James Dalgety’s Pythagorean Puzzle

I know – you really don’t deserve this... but I remember a shaggy dog story from my school days that went something along these lines: 

There were three Indian squaws. One slept on a deer skin, one slept on an elk skin, and the third slept on a hippopotamus skin. All three became pregnant. The first two each had a baby boy. The one who slept on the hippopotamus skin had twin boys. This just goes to prove that... the squaw of the hippopotamus is equal to the sons of the squaws of the other two hides.

The really sad thing was that we all heard it after we’d learnt about Pythagoras’ Theorem, and I still had to explain it to some of my mates ... right, where was I? Back to James’ puzzle...

I acquired my copy of this puzzle, James’ IPP30 Exchange Puzzle, from Wil Strijbos when he was visiting for our last MPP. He had a couple of copies in his crates for sale and I thought it looked quite interesting so bagged a copy for myself.

The puzzle is made of acrylic and has six pieces resting in a black tray – with each piece having an obvious space as they’re all different sizes and / or shapes. The accompanying instruction sheet tells you that your quests are to:

• Prove Pythagoras’ Theorem using all 6 pieces, and make rectangles using 3, 4 and 6 pieces at a time.

I set about the first task, pretty sure that I knew exactly what was being expected of me ... Pythagoras’ Theorem holds that the sum of the squares of the two shorter sides of a right-angled triangle equal the square of the length of the side opposite the right-angle ... and it’s often represented as showing that the area of the two squares sitting on the shorter sides equals the area of the square that sits on the longest side. Can you see where I’m going with this? (Seriously, if you can’t, you’re reading the wrong blog!) 

OK, deciding on a suitable right angled triangle isn’t too tough and the first part (the two smaller ones) wasn’t too tricky – so I had a bash at building the larger one ... and it wouldn’t quite work ... so I fiddled around some more and started experimenting – rather a lot – and every now and then I’d find a smaller rectangle and tick another of my quests off the list, but that larger thingamabob evaded me for quite a while. At one point I even found myself chatting to James on the phone about some arrangements and asked him if there was some sort of a sneaky trick and he set my mind at ease, and really just told me I hadn’t tried hard enough, but in a really nice way! :-)  He also told me that the really hard one was the large rectangle...

 

So I kept having a bash at it every now and then, whenever I had a chance, or whenever Gill had hijacked the PC, until eventually I only needed the two largest constructions – but I kept plugging away until eventually I found the second half of my proof, and it was a little sneaky, but I kept my head and thought things through a bit and mulled over whether I could get away with calling a square a rectangle (Technically I believe I can – it’s a special case of a rectangle, I think) and thereby bag both of my final two quests in a single shot – but the challenge got the better of me and I duly came up with a real rectangle a couple of minutes later (and yes, I guess that could be a teeny little clue for anyone still playing with this puzzle).

I quite enjoyed playing with this puzzle – the odd shapes play havoc with my little pea-brain yet the angles all seemed to combine to produce just the right angles required – even when the sides weren’t combining the way that they should! There are stacks of blind alleys to explore and having a couple of different challenges to keep you moving along is always a nice idea.

Gillen Bolts

Marcel Gillen has been a prolific puzzle designer and manufacturer for quite a while now. Possibly best-known these days for his good-looking aluminium chess pieces – every collection needs at least one of them – he’s been making handsome brass and aluminium puzzles for years. With the advent of the Bits & Pieces versions of the chess pieces, there are certainly a lot more of them around – but I suspect that the quality of the originals can’t be beaten – although 'can’t be found for love nor money' might also be appropriate in that sentence!

I’d at least seen some pictures of some of the original chess pieces in photos of various esteemed collections around the world, but when Wil Strijbos offered me a few Gillen Bolt puzzles, I drew a blank … I hadn’t heard of them and couldn’t remember ever seeing mention of them, so I did what anyone else in my position would do, and asked Google.

Turns out Google knew – and directed me to an early lot in Nick Baxter’s puzzle auction – where a couple of Gillen Bolts #6 had been sold a while back – and Jerry Slocum’s collection which has pics listed of Gillen Bolts #1 and 2.

