Sunday, 24 October 2021

Holonomy Mazes


Henry Segerman has been designing puzzles and wonderfully interesting 3D-printed mathematical structures for a while now. He recently shared a video of a new sort of maze he’d designed which uses an interesting property of moving something around the surface of a three-dimensional ball-like object: moving around in a closed loop on the surface changes the orientation of that thing relative to the ball… which is interesting, as Laurie always used to say. That property is called holonomy and Henry’s mazes use that property to make traversing the maze depend not only on where you are, but how you got there…

The first two mazes he published on Shapeways were based on octahedral geometry projected onto a ball. The shuttle, which he calls a rook based on the shape of its foot that engages in the maze, starts in one place in a forced orientation thanks to the little projections either side of the insertion hole… the object is to return to that starting point in a different orientation so that one of the rook’s arms is trapped under the overhanging lip on one of those starting projections.

Travelling around the surface, every time you take the rook around one of the triangles on the surface, it rotates 90 degrees – which is helpful, because there are a bunch of pegs on the surface of the balls that will stop your progress depending on which way round the rook is positioned…  so your task is to find a permissible route around the ball that takes you back to the start, but gets you there in the right orientation – see, it doesn’t just matter where you end up, but it also depends on how you got there… nice! [Henry does a much better job of explaining all that than I do - watch his videos!]

Right – that’s the theory – how do they play?

The first two Holonomy Mazes Henry released were octahedral, as I’ve said - that gives us 24 possible nodes if we were to graph them and definitely provide a non-trivial little puzzle. There isn’t all that much space on the ball, so you never really feel like you’re lost – it’s always just a case of working out which routes are currently available and whether you want to go straight toward your goal of via a detour or three to change orientations.

The mazes and rooks are cleverly designed to allow only the valid moves and after an initial bit of playing any roughness on the prints is smoothed away… I quite like these little mazes because despite having such a small physical area, they provide a neat little challenge.

A few weeks later Henry presented his Dodecahedral Holonomy Mazes so I had to give those a bash as well. This time you have 120 nodes potentially available (before the pegs begin to limit that space) and a circuit of any one of the pentagons will translate the rook by 60 degrees this time… where the smaller mazes feel like they should be simple, the dodecahedral ones feels a lot more complex, at least to me they do – and watching the videos where Henry describes the process of deciding which mazes would be interesting, I’m not surprised – he’s deliberately chosen layouts that have lots of spaces where a puzzler can easily run around in circles for a while (yup, I’ve got the t-shirt!) and also have some bottlenecks in the middle so if you don’t pick the right path at the right time, you’re doomed to wander around in those almost-closed loops.

These puzzles are not only fun to play, they’re also interesting for how make use of such a relatively small space while producing interesting, non-trivial puzzles. 


Sunday, 17 October 2021

Nuts N' Bolts

A couple of weeks ago I spotted an announcement from Phil Wigfield on Discord that he’d be releasing a new brass bolt puzzle in a couple of weeks’ time, so I made a mental note to keep an eye out for it on his Etsy shop

A couple of days later a package arrived from Walsall out of the blue – which surprised me at first, but the note inside really blew me away. It was a letter from Phil gifting me a copy of his latest as-yet-unavailable puzzle Nuts N’ Bolts. Thank you, Phil!

I was quite keen to play so I opened up the customary little wooden box and lifted the little contraption off its satiny pillow – it’s an interesting looking little beastie – a pair of parallel bolts courtesy of a pair of fat conjoined nuts seem to be held together by a single nut and bolt combo that pierces the whole lot of them… and trapped far out of reach is a pair of washers that you’re aiming to remove.

Seems obvious that you need to remove the crossing bolt and then you’ll be able to remove the big bolts and Robert’s your mother’s brother. Only it’s not quite a simple as that… you might find the first step works pretty much as you’d hope, only from then on things get “interesting” – and by “interesting”, I mean all progress ceases!

Definitely time to Think(c).

There is a beautifully elegant solution that leaves you with a pair of freed washers and a nice smile on the face.

At this point you’ll know exactly what he’s done to create this little piece of glorious engineering, but I defy you to find the traces of his handiwork… he’s gone to a lot of trouble to keep things unseen that should not be seen… it is beautifully made, and a lovely puzzle – and if I hadn’t just been given a copy, I’d be queuing up for a copy when they’re released...probably tomorrow. ;-) 

You're welcome!

Wednesday, 6 October 2021

Popplock T13

Some things in life are very reliable – take Shane’s opinions on puzzle locks for example: if he rates one highly, then chances are good that any mere mortal is going to find that very thing absolutely astounding, so when he put a picture of a new T13 on Facebook and began singing its praises, I knew we were in for something really special…

Of course, given the opportunity to buy a shiny new puzzle from Rainer, I’m more likely to mortgage a kidney than pass up the opportunity, so when the opportunity arose, I accepted, perhaps a little more eagerly than usual given Shane’s unbridled enthusiasm.

First impressions of the T13 are, indeed, impressive – this object has presence – it demands attention – it also demands a sturdy surface to play on given that it’s a huge two kilogram lump of steel and brass.

