Another Fuller Trio

Tom Jolly’s Square Dance is an intriguing little puzzle that sort of looks like a little 3*3 sliding tile puzzle – at least inasmuch as there appear to be 9 square tiles in a frame and one of them can be popped out to enable you to move the remaining tiles around, a bit, except there are no markings or pictures on the pieces. Now I’m not sure if that should make it a really easy puzzle (after all, any assembly must be right!) or a really difficult one (what if there are other complications?).

Popping out the first corner square (it’s kept neatly in place with a pair of magnets) gives you your first hint at what lies ahead – there is a track around the inside of the frame, and on some of the pieces, and each piece has a series of tabs sticking out to engage the other pieces and the frame … which is fine, except that the Padauk frame then has a series of strategically placed blocks stopping you from moving some of the bits where you want to, and a little experimenting soon shows you just how unexpected some of those tabs really are.

At first there’s only really one path to be followed – moving the piece that can move releases the next one and so forth – until there’s a fork in the road and then things start getting interesting – and indeed I was quite surprised after quite a bit of fiddling around when the first piece was ready to pop out – because it came out in a rather odd way – and you have to admire the design that achieves that…

The next piece was not much easier in spite of all that extra space created by getting the second piece out of the way. Indeed the extra space means more opportunity for even more forks in the road as it were …working reasonably deliberately you can try and release pieces in turn until you find the right one, in the right spot … until there’s enough space that only a numpty wouldn’t be able to extract the last few pieces…

The tiles themselves have been mostly milled from a single piece of Holly each – the resulting fit between the pieces is terrific, with little or no play between them and no bowing at the centre of the grid at all when the pieces are in the frame. The result is a pleasingly positive feel where the pieces move smoothly when they’re properly aligned and don’t move when they aren’t.

I did spend a while trying to construct a solution outside of the frame that allows for the obstructions inside the frame itself – and while that may be feasible, transferring that into the frame without losing my mind turned out to be somewhat harder … although in my defence, Burr Tools reckons there are a total of 2166 assemblies, of which only 4(!) are actually achievable inside the constraints of the frame - which somehow makes me feel slightly less of a failure as a puzzler!

[UPDATE: Neil got in touch and made me revisit my Burr Tools model to find that actually if you exclude rotations and reflections, there are only 960 possible assemblies but only two of them are achievable - however, there are two identical pieces, so those figures reduce to a unique solution(!) out of 480 possible assemblies. Thanks Neil!]

Helpfully Burr Tools demonstrates the steps required for reconstruction and I’ve relied on it each time I’ve put the puzzle back together again so far … maybe one day I’ll be struck with some sudden insight into how to ‘see’ the solutions for these sorts of puzzles – but I wouldn’t hold my breath…

Sun, designed by Jos Bergmans, is a fiendishly simple-looking two-piece tanglement in wood (mine’s Maple) where the object is to join (tangle!) the two pieces so that the two halves of the sun (Sapele veneer on mine) are joined up. Eric (rather unsportingly!) ships this one in two bits so you have no choice but to solve it yourself!

Eric’s description of the pieces pointed out some of the finer points that non-craftsmen (like me!) might not fully appreciate – firstly the edges are all square, which is unusual for this sort of puzzle, especially ones where rotations are (!) required and secondly, he’s paid special attention to the fully mitred joints – and looking at one of the triple-mitred joints shows just how accurate they are.

Fiddling with the pieces is quite fun and needs to be fairly precise – remember the bit about the square edges? But that means that when something should work, it does and when it shouldn’t there isn’t much ambiguity, which can sometimes happen when the pieces have a little give in them (no chance of that here) or have rounded edges (you have been paying attention, haven’t you?). There are some surprising moves and I really enjoyed the way the final solution sort of snuck up on me and all of a sudden it was right there! Even after taking it apart and putting it back together a bunch of times, I still find some of the movements interesting and unexpected – great little puzzle to fiddle with in an idle moment.

Alchemy is an Altekruse-ish puzzle designed by Brian Young, based on ideas in Stewart Coffin’s Puzzling World of Polyhedral Dissections. The book points out that variants on the Altekruse theme can be improved (read: made harder!) by adding pins and holes in them and Coffin gives some examples of them in his book … Brian Young then took that encouragement to extremes and came up with a design that uses 14 unique pieces(!).

Eric’s version is made in Ash and has Walnut pins – as usual the tolerances are indecently good – things move smoothly when they should, and don’t move at all when they shouldn’t.

When I described the puzzle as Altekruse-ish – that probably wasn’t particularly accurate – the basic structure is an Altekruse assembly – but the pins and holes make the positioning of the pieces and the order of assembly somewhat more critical than on a standard Altekruse – and before you ask, it’s way too hard for me to consider assembling without Mr Roever’s computational assistance!  