Wil had come across a set of three Gillen Bolts (#’s 1, 5 & 6) and after my brief bout of Googling, I eagerly agreed to take all of them. Wil reckoned he hadn’t seen these puzzles around in absolute ages and Nick Baxter’s auction site lists them as “pre-dating 1994”.

When they arrived, the first thing that struck me was the sheer weight of them – these aren’t little bolts that have had a trick mechanism inserted into them – these are chunky hand-turned brass puzzles loosely in the shape of a bolt – a very large bolt – picture the sort of bolt you might use to keep a bridge together!

I started fiddling around with them and managed to sort out #1 fairly quickly – it’s a reasonably straight-forward mechanism and depending on how you handle it, you may get lucky as I did and not be too bothered by the locking mechanism … one down, two to go…

…and this point in the story coincides with our Midlands Puzzle Party #6 – so I took them all along for the world to have a bash at them – a few folks opened #1, but nobody got anywhere on the others, which made me feel a little bit better about not having opened them yet. At MPP6, Wil had brought another copy of Bolt #5 (or was it 6?) along and Ali snapped that one up – and then duly went and solved it that evening, proving he’s way better at this than I am!

The Bolts then stared at me from my shelf-of-puzzles-to-be-solved for a couple of weeks and then two Sundays ago I decided I needed to clear some things off the shelf, so had a more serious go at #’s 5 and 6…

This time I applied a more methodical approach, and a Sharpie pen in the quest to open these puzzles – and the method paid off as I was able to understand first #5 – “seeing” where I could and could not go, and making some Sharpie marks on the bolt – and then working out how to get around the “obstacles” – great feeling when the nut lifted clear of the bolt.

Flushed with success, I threw myself at #6 and spotted some similarities in the way that the nut behaved – but got a bit confused when “coming” and “going” didn’t seem to work the same way – a little more brain was engaged, a theory concocted and duly tested, to provide a great little moral boost when it actually worked.

As puzzles, they’re really interesting – having seen #’s 1,5 and 6 – there is a definite progression in terms of complexity – and a change of gear somewhere in between. Filling in the blanks a bit, I’d guess that the set from 1 through 6 would provide a lovely set if increasing challenges to a puzzler. The craftsmanship on these puzzles is excellent – some of the parts have an amazing array of moving bits and pieces that all work absolutely perfectly – twenty years on. Testament not only to the design, but also to their crafting … they may look similar on the outside, but they’re anything but! And the relative simplicity of #1 belies the trickiness of #’s 5 and 6, whose elegant design makes some very clever use of some aspects that hide the true goings-on in there beautifully.

Very chuffed to have been able to add these rather rare puzzles to the little hoard – thanks Wil!


Postscript: Last weekend I got to spend some time at James Dalgety's Puzzle Museum and I asked him if he happened to have any of the other Gillen Bolts?

Hey, I thought it was worth a try!

Anyway, he points me at a drawer and I dive in to find piles of the things! So not only did I get to have a play with numbers 2,3 and 4 (and solve them all), but I also got to fiddle with number 7 (and I had a pretty good idea of how to get that one open but I didn't want to draw on it!) and play with a couple of unnumbered prototypes... Thanks James!

Coffin Involution Cube

A short while back I was trading emails with Scott Peterson when he mentioned that he’d made a couple of copies of Coffin’s Involution and there was one going if I was interested –about a week later it was in my grubby paws. 

Scott was telling me that Involution is possibly one of Stewart Coffin’s less well-known designs and was an interim stage in the development of the Involute Cube – with Mr Coffin then favouring Involute over Involution. Having played around with both of them, Scott reckons he prefers Involution – and frankly I was sold on the idea from the point where he said he had one available! 

