72 Pencils

Watson! What have you done?

I first came across pictures of George Hart’s 72 Pencils structures on the internet ages ago. I’d thought to myself “Those look interesting,” and mentally filed away a note to have a bash at making one at some point and left it at that. And life was good.

And then I bumped into Martin Watson at Peter’s EPP – one of his puzzle “finds of the year” was a copy of 72 Pencils that he’d put together for himself… along with a few variations on the theme that he’d brought along to trade away (because, he keeps telling us, that Alice has told him he needs to get rid of them because they don’t have enough space for any more puzzles – it’s been a theme for a while now!).

I didn’t have anything there to trade for one and Martin wouldn’t accept cold hard cash, so he ended up insisting on giving me one – just as well I’d driven across and not taken the train!

We then spent a short while discussing building them and I admitted to a long-standing intention to have a bash myself – fatal error – within a couple of minutes Martin had dispensed just enough wisdom and encouragement to have me thoroughly hooked on the idea of making some up…

…and within a couple of days I’d ordered several hundred pencils from my favourite on-line retailer (other major rivers may exist) – you should see the weird recommendations I get on there now!

The following weekend I settled down in front of the television with a handful of rubber bands, 150 pencils and my iPad tuned to a particular website.

Starting with a fistful of banded together pencils, I began the process of inserting pencils through the major axes, adding lacky bands – finding the fourth axis – the only vaguely tricky part – and then shoving pencils through every single hole I could find for the next hour or so…and swapping lacky bands every now and then when they got too tight.

When it started getting reasonably large, I started paying slightly more careful attention to the shapes and getting things even across the different sides until I had a completed set of neat hexagons on each side, all with four pencils along each edge.

From there it gets fun – man-handling the whole thing to get everything neat and tidy and all the ends neatly lined up… check on the lacky bands and get them evened out, and then you can remove the inner layers of pencils – until you’re left with just a layer or two in each hexagon – et voila!

Now the next step, if you’re keen, is to glue the corner sticks in place on each side…which will allow you to ditch the lacky bands for good… makes things look neater …

Oh, and a couple of words of warning: if you’re using pre-sharpened pencils, you will stab yourself – probably multiple times, and you will end up drawing all over whatever surface you’re using to align the pencils from time to time – I spent a good ten minutes erasing the esoteric pencil markings that covered our coffee table after putting that one together… and I now put a sheet of sacrificial paper on the desk / table although the scribbling isn’t quite Jackson Pollock!

THAT is a match cube

I wrote about my attempts at making match cubes a little while back and subsequently swapped a couple of emails with Chinny the Australian lathe-meister. It turned out he’d co-presented a workshop at IPP in Prague with Sandor Bozoki – between them they’ve created some pretty darn awesome match cubes, variants of match cubes (match cube in a bottle, anyone?!) and many similarly impossible objects. Chinny sent me a copy of their workshop notes and some pics “for inspiration” – NO WAY am I likely to get anywhere near some of those! 

 

One of the things that I thought might be within reach was a filled match cube – so I took one of recent cubes and set about adding some filling and I must say that I rather like the results ... and they make the resultant cube pretty much bullet-proof as well!

...on a vaguely related note, I was chatting to Nigel about these things and he mentioned that he’d wanted to have a bash as well, and he’d thought of trying a giant-sized cube – and that sounded like a fun idea... so I went off down to the local Tesco and picked up a few boxes of extra length matches and set about trying to build a cube along my usual lines – only to discover that although they are a little thicker, the extra length tends to make them more susceptible to warps, so a lot more or them need to get turfed out than with the smaller matches ... in the end, my three boxes were reduced to two, and that wasn’t enough to get past adding the roof...

So I bought another three boxes and tried again – and this time we had enough, and things held together ... now THAT is a match cube!

After my blog post on platonic playing card thingies, Derek encouraged me to have a bash at a couple of George Hart’s structures – and as I happened to have a copy of the relevant edition of CFF lying around [#88 in case you're interested], I thought I might as well give it a bash...

The smaller of the two consists of 12 cards and has reasonably deep cuts and a corner-to-corner fold on each card. Once you’ve put the necessary cuts in them and folded them to about 60 degrees, you start by assembling them in interlocking sets of three. There’s a knack to getting the third card of each set properly introduced and they need to all interlock with one another, at the same time. 

My technique certainly wasn’t pretty, but by the time I was almost done it, was passable. The 12-card structure produces quite a spiky, dense ball when you’re all done.

After I’d reported back to Derek that I’d done the 12-card version, he helpfully goaded me onto trying the 30-card version ... so I cut out a set of cards (shallower cuts on this one) and bent them appropriately and then had a bash at joining my first set of three ... I had a picture of the completed structure for reference, and I knew that in theory they had to go together more or less the same as the 12-card version, but I could not get them to lock together properly. I made several attempts before putting them to one side and retiring hurt ... until a couple of nights later when some further fiddling managed to get one set properly linked. Flushed with success, I put them to one side and focused on something else ... hey, I happen to have a really short attention span!

I kept coming back again and again, generally not managing to add much to the structure at all, but every now and then managing to add a few more cards. Yesterday I decided it was now or never and set about finishing it and finally managed to lock the final card in place ... producing a pretty decent structure of thoroughly interlocked cards – but I can honestly say that I still haven’t mastered the technique for interlinking these ones properly ... looks good though!