Some IPP31 Exchange puzzles from Puzzlewood

Bernhard Schweitzer is purveyor-in-chief at Puzzlewood and seems to be one of the central ‘fixers’ in the puzzling community, applying his extensive connections between designers, manufacturers and puzzlers to facilitate exchange puzzle production for a number of IPP attendees each year. This year was no exception and shortly after the conclusion of IPP in Berlin, Puzzlewood announced the availability of some of the exchange puzzles in limited quantities. A quick email to Bernhard confirmed availability (and very reasonable pricing!) of a couple of interesting looking items produced by the New Pelikan Workshop and a few days later they arrived in Barnt Green.

Brandenburg Gate

Marti Reis’ exchange puzzle was designed by Jos Bergmans in 2010, the completed puzzle looks a bit like the Brandenburg Gate (and helpfully it says exactly that across the top) and the aim is to “open the gate”. It was made in oak and in maple and the finish on the assembled puzzle is that good that the first move is quite well disguised even if it isn’t all that deeply hidden. 

 

Removing the first piece will half-open the gates in a fairly tantalising manner, but as with a number of Jos’ designs, that’s just the beginning. A bit of fiddling around will soon convince you that rotations may be required, or perhaps that the designer is having a laugh and that they have been glued together in situ. At this point there are quite a few ways of encouraging the pieces apart – some requiring more “encouragement” than others, but if you persist a little, there is a very neat solution that allows the pieces to pass by one another virtually effortlessly – as long as all three pieces are properly aligned – neat little puzzle with a satisfying solution.

 

Reunification (Twins)

Reunification was Rob Jones IPP31 exchange puzzle. It’s a slightly re-badged puzzle designed by Bram Cohen in 2010 under the name Twins. This is a two-piece assembly with a bit of a twist to it – this time the twist is figurative though, not literal: the pieces are identically shaped and combine to form (most of) a 4*4*4 cube. 

 

The two halves slide together in a satisfyingly non-linear manner over 6 moves. Really nicely made with tight tolerances, with one face of the completed cube resembling a pair of interlocking F’s.

Röver 6 Piece Burr Variation II

This great design from Andreas Röver takes six simple, identical burr pieces and then adds 3-unit L-shaped blocks to each of them in odd orientations to produce 6 unique pieces and a unique 6-move solution. 

The New Pelikan workshop have produced the pieces with the L-shaped additions in a contrasting colour – that makes for a neat little surprise when you start taking the pieces apart as the contrasting colour is all safely hidden away on the inside in the completed state.

3-Piece What’s It

George Bell designed his own exchange puzzle that was produced in Maple & Robinia by the good folks at the New Pelikan Workshop.  Even though the puzzle is made up of cubes joined at right angles, the offsets make it quite a disorienting puzzle. 

Mine arrived solved, and I suspect that if it hadn’t, I’d still be hunting for that symmetrical solution – even though it only has three pieces!! “Difficult” puzzles don’t need to be complicated.

Microcubology

Pocket-sized puzzling

It was great having Richard Gain (the Microcubology-guy) join us at the last MPP – not just because he’s a thoroughly nice bloke who likes talking and playing puzzles, but also because he designs and makes puzzles – and he brought a pile of his wares along for everyone to have a bash at them and potentially buy a couple – I bought 5 of them and Richard rather kindly tossed in a tiny 3-piece 3*3*3 cube for nothing. 

Richard sells his puzzles on the web through two shops – the Shapeways shop  will sell you the puzzles directly in a single colour, or you can buy them from Richard’s Etsy shop (for a little more) all ready dyed in multiple colours – IMHO that little bit more is well worth it – you’ll save yourself several hours as well as the cost of the dyes etc. 

Most of the puzzles in his shop are 4*4*4 cubes with 3cm sides – they’re manufactured using the standard Shapeways laser-sintering process and the pieces are pretty rugged (which turns out to be a rather good thing!). Given their compact size and relative strength, I reckon they make excellent puzzles for just tossing in your pocket on the off-chance that you might a puzzle to play with while you’re out or if you want something to tease / annoy / entertain (delete as appropriate) co-workers with. 

Having had the small pile of micro-cubes staring at me from my desk for a couple of weeks, I spent some time last weekend playing with them properly, and really enjoyed myself – bang-for-buck-wise or smile-per-size-wise they are simply tremendous. 

Richard has collected a couple of really interesting little cubes here – there are some by Jos Bergmans and a couple of Richard’s own designs. It’s pretty clear from his selection and his designs that he has a rather twisted mind (and you’ll see that I mean that purely in a ‘rotations required’ sort of way!).

Three tiny pieces is the cute little 3*3*3 cube that Richard was handing out for free to anyone buying his wares at MPP – it’s literally only about 15 mm on a side and requires a little precise manoeuvring - especially when trying to take the last two pieces apart: one move removes the first bit and then another four moves are required to separate the last two from one another. Given its size, it’s not likely to become the most prized puzzle in any collection – but it does demonstrate just how good 3D printing has become – the individual cube building blocks are all hollow and the walls are incredibly thin, yet the pieces are quite solid enough to produce a perfectly serviceable puzzle.

