly proud of the fact that I have posted something here every week for many years with only my mother's death and now my own frailty preventing me keeping a perfect record! Let me explain a little...

There had been a rather large outbreak of Covid-19 on one of the wards in the hospital that I get to visit pretty frequently. Quite a lot of staff and patients who have visited that ward have unfortunately been struck down. I was unaware that they had a problem there and visited to assess patients for surgery as I always do. The aortic aneurysm repair went well and I had no inkling that there was a problem at all until 4 days after visiting the ward. Whilst working one Saturday doing an orthopaedic trauma list, I developed a headache (literally that was it - just a headache!) I didn't think much of it - I was not aware that I had been in contact with anyone infected and I had no fever, no cough, none of the "cardinal" symptoms! The headache got progressively worse and at the end of the day, I was glad to get out of the PPE (7 hours in an FFP3 mask is VERY unpleasant with a stonking headache!) On the Sunday the virus hit me...hard! I had a high fever, muscle aches, feeling very unwell and just a slight cough. Oh damn - here we go! I spent most of the day in bed and arranged for a Covid test the following day. The drive to the testing area at work was unpleasant with a high fever. I was absolutely not going to risk having a false negative test! The false negative rate is 40% partially due to the fact that taking the swabs properly needs a really good swipe and is very unpleasant (I suspect that most people who do that to themselves don't do it properly. Swabs taken, I had to wait 5 minutes before my eyes would stop watering enough to be able to drive away! At 7pm the virologist called to tell me the result - Mrs S was convinced already because, of course, I had managed to infect her already and she was feeling really rotten! She's too weak just now for a Whack! Ouch! but I am sure it won't be long! In my wake, over the next 24 hours, a whole bunch of people were sent home to self-isolate and I appeared to have become the Typhoid Mary of Sheffield - they're calling me "Covid-Kev"!!! In my defence, I had none of the suspicious symptoms until 2 days into the illness. As far as I know, no-one has caught it from me.

This virus is horrific! For many there are no symptoms but for others it kills and you do not know which way it will go until it reveals its' path to you. I had already been a little worried, due to pre-existing health issues, that I might fare badly and was really very worried that I might have killed Mrs S! For me, I have never been so ill in my life! The fever lasted another 2 days and the myalgia with it. Cough has been a relatively mild symptom but the fatigue has been appalling! Every small thing has required me to lie down afterwards. I spent 9 hours or so writing the on-call rotas on Thursday (if I was forced to be at home, I figured that I might as well do some office work) and the following day I felt like I had been run over by a truck. A colleague summed up my stupidity:
"Thanks for summoning the energy to do a rota whilst infected with a life-threatening viral illness"
That sort of puts my stupidity at the forefront! I should have realised how sick I was when I just left a fabulous package of new toys from Mine unopened in my porch! A puzzle parcel remaining unopened for 6 days is an indicator of just how severe this illness can be!

Please continue with the social distancing, wear a mask when you have to be close to people outside your immediate family bubble and, for goodness sake, stay away from Trump rallies!!! Nothing clever will be said there and you may well catch something lethal!

Now, before I got ill I had been playing with one of the wonderful spherical puzzles from Leslie Le's VeryPuzzle. I started with the Behemoth that is the Rhombic Tuttminx - I own an ordinary Tuttminx and have never had the courage to scramble it. Like the original, the Rhombic Tuttminx consists of pentagonal and hexagonal faces but they differ in that the hexagonal ones are not able to rotate through 60º angles, they are limited to 180º turns. I figured that this should make the puzzle a little simpler to solve.

