The last Dvořák goodies for now...

...and so onto the third instalment covering my little order of puzzling-goodness from Jakub.  This post includes three designs from Japanese wiz Osanori Yamamoto - each of which is rather 'different'.

Cockpit  is a cubic cage with three C-shaped pieces that interfere through the centre ... one of them has an extra cubie that really manages to get in the way disproportionately for such a small piece. Four of the cube's faces have crosses cut out of them and the remaining two have a full 3*3 square opening. 

As you can imagine, solving Cockpit is going to rely on manoeuvring the pieces apart in order to free up enough space to allow the pieces to pass one another (similar to Estergon and co.) The trick here is that the crosses on most of the sides mean that you're constantly having to move pieces around in particular order to enable the next move as you go first one way, then the next ... which gets you up to 16 moves to remove the first piece - and once again, an awful lot of scope for blind allies to lose yourself in!

Ice Pillar is a great name for the next puzzle as the finished puzzle looks like a classical pillar with four burr pieces passing through a hollow column. Right from the get-go there's a lot of movement - in fact every single piece will move in at least one direction - and some of them will move in several - so you're totally spoilt for choice trying to find the 30 moves required to release the first piece. 

 

In taking it apart I invoked Walker's Patented Solution of randomly fumbling around trying to make as much space in one area as I could, and whenever I ran out of opportunities, switch attention to a nearby area and try and move the space over there, until you eventually stumble across the right spot with more or less the right amount of space and you can see a route toward removing the first piece ... then it's not too hard... although along the way you can get the pieces dangling out in the breeze where you'd think they would just about fall out of their own accord, except they're still steadfastly stuck!

Putting it back together again is another story entirely! There is a single solution possible from a potential 1500-odd assemblies ... there is no way my brain will stretch to that, so I invoked Master Rover's gift to puzzledom to find my way back... and to some extent sort of surprised myself that I'd managed to take it apart unaided... this one's a toughie!

The last puzzle in the group isn't the hardest, and possibly not even the best looking, but it's my favourite.  Two Pairs One is a confusing looking little puzzle - at first it appears to be a cubic frame with two burr running through it, until you start moving the bits around and realise that the frame splits along the diagonal in a step-wise manner... and then the fun begins!

 

Successively moving the burrs in and out and the frame apart along the diagonal opens up the frame - until you find you can't go any further ... this puzzle has a habit of mocking you along the way - it certainly mocked my (in)abilities along the way - it might only be a level 9 puzzle, but there are a lot of entertaining little byways along the way to lose yourself in ... and you'll hear it gently laughing at you when you do that... I found that mine laughs quite a lot!

More Dvořák Goodness

Next up in my latest order from Jakub Dvořák is a set of three cubes that share a common theme again - two of them from the fertile mind of Yavuz Demirhan and the third from Japanese puzzle designing legend Osanori Yamamoto. All three target a cube shape and each has three burr pieces to be inserted into a holey cube frame ... which almost makes it sound like they should be pretty similar - except they ain't!

The first is called Estergon and was added to Ishino's website back in 2011. It's a 5*5*5 unit cube with three identical (save for colouring) "almost skeleton" burr pieces. Each of the burr pieces is offset into a corner of the cube faces, so you'll realise that the order / combination of the movements is going to be critical since the pieces are going to interact inside the cube. 

When you start playing with this puzzle, and indeed the other two in this post, there's a lot of movement available - it just all seems to be pretty useless! In fact if you push the burr bits out to their extremities, they can almost dangle precariously, mocking you but steadfastly not coming out!

A more methodical approach will identify a couple of possibly less expected moves that then allow you to develop some space, and ultimately allow pieces to pass one another inside the cube and then let the first piece out in a mere seven moves ... albeit seven moves that eluded me for absolute ages!

Estergon 2 ramps things up a bit by moving up to a 6*6*6 cube and giving the ends of the three skeleton burr pieces a 3*3 head. That little "improvement " brings some interesting positions for the internal sticks and makes it a whole lot harder. Given the increased size of the burr bits' heads, this one's even more floppy when you start pulling the three burr pieces out, and yet you won't be able to get past the other pieces inside there ... it will certainly tease you, but it won't give its secrets away without a fight...

This one also took me an inordinate amount of time to work out - there are some unusual little moves and you're pretty spoilt for choice in terms of what to do along the way, so there is plenty of opportunity to wander down a blind alley along the way - or that's my excuse at least!