My copy is made of wenge with olive wood picking out the corners. I’ve waxed lyrical about Scott’s craftsmanship a few times in the past and this puzzle is no exception to that rule. The fit is that good that Gill was convinced it was actually a box or a solid block – there is no clue to where the first piece is going to come out at all, and given this is a Coffin design, you’re not going to find it easily and it’s probably going to involve some sort of a strange Vulcan grip. Visual inspection is totally pointless given Scott’s fine craftsmanship, so I reverted to a methodical fondling to find something that might move...

 

Like Involute, there’s a key piece, slightly more oddly shaped on this puzzle and removing it allows one or two other bits to move, which in turn allows some funky stuff to happen. The family resemblance between Involute and Involution is hard to miss – there’s a really interesting section a little way in where both will let you have plenty of movement, without any pieces looking like they’re going to come free ... and Burr Tools won’t help with either of them! :-)  If anything, the funky bit in the middle is slightly simpler on Involution than on Involute – and perhaps that’s why the great man favoured the latter.

The first time I took Involution apart it really felt like a voyage of discovery – each successive move was incredibly well disguised – the fit is that good that the pieces cling together and don’t move at all, until you find the right places to put pressure on the assembly to get something moving. This puzzle doesn’t give up its secrets easily and the combinations of movements required, and indeed the rotations required keep things interesting. 

Some designs begin giving up their secrets more and more rapidly as you progress – somehow this design doesn’t do that and it continues to force you to think and analyse the possibilities right through to the end ... in fact, there’s a spot about halfway through where you’ve already removed four pieces, but there’s no clue at all as to where to look for the next piece to come off ... and Scott’s work is that good, that even the last two pieces stay solidly together until you work out what the two shapes are and how they come apart.

Another cracking Coffin design expertly crafted by Scott Peterson – thanks Scott!

Slow Waltz

I was really looking forward to getting my grubby paws on Eric Fuller’s version of Jeff Namkung’s Slow Waltz. I’d played around with a couple of Jeff’s designs courtesy of Richard Gain’s Shapeways versions and found the designs were excellent, so the prospect of getting my hands on a beautifully crafted wooden version was more than a bit tempting. 

My copy is made of sapele and macassar ebony and lives up to Eric’s normal exacting standards. The two woods give a bit of a clue to the shapes of the pieces – but don’t really make it too easy, after all this is a level 14.8 puzzle, so there’s quite a lot of business to be done before you can release any pieces at all – and it stays interesting pretty much all the way through to the end, with the last two pieces not exactly falling apart either. 

The puzzle starts with an almost complete 4*4*4 cube – there’s a cubie missing from one of the faces. From there you start by opening things up a bit and making some room so that you can get some of the more useful bits moving around – there are a couple of really unusual moves that might evade you for a while, depending on how you grip this puzzle. I discovered a couple of blind alleys during the disassembly (and several more on the assembly!). It’s a fun puzzle to sit and resolve as the movements do seem quite choreographed with things first going one way, and then the other. 

It may only have five pieces, but this is a really good design ... for ages I found myself stumped on working out how to introduce one particular piece because the “obvious” way to do it turns out to be less than useless. This is probably the cube that I’ve had to take apart and reassemble the most in order to get to know it – it’s a great little challenge.

...now if only I can get myself to stop counting 1-2-3 ...   

   1-2-3 ...                           

as I'm taking it apart...

[Kevin's written about his thoughts on the Slow Waltz in this post.] 

Wil Strijbos' First Box

One of Wil Strijbos’ recent emails contained a couple of new puzzles: a new variant of an impossible dovetail joint and a blue box that sort-of resembled a tardis from Doctor Who – called First Box.

First Box as you might expect from the name was the first puzzle box that Wil designed many moons ago. When I visited Wil last year, he'd pointed out a black and aluminium box on one of the puzzle shelves that housed several other Strijbos originals and he'd mentioned that it was his first puzzle box and that he was hoping to have some produced in the future. He wanted to give me a shot at it, but sadly whoever had played with it last hadn't locked it up properly, so it was placed back on the shelf...

