Three terrific tray-packers

Truth be told, I came back from Japan with piles of puzzles… so there is no way I’m going to be able to blog my way through all of them – the best I can possibly do is tell you about some of the highlights…

Today I have three tray-packing puzzles for you… selected for three very different reasons!

10 Cutter Blades was Mitsuhiro Odawara’s entry to the Nob Yoshigahara Puzzle Design Competition this year. I’d had a look at the entries on John Rausch’s website before going over to IPP so I recognised it when I spotted a copy in Mine’s stall outside Izumiya in Hakone, and picked up a copy for myself. 

This is one of those straight-forward packing puzzles with a set of 10 blade-shaped pieces of varying sizes to be packed in a rectangular tray… helpfully there’s a space to hold one of the pieces on the side of the tray. 

The start position has a reasonable amount of slop in it, but nowhere near enough to fit an extra piece into the tray. The shapes are really interesting because there are tons of ways of combining them into regular-looking shapes and it’s very tempting to use those as the basis for a solution. 

Tempting? Maybe. 

Useful? Nope!

The solution is a long way from anything that I’d envisaged along the way and almost seems to be entirely void of any form of symmetry, in spite of the pieces lending themselves toward symmetrical combinations and there being five pairs of identical pieces. 

A hard-core packing puzzle!

I bought a copy of Four Bent Nails from Vladimir Krasnoukhov at Sunday’s Puzzle Party. It is an acrylic packing puzzle – and is almost the antithesis of 10 Cutter Blades as a packing puzzle. This one has four identical bent nails cut out of clear acrylic that need to be placed in the square tray. 

It might be an old, well-used idea, but it’s nicely executed and a fun little puzzle to hand around to folks who are reasonably new to puzzling as it looks totally impossible at the start, but once you start experimenting you can develop an idea or two and solve it in a few minutes… of course if you insist on trying the wrong things over and over, you can get a lot more enjoyment out of this cute little puzzle. 

I ended up spending an awfully long time getting to know Triangle Eyes by Mine – I’d picked up a copy from him in Hakone and it pretty much became my go-to puzzle of choice for the remainder of the trip. It’s a great challenge, it’s really compact and it’s brilliant for passing around for folks to have a bash at.

 You get a double-sided tray with different-shaped openings on each side and a set of multi-coloured cats, with triangles for eyes. Your first task is to pack all five cats into the hexagon-y-shaped side of the tray. There seems to be plenty of space for this, it’s just always in the wrong place –you either end up with a cat with a head that’s too big to fit in the last remaining hole, or a cat with a leg in the wrong place. 

I must have spent literally hours solving the first side and really felt a sense of relief when I finally stumbled across the solution. 

The challenge on the second side is to pack any four cats into the squashed-hexagon-y-shaped tray. You have all the same problems that you had with the first side (misbehaving malformed moggies) compounded by not knowing which of the cats to try and force into the tray… 

I spent quite a while on this one and by a stroke of luck (or genius?) I guessed which four were most likely to be in the solution and concentrated on them, until I managed to find the one and only way to pack them all into the tray. 

…Oh and don’t believe Strijbos if he tells you that you need to find a solution for each set of four cats for the second side of the tray – there’s a single solution for one set of four cats, only … I know because I asked Burr Tools to check for me!

Kostick’s Oct-Tetraxis Assemblies

Jane Kostick entered another of her wonderful magnetic assemblies in this year’s Nob Yoshigahara Puzzle Design Competition. I’d been trading emails with her in the weeks running up to IPP33 and she’d said that this year’s entry was definitely a bit harder as a puzzle than her previous entries, and having seen some pics, I knew that they looked smashing, so in the course of those emails I asked if there might be a set for sale ... and duly secured one of them.

Knowing that I’d bought one of the sets, I just had a bit of a play with them in the competition room at IPP33 but didn’t really get very far at all… not because I wasn’t able to, you understand, but because I wasn’t really trying! [Well that’s my story and I’m sticking to it!]

In fairness, I had a pretty good bash at it and got nowhere! 

After the end of the competition I picked up the spare copy from Nick Baxter and a couple of days later I got to spend some time playing with it.

There’s a solid cuboctahedron (picture a uniform polyhedron made up of square faces each of which has an equilateral triangle hanging off each side – 6 square faces and 8 triangular faces in total) and two sets of sticks. The object of the two challenges is to use a set of sticks to properly cover the cuboctahedron.