[A little word on the craftsmanship here: Jakub made these two at the same time and I guess he knew folks would be getting them together, seeing as how they're one and two of a set... so he resized the sticks on Estergon so that the cube was the same size even though it's a 5*5*5 cube next to Estergon 2 which is a 6*6*6 ... nice touch!] 

Castle Hole by Osanori Yamamoto shares some similarities with Estergon in that it's a 5*5*5 cube with three simple burr pieces running through it, but whereas Estergon has solid sides in its target state, Castle Hole has three faces with three missing cubies on each... and those little holes make all the difference. 

 

Being "just" a 5*5*5 cube, the pieces don't tend to dangle around quite as much as they do with Estergon 2, and working out where you can move the pieces using those extra little holes will yet again provide plenty of blind alleys to wander aimlessly around - ask me about them, I suspect I explored them all along the way! 

In the end, there's a single, rather elegant solution to freeing up just enough space to remove the first piece in 11 moves...  a great little puzzle - really like the wood on this one.

Four from Yavuz Demirhan

It feels like ages since I sat down to write about puzzles... not just because there have been a bunch of posts about strange geometric constructions, but because I've been swapping out my old PC for a new one and that invariably ends up swallowing several hours / days / weeks until I've got things back the way I want them ... anyhoo - as of yesterday, I think that little piece of joy is now behind me... so back to the puzzles!!

Ali, one of my puzzling partners in crime recently dropped me an email passing on an offer of some new puzzles from Jakub Dvořák at the New Pelikan Workshop. The email listed a bunch of puzzles from Yavuz Demirhan and Osanori Yamamoto and the accompanying pictures looked pretty good, but to be honest, the prices listed made them just simply too hard to pass up ... so I felt a little guilty when I went back to Ali and asked if he could add one of each onto his order - until I discovered that that was exactly what he and Nigel had done as well... and so the three of us ended up ordering a set of Jakub's latest puzzles each. 

They duly arrived a little over a week later and I was well and truly gob-smacked at the quality of these puzzles that had effectively cost me an average of fifteen quid each - absolutely fantastic. 

The first four puzzles are all designs from Yavuz Demirhan and you'll see that they share a common family theme - they all consist of fixed frames with a set of burr pieces to be inserted / removed from the frames. Each has a unique solution and as you might expect, as the number of pieces rises, the level of the solution rises with it...

 

Pylon 2P2C is the simplest of the group having two burr pieces (2P) trapped between two columns (2C) ... it looks like there's a fair amount of open space between the columns, but the protrusion in the frames severely cuts down what you can do with the pieces... that said, there are a few things you can do with the pieces, and a little experimentation will take you down the pathway to the level nine solution and removal of the first piece ... and then another nine moves will release the other piece. It's a nice little puzzle that shouldn't hold up a seasoned puzzler for more than a couple of minutes. 

Columnata 2P3C ups the ante a little by throwing three columns into the mix along with two skeleton burr pieces. Adding the third column, even though it only has a single internal protrusion, takes this up to level 12. 

 

Although it's not as straight-forward as Pylon 2P2C, a little experimentation will show you what can be done, and how the pieces might be able to get past one another and then ultimately out of the frame - again, this one should be accessible for most...

Columnata 3P2C makes things a lot more "interesting" with several protrusions inside the two columns and a lot more wood in the three burr pieces - so instead of dealing with simple skeleton pieces, they now carry a lot of their own restrictions with them... and that brings a lot less freedom to the equation. Experimentation will show you where the main problems are going to come from but not going to show you a way out very quickly ... this puzzle takes 19 moves to release the first piece, after all. 

After a little playing around and trying to find an exit, I switched tack and rather than trying to find an exit that worked, experimented with swapping pieces around, and then trying to find an exit ... and that strategy ended up paying dividends ... this is a really neat little puzzle...

The last in this set is called Guillotine - it looks a bit like Columnata 3P2C, except there's an extra board inserted between the two columns ... and that board is free to ride up and down in the tracks - much like a Guillotine , only slightly less terminal. 

The burr pieces on Guillotine are once again skeleton pieces, but the combination of the frames with a few interesting protrusions and the moving board with not a lot of extra holes in it makes for a really interesting puzzle. 

Even though this one "only" has a level 18 solution, it's easily my favourite in the set. The combination of the board moving in two axes while the burr pieces are "free" to move in three axes, albeit trapped by the fixed frame, makes this a great puzzle to get to grips with.