Since then Wil has taken the opportunity to improve on the design (read: make it harder!) and has also found a neat solution to an aspect that concerned him about the original version. The original came with a separate tool - which bothered Wil a bit - so he toyed with the idea of not including it and suggesting that puzzlers make a trip to their local hardware store and buy whatever tool they thought might be useful to get into the box - however recurring nightmares of puzzlers merrily heading off to their local ironmonger and purchasing a large hammer stopped him from trying that. So the new design dispenses with the external tool... :-)

Father and son

My copy arrived literally days after I’d ordered it and first impressions were that this was a really heavy little puzzle – it’s very clearly not a box with a lot of space inside it … which probably means that it has a lot of gubbins inside there making sure that it stays locked closed. The lid has very little play in it to start with and has a large nut screwed into the top of it. The front of the box has Wil’s signature and a production number in the bottom right hand corner. There’s a small dark hole in the middle of the back of the box and a hole in the bottom that lets you see a small steel cylinder – which Wil has helpfully told us we are to get out of the box – although rather unhelpfully, that hole in the bottom of the box is too small to allow the cylinder out…

OK, so you have a seemingly impenetrable blue anodised box – you can see the lid has a little bit of play in it – there’s one obvious thing to try, so you do, and that’s not spectacularly useful, so you think for a while and explore a few more avenues before finding what one might loosely call “some tools”. Trying out various things with the tools you’ve discovered leads to some further discoveries – among them that sometimes the lid of the box feels a bit looser, sometimes there is a pin across that hole in the base, and sometimes there’s a pin across another hole.

First First Box opening

Wil’s helpfully told us in his email that there are no magnets and that no bashing is required – yet I suspect that most folks will be tempted to try that, if only a little every now and then…

During the course of your explorations you can start piecing together some of what must be going on inside there – part of the clues come from the sounds inside when you tilt the box this way and that – but the confusing thing is that those sounds don’t always appear to behave the same way! [Pixies!]

Add in the interaction of the tilting with the use of those tools and there is more than enough to try and keep track of – and if I’m honest – the first time I opened the box there was more luck than skill involved and I ended up spending a long time examining the innards to work out what I was doing… and then even longer to work out why my method actually works! (There’s something a little disturbing about finding a method that works absolutely reliably- but realising that theoretically it really shouldn’t work …and it took me a couple of days to work that one out!)

Solved!

This is a really good little sequential discovery puzzle – the tools are nicely hidden; the internal mechanism makes it virtually impossible to fluke a solution – the machining is really superb so everything fits beautifully (and slides around like steel on wet ice) … but once you’ve worked it out, everything is totally predictable – definitely a well-behaved puzzle – doesn’t leave anything to chance and doesn’t let you do anything you can’t undo … although I realise that until you’ve opened it, you might disagree with one or both of those wild allegations!

[And you don't have to take just my word for it - you can read what Jerry thought about it over here...] 

Some random bits and bobs

The last time I visited James Dalgety, he was having a bit of a clear-out and had put aside a bunch of puzzles in some plastic crates for swap or sale, including a special crate of interesting items to be offered on a future puzzle auction – those were well beyond my financial reach on the day! (I hadn’t ever seen a new-in-box Panex Gold Puzzle before … didn’t think they still existed …)

After I’d done a sweep of the duplicate books shelf and picked up some interesting titles and half of a set of Cubism For Fun magazines*, I turned my attention to the swaps boxes and picked through a veritable treasure trove. I seemed to keep stumbling across things I recognised as being rather special, from my puzzle-reading and it would have been very easy to spend a whole lot more.

I picked up three rather interesting little puzzles that afternoon.

Peppermint Twist was John Ergatoudis’ IPP17 Exchange Puzzle. Reminiscent of a twisted sugar cane, this is a sweet little puzzle. (Sorry, I’ll behave.) It consists of four twisted steel strands that fit together to make a stable, neat structure … as long as the pieces are in the right place.

Starting from the solved position, it soon becomes totally clear that the only way to get these pieces apart is to slide one of them out the end by twisting it out of the bundle, and once the first one is out, sliding the next one out is easier, and soon enough you’ll have four twisted bits of metal that all look rather similar.