The shackle appears to be made of three thick sheets of hardened steel riveted together – reinforcing its pedigree as a proper, if somewhat oversized, lock. The keyhole is offset at a jaunty angle begging to be played with. The back has a springy disk with Rainer’s customary logo and the lock’s name engraved on it… and the only other slightly unusual feature are two disks on the top of the lock inside the shackle… the rest looks pretty, er, lock-like.

I started by doing the obvious and immediately I knew by the gentle click and my inability to reverse my actions that Rainer was already laughing at me… I’m sure it’s only me, but I got suckered in and knew I’d done something a little silly right from the very beginning. (In my defence, I think you have to…)

I won’t bore you with all of the details, but I will tell you that the solve took me weeks. I spent a long time thinking that there was absolutely nothing else I could try, explore or experiment with, only to make the tiniest little discovery a few days later and then find myself trapped for a few more days.

The solution path on this one is well and truly long and winding, but along the way you will be rewarded with several fantastic “A-Ha!” moments when this little lump of metal does something utterly wondrous – if your jaw doesn’t hit the deck at least three times when something strange happens, then you aren’t human!

This puzzle keeps on surprising you right up until the very end… and even the final element is good enough to hold up a seasoned puzzler for the best part of a week or more (not me, a friend – I’m not that seasoned!).

Another phenomenally good puzzle lock from the master-craftsman – a worthy successor to all of his foregoing Tricklocks – another Jaw-dropping mechanical masterpiece… Oh, and Shane was absolutely right!

Wednesday, 29 September 2021

Play-Boy 2

If Fermat was my favourite from the latest Pelikan release, then Play-Boy 2 from Alexander Magyarics runs a pretty close second.

I really enjoy Osanori Yamamoto’s apparent cube puzzles - just how creative he’s managed to be with a simple box with some heavy restrictions on entry and a few pieces really blows my mind.

Play-Boy 2 is a wonderful riff on that theme from Alexander – not content with just coming up with a restricted entry box, he’s also taken the liberty of squashing the box from one corner to the other, resulting in some wonderfully delicious geometry that forces things to be handed… which is both really helpful and really unhelpful at the same time.

On the one hand, it really helps you to cut down the number of possibilities for the assembly – but on the other hand, if you were hoping to get a particular piece in a particular place in a particular orientation, you might just be disappointed!

It’s also great for really messing with your Euclidean headspace!

Given the really limiting entry-ways, you can derive some things right off the bat… which is always a nice way to start a puzzle solve. Armed with that it isn’t too difficult to come up with an assembly or two outside of the box – and from there you just need a little imagination to think through how those pieces need to dance around one another in order to get them in or out of the little box…

What makes me really like this design is that there are several features that work together to guide the solver toward the solution, as long as they take the time to Think (c) a little along the way.  (Either that or I got really lucky – but I’m going to blame it on good design!)

It's not super-tough, but it’s a fun solve and it really looks terrific on the shelf – a real stand-out from the Pelikan-folks - and they still have some available for sale over here. (You're welcome!)

Monday, 20 September 2021

Polar Burr

Many weeks ago, Steve included a copy of Derek’s latest helical burr in one of my regular care packages. Polar Burr is the product of Derek’s relentless research into all possible helical variants – this one comes with the dubious title of being the highest level helical burr to date… at somewhere over 30 moves to remove the first piece.

That probably won’t scare you – like me, you’ve probably been victorious over many level-30 burrs in your time. Heck, you’ve probably even done plenty of them with a lot more pieces than this one… and yet this one is very, very different! You should respect this one, even approach it with deference… and if you don’t, it will bite you on the bum – guaranteed.

Now I’ve acquired several helical variants over the years – and virtually all of them have been great fun. Sure they mess with your head a little when you start playing with them, but once you get used to the movements and the interactions and you start forming a mental picture of how the blockages and passages inside are interacting, you can almost picture a route through them… or you can just blindly fiddle and often that’ll be enough to take them apart. Of course blind luck is seldom sufficient for reassembly!

Polar Burr seriously ups the ante however… I must have spent hours over the course of several weeks trying to get the darn thing apart without making the lightest bit of progress. Sure, I could get the pieces to start coming apart – heck, I could get them to the point where they were literally hanging together by a thread – but get them totally apart? Nope – not a sausage.

Truth be told, if it hadn’t been for the kind offer of a BurrTools file from a fellow-puzzler, that thing would never have come apart. Even with the BurrTools file it’s a pretty tricky task! 

There are some wonderfully sneaky little moves in there that casual fiddling (my usual approach to solving puzzles!) will simply never find… so if you want a thoroughly serious helical burr, hit up the Two Brass Monkeys for a copy of Polar Burr – but please don’t blame me if your vocabulary gets a lot more colourful than it ever used to be as a result.

Derek 1 – Allard 0

Sunday, 12 September 2021

Enter if you can…

Peter Hajek’s new book, “Enter if you can – The art of puzzle boxes” will be available for sale at both Pelikan (already!) and Cubic Dissection (shortly…).