The simpler of the two challenges uses 12 sticks that are all roughly the same length. This set consists of 4 different coloured sets of sticks and there’s a fairly clear difference in the angles on some of the pieces … fiddling around with how the sticks snap together around the block you can work out more or less how they’re going to go together and once you have the beginnings of a little nest for the block, the rest goes together reasonably simply … and then when you’ve got a nice solid structure you might want to pay some attention to the colour symmetry and get each of the three and four-fold joints so that there aren’t any duplicate colours – and then notice the overall colour symmetry that always gives you a pair of like colours parallel to one another on each side – neat! (...unlike the construction in these pics!)

The second of the two challenges is supposed to be a little harder (and IT IS!) – it uses 24 sticks in two lengths, the shorter ones in Bloodwood and the longer ones in Tigerwood. (The eagle-eyed might spot that it’s not quite the same construction as the main set used in the Design Competition.) 

Fired up with my victory over the first challenge, I launch myself into the second and start building random structures around the block hoping that I’ll stumble across something that looks promising that I can develop into something useful…

I seem to spend quite a while playing before I realise that the structures I’m coming up with aren’t behaving as predictably as I think they should, and the one time that I think I’m getting close, I find that the last couple of sticks don’t sit flush – and I know that there is no way that Jane would have allowed a piece out into the wild that didn’t fit perfectly – I know that I’m doing something wrong.

So I go right back to basics and lay out the pieces in groups of identical pieces, except that I find that they aren’t quite, or rather, there are more types of pieces than I’d realised … and the number of types leads me to think of a particular sort of sub-structure … and when I find the right one, it hangs together properly – not like the sub-assemblies I’d been trying earlier that hadn’t wanted to hold their shape at all… from there it was a short hop, skip and a mental jump to work out how to wrap those sub-assemblies around the block and in-between one another to form a very elegant, and perfectly fitting assembly that totally covers the block. 

As usual the eventual assemblies are beautiful objects. The pieces are perfectly crafted to snap together solidly, and they provide a rather nice puzzling challenge... Thanks Jane!

Dissecting Letters from IPP33

10 K’s

The first time I picked up Lixy Yamada’s 10 K’s exchange puzzle and actually tried getting anywhere I was sitting in front of the telly. I had a go at a couple of the constructions and ended up with a few that looked vaguely like K’s – if you squinted your eyes and used your imagination. 

A short while after that I read George’s description of it and realised that I’d missed something important - all 10 constructions give you exactly the same K-shape! Having totally missed the point – or come up with an ingeniously creative solution – I decided I need to have another bash at 10 K’s – so when I recently went around to Nigel’s one evening to play with puzzles, I took my copy along. 

10 K’s has 10 different (very different!) dissections of the letter “K”, each in a different colour and all the pieces are neatly packed into a single sheet when not in play, although Lixy has also thoughtfully provided a set of individual Ziploc bags for each set of pieces. 

Back at Nigel’s I picked a benign-looking set of pieces and set about trying to make a K – and after a short while I realised that I’d started with the wrong one and tried to find a simpler one … and indeed after a brief search I’d managed to make a reasonably convincing “K” from the pieces … and then applying George’s rather handy strategy of building the next one on top of the first one, worked out where some of the pieces had to go, and where the others were likely to go…

The 10 different dissections really are different! 

I thought I’d seen a classic “K” dissection before, but I didn’t recognise it among the set in this puzzle. A number of the dissections have a couple of pieces that look similar, possibly even identical, and while it might seem to make sense to use them in similar positions symmetrically, that often isn’t very useful. Don’t you love it when logic proves useless in a puzzle?! :-)

IPP Dissection

Noji Tsugumitsu is pulling together some research into letter dissection puzzles and was dishing out a set of three of three dissections at IPP33 – and he kindly gave me a set of them of while we were visiting Kanazawa on our post-IPP trip. 

There are two different P-dissections which are reasonably confusing, but the I-dissection is positively devious, taking me several times the total time expended on the two P’s. 

Noji is quite keen to hear from anyone who has any interesting or unusual letter dissections, so please let me know if you have any and I’ll put you in touch with him …  he had a pretty large collection in a flipfile that he was showing around at IPP33 and he intends to publish them in some form in the future.

E&H

Emrehan Halici’s exchange puzzle  consists of a set of L-shaped pieces of different widths and lengths which you are asked to construct an “E” and an “H” from. The L’s are laser-cut acrylic pieces and come in 3 identical pairs … which might strike you as helpful, and indeed it may be helpful, however when you start trying to build the two target letters, you’ll probably find that you don’t really want a pair of everything – I kept finding a perfectly acceptable looking answer (from my perspective at any rate) only to have a piece left over… 

The two constructions required are really different, so solving one of them gives you absolutely no clues on solving the other … a pair of neat little challenges that use the same set of pieces – clever!