Reassembly isn’t totally straight-forward as there are a number of ways of putting three strands together that look pretty good only to find that the last one won’t engage… and there are some almost-solutions that leave the last piece so tight that you may well damage something in the process of trying to slot it back in … but when you find just the right combination, the last piece slides in ever-so-gently, just like it was meant to.

A fun puzzle to fiddle absent-mindedly with…

I first spotted a copy of the Perplexity puzzle on Rob Stegmann’s mammoth web-site and thought it looked neat, so when I found a copy in the swaps-bin I put it on one side.

According to Edward Hordern’s Sliding Piece Puzzles book (acquired from James on an earlier visit) these puzzles were the subject of a 1900 patent and have been produced in several forms over the years.  Rob’s collection includes several variations on the theme in his section on Sliding Block Puzzles.

The one I got is a pretty tidy example of the main variant that was first produced in 1919 – I’m not sure exactly when this copy dates back to – but it’s almost certainly just become the oldest puzzle in my little collection, by a very long way!

The letters slide up and down the main track, with a couple of branch lines permitting a bit of storage and shuffling space and the aim of the puzzle is to spell out PERPLEXITY along the main track – first backwards, then forwards. 

My first thoughts were that it wasn’t tremendously difficult as a puzzle because there’s a fair amount of space on the sidelines and there are a couple of pairs of letters that are interchangeable – however I’d totally missed a couple of subtleties about the buttons and totally failed to understand why sometimes there seemed to be a lot more space to work with than other times ... and I only discovered those after reading Edward Hordern’s notes on this little puzzle...

It’s a cute little historical artefact that’s survived many years so far – I’ll try and keep it going for a bit longer… 

[Jerry wrote about his copy over here if you're interested in some more thoughts...] 

My third interesting little find in the swap-boxes was a copy of Allan Boardman’s IPP13 exchange puzzle – a Circular Tangram. At about two inches across it’s a dinky little puzzle, as you might expect from the chap whose burrs are usually measured in single-digit millimetres across. It’s a maple tray with a set of tangram pieces resting in it –and when I first had a look at the pieces I assumed they were some sort of thin acrylic sheet – they’re only about 1.64 mm thick and are black as night. 

I was somewhat embarrassed when a bit more research on t’internet informed me that the pieces were in fact finely cut ebony – wow – of course I then added to the embarrassment by admitting this to one or two more experienced puzzlers who had a good laugh at the fact that I could have thought mister Boardman would have used acrylic – I mean, really! <Blush>

* … and since then I’ve been in touch with Rik van Grol at the Nederlandse Kubus Club and managed to purchase copies of all of the other Cubism For Fun back issues that I was missing, so I now also have a complete set of (the English editions of) those magazines as well – plenty reading lies ahead.

Stickman Milestone Puzzle

...Some say he dreams about new puzzles and when he wakes up in the morning there’s a working prototype in his workshop.

...Some say he can fix broken puzzles by the power of thought alone and that he once suggested that Stewart Coffin look into using rhombic dodecahedrons.

All we know is, he’s called the Stick (man)!

With thanks and apologies to Top Gear.

Robert Yarger’s latest creation has been dubbed the Milestone Puzzle – and it certainly is a milestone in so many senses:

•  it celebrates a decade of Stickman Puzzles,
• passing the 1000^th Stickman Puzzle produced
• it’s the 25^th numbered Stickman Puzzle, and
• it’s an incredible mechanical achievement.

Rob teased us with some pics of his latest work-in-progress on the Renegade Puzzlers Forum back in February and it’s probably fair to say that it created a fair amount of interest. He showed us pictures of a half completed framework with all manner of interesting-looking gears, screws and gadgets – and a chain, made of wood(!).

Roll forward a couple of months and I’d taken Rob up on his offer of a puzzle and been tracking it’s progress from Oklahoma to Barnt Green ... en route it was intercepted by Her Majesty’s Revenue and Customs who duly sent me a ransom demand (or VAT invoice if you prefer) a few days ago. Yesterday I managed to get up to the Parcel Force depot to pay the ransom and get my package released ... and then I had an absolutely brilliant time exploring Rob’s latest masterpiece.