It is an absolute beast at 14.5cm diameter (5.7in) and weighing in at 0.37Kg/082lb. I paid a few dollars for the stickering to be done for me and I have to admit that was worth every penny - it looks like an absolute nightmare to sticker. When I showed it off at work, it got plenty of admiration for being a very attractive puzzle.  Derek, told me that it wasn't that tough to solve but he's a genius and I was really not sure that I would be able to solve it. It finally took me about 2 weeks of carrying it around with me before I got the courage to scramble it:

Just as gorgeous scrambled
It took me about 2 hours to achieve an adequate scramble and move the pieces as far away from their origin as possible. Then where to start? On Facebook someone had suggested that a Megaminx (standard dodecahedron) approach would probably suffice and I tentatively agreed with them. Hence, I started with a pentagonal centre which would leave me as another pentagon as my final face to solve. The movement is stunningly smooth (considering there are 302 visible moving parts) and the initial solve process is nothing more than intuition. The texture on some of the stickers adds a little to the complexity but not too much and the recreation of the solved conformation progresses in a very pleasant and fun manner. I almost found it soothing!

Having reached the equator, I was a little worried that the level of difficulty would escalate but just carried on as a fully intuitive solve. I really enjoyed it despite the sheer size of the process. Finally, I was left with the last pentagon and surrounding hexagons. Far less movement was now possible and I realised that it was very similar to a Megaminx except for the 180º limitation. This actually made the puzzle rather similar to a 3x3x2 cuboid. Once I had realised this then solving the corners around the pentagonal centre proved to be remarkably straight-forward until I was left with this:

Just 2 pieces were interchanged! What on earth? I spent an unfruitful hour or so trying out various 3-cycles to unravel it before realising that this scenario is physically impossible! On a puzzle that is "odd order", a 2 piece swap or parity cannot occur without there being an error elsewhere or without someone having peeled stickers off.

I knew that no-one had spent enough time with it to peel any stickers off behind my back so I had to spend a frustrating time hunting for my mistake. Many of the colours are pretty similar and in the end I had to go out into the garden to get really good sunlight and discovered the error of my ways:

So similar - it took me 2 days to find it!
One face has lovely shiny sparkly stickers which unfortunately look almost indistinguishable from each other except in very bright light. Having discovered this, a bunch of set up moves and 3 cycles were quickly arranged and it was solved!

This puzzle is stunning! It is gorgeous to look at, beautifully made and a fun solve which is 95% intuition. If you have any kids who are just getting into twisty puzzles and they may want something that looks fearsome but still within their capability then this is just the ticket! This was the last puzzle I played with before I got sick and I am looking forward to playing with it again when my attention span improves. I also have a few new toys from Mine to play with as well.

Stay safe everyone - do not take any risks! It just isn't worth it! If you work in a hospital then you have no real choice but if you don't have to go and mingle with people then don't do it!

Sunday 14 June 2020

Too Sick to Puzzle or Blog

Hi everyone,

I’m sorry to say that this will be the first Sunday in several years that I’ve missed. Unfortunately, I’ve either got a very bad summer cold or I’ve caught Covid-19 at work. Basically, I’m more or less bed bound and feeling like death warmed up. Will be tested tomorrow and hopefully negative but definitely not up to blogging today. I do apologise! Hopefully normal service will be resumed next weekend.

Sunday 7 June 2020

A Puzzling Pot-pourri from Hawaii

A pot-poured of positively perfect puzzles
Yet again in my hour of need, I receive an email from the Mike Desilets, the official PuzzleMad foreign correspondent, offering help with a truly wonderful article. I have been working on a particularly fun and beautiful puzzle for a couple of weeks now but have gotten to a point where I’m rather stuck. I’m currently waiting for inspiration to strike me but with the dirty looks that Mrs S is giving me, it may be her who strikes me instead! I need to stop swearing at puzzles whilst she is watching TV. Without delay I’ll hand you over to Mike for a fascinating romp through a wide range of challenges.

Aloha Kākou Puzzlers,

Today’s Foreign Office installment will be a puzzle pot-pourri. I have a few tightly-focused articles in the works, but none of them seem anxious to finish themselves. Sometimes this stuff becomes actual work and motivation drops off a cliff accordingly (Ed - I know that feeling!). So, in the interest of procrastination, I decided to adopt a more classical blog approach and simply take pictures of stuff I have worked on recently and opine. Less depth, more variety.