Four fantastic little puzzles from Jakub and the guys at the New Pelikan Workshop - tremendous quality puzzles and fantastic value for money... can you tell I'm a big fan?

Office supply art

Having seen a pic on Oli’s flickr stream I’d been reminded of some rather interesting-looking constructions made out of binder clips – and decided that in the spirit of my current explorations of all things creative and vaguely mathematical (using both terms extremely loosely!) I should have a bash at them ... so I did what I’m sure everyone in my position would do, I ordered a large box of binder clips from Amazon and spent some time surfing. 

I’d drawn quite heavily on George Hart’s stuff on the web – particularly his Math Monday blogs (which I think are great!) when I was fiddling around with playing cards – and during that research (!) I’d come across Zach Abel’s web site and seen some thoroughly awesome structures made out of binder clips and paper clips – and knew I had to have a bash at some of the simpler ones... I was going to have to restrict myself to the simpler ones as I’d only ordered a hundred binder clips! (Well that’s my excuse, for now...) 

I started out with a couple of “Stressful” structures like the ones I’d seen on Oli’s flickr stream. The little monsters have three pairs of binder clips forming the X, Y and Z axes – and the only catch is that the clips are all back-to-back and stretched in the open position – so every single clip is in a pretty stressed position and the entire structure probably has quite a lot of potential energy hanging about in it – yet the final structure is pretty well balanced and fairly safe to handle – well safe enough to toss across a table to an unsuspecting fellow puzzler, at any rate. [Nigel survived!]

 

Zach’s web site includes a note that the although the structure has a huge amount of tension in it, actually building them shouldn't require much more force than you’d ordinarily use to squeeze them open... and I’d add to that you don’t need any additional tools or jigs either – just a pile of binder clips.

One word of warning might not be amiss here – during the construction process, before things are nicely locked together, you might want to be a bit careful – I had several clips launch themselves at high speed in random directions around the puzzle-cave.  [No dogs or puzzles were damaged in the production of these structures. Professional driver on a closed course. Your mileage may vary. Objects in the mirror may be closer than they appear.]

Next up I wanted to try my hand at one of the larger structures and decided on the 60 clip sphere over here. This structure relies on the interlocked arms for the shape and support so it’s a lot ‘safer’ than the previous structure. You make up sets of five interlocked clips forming a Borromean structure using one arm from each of five clips. The spare arms are then joined in sets of three interlocked arms in the same Borromean structure to another set of five, such that you end up with exactly two common sets of three between every adjacent set of five ... if you’re struggling with that, think of a football – or a truncated icosahedron if you’re that way inclined! [Although, if you were that way inclined you were probably asking yourself why the heck I didn’t just say that right at the beginning!]

I made up a dozen sets of five and then set about joining them all up in the prescribed manner... about two thirds of the way through I was having some trouble working out what went where and keeping the shape right – I found it was collapsing on itself – I persevered and fitted the last section hoping that would magically pull everything right ... except it didn’t. I’d noticed that the joints had all gone a bit floppy, so I began pulling them outwards to tighten them up, again hoping that would be the magic solution – it wasn’t... at that stage I enlisted the extra pair of hands in the house and we tugged and finessed and fiddled around but it was still pretty floppy (Gutter. Mind. OUT!). 

At that point I spotted one or two of the sub-assemblies were going the wrong way ... so instead of a clockwise Borromean structure, some of them were anti-clockwise ... i.e. some of them had been inserted upside down. I detached them and inverted them one by one and then something magical began happening as the whole structure began to sit up and fill out... and by the time I’d fixed the final one, the structure was totally self-supporting – all I had to do was squeeze the joints a bit to tidy them up and even out the structure. Et voila – one truncated icosahedron made up of 60 interlocked binder clips.

At this point I still had quite a few clips left over so I made up a bunch of “Stressful”s to throw at random puzzlers I might come across in the next few weeks and then tried my hand at the basics of one of these – I got as far as locking 11 clips into the basic structure and I have to say that Zach has earned a huge amount of respect from me – the work involved in doing just a tiny bit is significant – I can’t imagine how long it must have taken to build the complete Impenetraball – it’s quite amazing how the basic structure already demonstrates the beginnings of the curve with only 11 clips in place... although how the heck he knew that would work in the first place is well beyond my ken.