For starters, this isn’t a small puzzle – the basic premise is that you need to solve the puzzle in order to open the framework that cocoons (read: securely locks in place!) the commemorative Stickman Milestone Puzzle Book inside. The cover of the framework has the most amazing set of interconnected mechanics I’ve ever seen: the left hand side has a drive shaft with two different sorts of screw thread – one of which in turn drives a set of helical gears and the other, via a couple of sprockets, drives a chain to transfer the movement to a secondary shaft in the centre ... but the more that you examine the mechanism, the more it perplexes.

There are a couple of bits that appear to be driven at different speeds by that drive shaft – except they’re quite firmly connected ... most of the gears and other bits have a little bit of play in them, but for quite a while, I couldn’t work out what was stopping them all from moving – I could see that they were interconnected, and thanks to the open nature of the framework, you can see almost everything.

I’d poked and prodded for a while before I started investigating a bit more widely and then stumbled across what I’d been missing up to now and all of a sudden a whole new world of opportunities opened up to me and I had my first opportunity to exercise the mechanics of this beauty – and it is absolutely mesmerising watching the various gears and sliders interacting to produce some rather unusual moments in the one half, while that chain drives the secondary shaft in the other half – the mechanics are staggering – how the heck they were first conceived is well beyond me, but the skills required to implement them are truly mind-blowing.

Playing with the mechanics is fun and can be a little instructive as things that were hidden at the start make their appearance and you wonder to yourself if that might just be useful later on – I found myself trying little experiments to try and isolate bits of the machine so that I could improve my understanding of how they were all interconnected – or not – and what was actually stopping the frame from opening, and then working back to what was stopping that from happening and so on – it must have taken the best part of an hour to work out the basic gist of the machine and then start actually trying to unlock it, and a few times I came close, but not quite close enough – until I spotted something else I’d been missing all along, and that was the final little piece in the jigsaw – although executing it all still took a while, but eventually I had released the catches and opened the frame to allow the book to be released.

Job done!

Well, not quite – actually the book itself is a puzzle too! The spine is beautifully crafted in wood (what else, right?) and has three arms locked into it that cover the front and the back – and they are in turn joined on the right hand side by a pair of cross-pieces that are pegged together ... and it took me another little while to force myself to think of this as yet another Stickman Puzzle – after which I managed to work out how to get into it... and there is treasure within the book.

Rob and Matt Dawson have pulled together a lovely book giving the background to Rob’s journey from hobbyist to puzzle-making rock star (my phrase – I think Rob’s far too humble to refer to himself that way). It was really interesting to read about how Rob started out making puzzle boxes with a single radial-arm saw (a.k.a. widow-maker) and how he still chooses to use it for all sorts of strange, unintended jobs today. It was nice to read about his early collaboration with Eric Fuller and their Camelot period (great description, by the way!) and to get Rob’s perspective on how he designs his puzzles. One thing that really attracted me to Rob’s puzzles was the fact that they’re all so totally different from one another – it’s hard to look at one of them and see a family resemblance to any of the other puzzles he’s produced – apart from the style of the work, perhaps – so it was interesting to read that Rob has always actively avoided making anything that looks like anything else already out there in puzzle-dom, and that sort of explains it all – his work really is unique.

The second part of the book contains descriptions and pictures of every Stickman Puzzle produced to date (and even obscures the details of his Apothecary Chest drawer so as not to spoil it for any of the other participants!) including details of the production runs and even a set of high level solutions to every puzzle. After that there’s a section on some of the prototypes or ideas that haven’t quite made it out into the wild yet ... all of which shows that having reached these milestones 10/25/1000 there’s still a lot left in the tank!

Here’s hoping that Robert Yarger, aka Stickman, will carry on adding beautifully crafted highly original puzzles to this list for ages to come.

Thank you Rob – truly a Milestone Puzzle to celebrate and enjoy!

[and thanks Matt for pestering him into producing the book and then doing all the editing – great job!]