We begin where we left off with Hip-flask. In the midst of writing the Hip-flask post, I ordered a copy of Felix’s Titan (in the UK get it here). It was bound to happen. The puzzle is just as advertised: two brass hemi-spheres, inexplicably joined. It is very beautiful, as only a metal sphere can be. This would be a worthwhile purchase even if it were not a puzzle. Having now seen the quality of the interior machining, I really wonder how this can be made so inexpensively, and in the UK no less.

Titan, by Felix Ure.
A nice even patina is developing; no polish necessary.
It didn’t take long to realize that my first impressions of the puzzle, based on various online sources, was correct. This puzzle falls squarely into the mystery-object category. There is an internal mechanism holding the pieces together and something is clearly rolling around inside. The hemispheres rotate past one another freely, until they do not. They also separate slightly, but nothing internal is visible. I tried the standard solutions, followed by non-standard guesses, followed ultimately and inevitably by random shaking, twisting, spinning, and pulling (Ed - now that is my kind of solution method!). After a solid week and a half of this, an hour or two each night in front of the television, I achieved separation. The early solvers were right, it’s a great feeling when it comes apart. By the time it happens, you have basically lost all hope. It’s really quite a pleasant shock. Of course, you shouldn’t pat yourself on the back too much. This is an exercise in patience, not cleverness. For myself personally, if not for the TV multi-tasking, I’m not sure I would have stuck it out. I’m not getting any younger, after all, and I can test my patience in other, more productive ways. That said, I am THRILLED to have opened Titan. The internals are the very definition of beauty. The mechanism is simple, principled, and obviously very effective.

Below is an image of the internals, if you are interested. It does not show everything, and certainly not the critical components. I doubt VERY much that this will help you solve Titan, but out of an exceedance of caution Kevin will put it behind a spoiler button:

B-Lock II - Brass body and steel shackle
Packaged in a beautiful embroidered bag
Nice touch Boaz!
Moving right along, I also had a chance to play with Boaz Feldman’s B-Lock II this week (Ed - I reviewed it in March). This had been on my shopping list for a while, but I always found some reason or other to push it aside in favor of other purchases. I enjoyed B-Lock I (Ed - reviewed here), but hadn’t heard or read much about the new release. Now that I have it, I regret putting it off, and you should not hesitate the way I did (Ed - both are often available direct from Boaz on his Etsy store). This is a really fun puzzle lock and I would even go so far as to say that it is underrated, or at any rate under-appreciated. With the likes of Rainier and Shane producing great stuff, and the legacy of Dan Feldman himself hanging over the sub-field, you can see why this might occur. But B-Lock II doesn’t have any pretensions at that level, and I think Boaz would be the first to admit that. What B-Lock II does have is a high-quality build and a very original and clever mechanism (to me at least, admittedly not a lock expert). I can tell you, without fear, that it has two components, and these must synchronize before the lock will open. One is a common lock ‘gimmick’ and the other is something new (to me).

B-Lock II is not particularly complex, just very crafty and efficient, especially given the limited material provided by an off-the-shelf padlock. After you initially open it, you will not know exactly why unless you study the internals. If you immediately close and reset, it could be a while before you get it open again. For me this puzzle provided a solid half hour of entertainment, which is precisely what I want from a lock in this range. In fact, I think we could do with more locks of this type: affordable, available, fun, and very well crafted. We often get the last two, but not always the first two. Overall, I think it’s a real winner from Boaz and I heartily recommend it. It is worth remembering that Danlock was not invented overnight (Ed - available here and here). With what we have seen from Boaz thus far, I can’t help but think that he is building toward something.

An unlocked lock.
Ok, enough of that. I can only take so much cutting-edge puzzlery (Ed - is that a word?). Time to retreat into the annals of history. Out of respect for my gentle editor, and in light of the possibility that he can write prescriptions (I can indeed!), and would do so for me if I please him sufficiently (not across the I won’t), the remainder of the post shall be not only historical, but also decidedly Anglo-centric.