Pivot is an interesting Jos Bergmans design where the name gives a clue as to the movements involved in the solution – yip, Burr Tools may be useful for working out how the pieces might form a cube, but it won’t tell you how to assemble the pieces due to the rotations required in the solution. 

Pivot has one unusually large piece that runs almost the entire length of the edges of the assembled cube, making it an interesting ‘feature’ of the solution – and in some senses, placing it to one side and working only with the remaining pieces to solve the eventual placement does simplify things. Once you’ve done that, there should be an obvious last step (if you’re assembling – first step if you’re taking it apart) and a reasonably clear first step – that leaves you a little experimentation to work out how the jiggle the innards sufficiently to allow each piece in and then get it into the right position. Disassembly is a non-trivial exercise given the jiggery-pokery required to moves the bits about to release each successive piece. 

Twist the Night Away is a six-piece 4*4*4 cube by Tom Jolly. Again there’s a single piece that sort of stands out as the one that going to cause the trouble – it’s a complete ring that will make up most of an entire layer of the assembled cube … so once again, setting that aside and building the rest of the cube and making sure that it has a suitable waist for that ring, seems like a reasonable place to start to work out the positions in the final solution. You can eliminate a couple of bits as being fairly straightforward, but that still leaves you with the toughest part of this little puzzle – putting the second piece into the puzzle literally takes a colossal 12 moves – including a very healthy number of rotations! 

I used to be a bit wary of puzzles like this requiring rotations, because some of them are invariably “a bit tight” – so I’m not sure whether I’m forcing it to do something unnatural, or whether it really just needs a bit of encouragement. Having spent some time playing with these little puzzles, I’m happy to confirm that the ‘right way’ generally requires very little encouragement of the agricultural sort and rather more finesse – so if you find yourself needing to squeeze things a bit harder than you feel you should – stop and find the better way. Once again, disassembly in decidedly non-trivial – in fact, it’s not a long way off being as hard as assembling from scratch. Nice design, nicely executed. 

Elevator is another of Jos Bergmans’ designs for a 4*4*4 cube with a twist. Once again, this puzzle has a large awkward piece (a cranked loop) that’s certain to be the major constraint – no surprises there! 

The name also gives a pretty good description of the likely movements during the important stages – in fact you’ll have a decent combination of pivots, rotations and elevator moves all going on at the same time when you get to releasing the last few pieces while disassembling. I found myself chasing my own tail a few times even though I thought I had a pretty clear picture of where I was trying to get to – once again, even though the moves are ‘unusual’, none of them is particularly tight.

The last two micro-cubes in this post were both designed by Richard. “Roll Up! Roll Up!” has some references to not only some of the movements involved in the solution (you’re starting to notice a pattern here, aren’t you?) but also to the Big Top, inasmuch as the pieces alternate in colouring when assembling or disassembling. 

Richard’s description of the puzzle points to the two troublesome parts on this puzzle (an ‘H’-shaped piece and a cranked loop) and suggest that you start by combining those two pieces, helpfully noting that it’s “not as easy as you might think!” – Indeed, without any other encumbrances, getting those two bits together properly takes five less-than-obvious moves – again including rotations that Burr Tools won’t help with. The next two bits take a few moves each, but aren’t too troublesome before the final two pieces lock everything together rather securely. Excellent little puzzle that Richard is quite rightly rather proud of. 

Last but not least is the interestingly named Angle-C – not for its shapes or moves this time (see, I was lulling you into a false sense of complacency!) but because it was designed while on holiday on Anglesey. Geddit?! This one had me scratching my head for ages while trying to disassemble it the first time – I’d found the first piece to remove quite quickly, but then couldn’t for the life of me find the next bit to move … time and again I’d take out that piece, fiddle around fruitlessly, only to replace that first bit and put it back on the desk to stare at me for a while longer … then last weekend I had a real go at it and realised what I was missing – effectively the fit on these little Shapeways puzzles is that good that I’d missed something large right in front of my face – something that Richard’s colour scheme does a good job of disguising nicely, by the way.   

That takes care of the next couple of pieces, and the following one isn’t that tough, but it leaves you with a pair of oddly shaped almost-complete loops – and getting them to part company is rather fiddly – you’ll probably recognise the similarities to a standard bent nail puzzle, but the shapes make it a bit more complicated to execute – providing a neat little four-move sting-in-tail for this disassembly … so starting from a set of pieces and assembling it without any ideas of orientation or final position in the solution is a significant challenge. Great puzzle Richard!

POSTSCRIPT: I wrote this blog post last week and since then Richard has entered one of his latest designs (Superstrings - now available from his Shapeways store) in this year's Nob Yoshigahara Puzzle Design Competition at IPP 31 in Berlin, and WON a Jury First Prize Award for his trouble! Well Done Richard!!