I was fortunate to be given an advance copy of this lovely book and I highly recommend it to anyone who loves puzzles – and especially those who love puzzle boxes. Peter has produced a beautiful coffee table book full of stunning photographs of hundreds of puzzle boxes (including some thoroughly unobtainable ones!).

The book takes the reader on a journey through the development of puzzle boxes over the years and then spends several chapters looking at some of the recent masters of the art. Peter’s gone to great lengths to try and entice new puzzlers into his love for puzzle boxes, and I’m sure he’s going to win lots of new converts with this lovely book.

So if you’re interested in the history of Sorrento boxes or looking to find out more about Frank Chambers’ puzzles, looking for a discourse on difficulty or what makes a good puzzle (box), Enter if you can has you covered.

Thank you Peter for putting it all together so beautifully and creating a record of some of the things that really amuse us puzzle box lovers.

Wednesday, 8 September 2021


When Volker reached out to me a little while back to ask me to have a look at some blurb he’d written for a new puzzle he’d designed, my interest was piqued. It was called Fermat and the blurb described a lengthy design process that resulted in a single solution for putting three innocuous-looking triangular pieces inside a slightly lipped box.

The box will be familiar to anyone who’s played with any of the Euklid series (and a few others) – there’s just enough of a lip that you can’t ignore it, but it hardly seems to block off any of the entrance at all – until, that is, you start to try and place pieces inside the box.

Several weeks later the good folks at Pelikan announced that Fermat was ready for sale so I loaded up the virtual shopping cart and checked out – I ended up buying quite a few things from that release, and Fermat is definitely a firm favourite.

There are indeed three slightly differently sized triangular wooden blocks to be placed inside the box, below the lip. Each of the pieces will readily slide in and out and once inside they can all be manoeuvred around… in fact putting two in simultaneously isn’t all that complicated either – however, putting three of them in at the same time is impossible. (I’ll just tell you that now to save you all the bother.)

I spent an inordinate amount of time working out how best to move things around inside the box and I’d pretty much decided how the pieces need to be in there for the last piece to be inserted (my go-to strategy for these sorts of puzzle). I found a lot of ways to do stuff, just not the right stuff.

At one point I did what I suspect is a bit of a right of passage for this puzzle: I encouraged two blocks to slide past one another with the teeniest amount of pressure and then had a real heart-hits-the-table-kind-of-moment when I realised that I couldn’t get in underneath those pieces to push it back with the same teeny-tiny amount of pressure. For the next few days I tried variations on variations for getting the pieces properly aligned and getting one to slide past the other – all with zero success… I let some of my puzzling mates know that I’d done something a little silly and they mustered all their sympathy and duly laughed uproariously at me. (Thanks chaps!)

I applied a little thought to the subject and came up with a handy way of getting myself out of my little predicament and thankfully that worked a treat – but learn from my silly mistake folks: literally NO FORCE should be applied – seriously.  

Newly invigorated by all my mates solving it and telling me how much they liked it, I set at it again, being a lot more circumspect this time… I spent a while exploring the same blind alleyways I’d tried over the past week or two and then changed my perspective entirely… and that proved to be the right thing to do – I broke it down into a set of smaller problems and solved those in turn and then bundled the whole thing up into one big solution – and I think it’s great…

Unless Nick says otherwise, I think Volker has successfully designed out all of the other solutions and forced the solver to replicate the exact set of manoeuvres he set out to build into the solution.

This is definitely one of those puzzles that suckers you in thinking “How hard can it be” and then shows you exactly how hard!

Wednesday, 1 September 2021


I love a bit of machined brass… especially the puzzling variety – so when I spotted a couple of pics from Radek on Facebook of a new chunky little brass caged hedgehog, I reached out to ask him if there might be any available for sale. His post mentioned he’d only made about 10 copies and two of them were already somewhat spoken-for – with one to them being rather permanently attached to a custom Harley Davidson – I didn’t rate my chances of snagging a copy particularly highly, but reckoned it was worth a shout and thanks to the marvels of an international courier, a couple of days later I had a copy in my grubby paws.

This puzzle comes in a neat plastic sleeve that holds some additional meta-puzzling and a leather bag that keeps the cage and hedgehog snug inside. Open it all up and you have a handsome hunk of brass machined into a chunky cage with a nice spikey hedgehog nestling inside.

As usual you need to release the hedgehog – and this one’s a classic design – nothing super-funky like some of Radek’s other takes on the genre – some of which might look like a standard hedgehog in a cage, but they are anything but!

A little sleuthing and a little fiddling about will soon enough release the little spikey fella, and normally at this point you’d be done, except Radek has added an extra little mystery or two in the form of a challenge card and map… which asks you to find the new home of the puzzle’s real secret.

This bit of the challenge will test your observations skills and your puzzling nous but when you bring everything together it’s all right there in front of your eyes, as clear as day… and of course that leads you to some wonderful extra material that I particularly enjoyed. (I really loved the little nod to the other mythology around this puzzle.)

Even if it’s “just a standard hedgehog puzzle” – I rather like this copy – the cage is machined from a single lump of brass and the back-story in the extra challenge is lovely bonus.

Nice one, Radek!