Bike parts
So let’s look next at a fun little puzzle called “BILD-A-BIKE,” which I gather from the Slocum Collection website originated in the mid-1950s. I imagine it was produced right through the 1960s as well, but I really don’t know and there is not much information available online. BILD-A-BIKE was produced and sold by Chad Valley, a company Kevin is no doubt familiar with (Ed - never heard of it! Have you heard of every small company in the US?). Chad Valley were, at least in the previous mid-century period, a premier English toy company (Ed - I wasn’t born then!). They have a fascinating history which you can find at the Woolworths museum webpage here.

Chad Valley was a toy company, first and foremost, but most every toy company had mechanical puzzles in their product lines at that time. In addition to BILD-A-BIKE, Chad Valley also produced a couple of boxed sets of entanglements, all of the standard sort. They produced a broad range of jigsaw puzzles as well. Otherwise the line was 99% toys and games. Despite a long and honourable history, Chad Valley basically ceased to exist in any meaningful way following their 1978 purchase by Palitoy. The product line was chopped up and sold off and independent production ceased. Subsequent owner Woolworths attempted to revive and capitalise on the Chad Valley name in the late 1980s as part of its ill-fated modernisation programme. During this effort, Chad Valley was reoriented as the face of a line of toys directed to the very young. The brand remains that way today under new owner Argos, virtually unrecognisable from its historical roots.

True enough, although the playing will flake and chip with normal use, a stainless version is needed
For the mechanical puzzle aficionado, BILD-A-BIKE is probably the most interesting Chad Valley product. It is a put-together puzzle in which you quite literally build a bike (or perhaps I should say bild? Check this). The pieces are nickel-plated iron, or maybe steel, I’m not sure. The pieces are “rustless,” as the packaging proclaims, but only to the extent that the nickel plating remains intact. You will probably have to look hard to find a pristine set. If you do find one, and want to keep it that way, then do not BILD-YOUR-BIKE!

As for solving, it is not any great challenge. The wheel/handlebar and wheel/seat connections are a little tricky. It is definitely a challenge to keep the front part assembled as you work on the back, and vice-versa. Dexterity is definitely required. Light force is also required, since the assembled bike is largely held together by tension.

Although obviously targeted at a younger demographic, BILD-A-BIKE is an enjoyable little puzzle for all ages. There is no Ah-ha! element to speak of, but it is very satisfying when the pieces come together and take the shape of a bike. I recommend this puzzle as a cool-down after solving Titan. In the final analysis, BILD-A-BIKE is a charming footnote in English mechanical puzzle history. I humbly suggest that my editor and patron MUST purchase one and also that he MUST give it a prominent place on his shelves. I await photographic proof. (Ed - I’ll see if I can find one)

Ok, time for one more, staying on the English theme. How about a shunting puzzle? I did a post a while back on these. Kind of a rare class, but they always fascinate me. When I came across a copy of Chunnel Trouble? a while back, I snapped it up without a second thought. Chunnel Trouble? (that question mark is going to get tiresome) was made by distinguished, though tragically inactive, English puzzle producer and seller Pentangle. Chunnel Trouble? is a fantastic revival of a classic shunting problem, probably THE classic shunting problem. It also sports a contemporary and quite ingenious design, packaging, and marketing approach. It is, in effect, a nineteenth century puzzle in new clothing.

Chunnel Trouble? Not really. 
Although there is plenty of shunting (or switching) involved with actual Channel Tunnel operations, it likely bears little resemblance to the Chunnel Trouble? layout. Regardless, Chunnel Trouble? is a delightful design. According to the box, the trains can pass each other in 33 moves. The siding looks like it will hold only two cars, if that. This puzzle can alternatively be solved using slips of paper, or whatever objects you prefer (except marbles); you don’t necessarily need to own the actual puzzle. Most shunting puzzles are that way. The physical version looks very well made, possibly in maple, and most definitely in England.

Why do I seem a little cagey in my description? Well, that’s because I have not actually played with, or even touched, this puzzle. It’s a rare occurrence. I cannot play with this puzzle for the simple reason that it is in its original packaging, sealed, untouched, and unspoilt. The Channel Tunnel was constructed between 1988 and 1994. I don’t know the actual date for this puzzle, but it should fall within that range, or close to. Kevin or the MPP chaps will doubtless enlighten me. I do know that it is currently 2020. So given the time gap, whatever it may precisely be, I clearly can never break the seal on this puzzle. I could not bring myself to do it when I first bought it, and after anguished consideration, I’ve decided that I never will. Pristine examples are a sacred trust. Also, given the fact that the puzzle can be ‘played’ any number of other ways, there is really no call to grub it up like a complete barbarian. Instead, I’ll just squirrel this copy away until it is the only unopened Chunnel Trouble? left in the world, the fundamental conceit of the vintage collector.

Instructions to help get you out of Chunnel Trouble.
This English puzzle jig is fun, and I definitely want to leave my editor brimming with tears of nostalgia (Ed - that would only happen if I could remember any of these toys). Here then, is one more. It slots in somewhere between the last two on the temporal plane. It is called Perfect Circle, part of the Waddingtons House of Games Mindbender series from the very late 1960s and early 1970s. There are at least six other puzzles in the series. Perfect Circle was apparently developed by House of Games, a Canadian company, and then licensed and manufactured by storied English game developer and producer John Waddington LTD. “House of Games” was traditionally part of the Waddington moniker, and it seems to have come and gone periodically over the course of the previous century. How it ended up in Canada I’m not sure. In any case, after a long history of service to the game-playing English public, Waddingtons was sold to Hasbro in 1994. I assume it is now no more than a residual-value brand name like Chad Valley. Check out this fun article for a trip down memory lane. If you want to learn about Waddingtons contribution to the war effort, definitely check this out. That must have been quite an A-Ha! moment for the boys.

Perfect Circle.
A low cost, high value puzzle from Waddingtons. 
Back to the puzzle. Perfect Circle requires you to make a perfect circle (is there another kind?) out of 16 variously-cut pieces of colored cardboard. There are four shapes and three colors, as the instructions indicate. This is not the whole story though. There are actually eight distinct pieces, because two of each of the four shapes is a mirror reflection of the other two. They certainly look the same, but they are not interchangeable. This is tremendously important, and starkly apparent, once you try to comply with the matching rule on your as-yet imperfect circle. The rule that makes this puzzle more than a simple geometric assembly is that no two colors may touch side-on-side.

The rule of engagement.
Initially, upon dumping the pieces out, it seems like Perfect Circle might be a hair puller. Soon, though, you realise the importance of symmetry and things begin to accelerate. You will also quickly differentiate the outer pieces with curvature from the inner pieces without. It all starts to come together as you mix and match pieces.

Although finding the solution on first assembly is possible, know that at least two distinct circles can be formed which will never meet the matching rule. I had to work through both of these before I discovered the correct assembly, and actually began to think my puzzle was broken at one point. I had become obsessed with certain circle designs that seemed so beautiful they simply had to be correct. The puzzle fooled me, to its great credit. Yet again I had willfully disremembered the Tungsten Rule of solving: once you establish the theoretical impossibility of a given solution, you MUST move on (Ed - where did that come from?). Anyhow, it was a really fun solve and I highly recommend this modest little puzzle.

Is the circle perfectable?
Kevin, capstone of my arch (Ed - I don’t think I’ve ever been called that before!), I think you can find Perfect Circle for well under a tenner at any given boot fair (Ed - not in this age of social distancing it’s not!!!). Take poor Mrs S out of the house for once in your miserable life- make an afternoon of it. Your ulterior motive need never be known. It will be just between you, me, and 100,000 random blog readers. Whack! Ouch! Ed - Mrs S will not ever go to a boot fair!! She only shops in the finest of retail establishments! I’ll need to look on eBay. 

That’s all for today folks. Hopefully this post was a good change from the usual foreign office material. It was definitely refreshing for me. Ok boss, over to you for the wrap-up...

Wow! What an odyssey! I enjoyed that a lot, thank you, my friend, for a fantastic romp through puzzles old and new, cheap and rather expensive, but all looking quite fun! I am really so grateful to you for taking the time to write for me and the readers and for providing me with some entertainment.  I always look forward to what you produce - it’s always something I’d never have found myself and it makes me think.