I’d played with one of them a while back and it had me
stumped.

….so when Brian Menold made a few more copies of Laszlo Molnar's original
L-I-Vator, L-I-Vator II and BDSM recently, I put in a little order from Wood
Wonders.

…and I was duly delighted.

Let’s start at the beginning – the original L-I-Vator Cube: Laszlo
Molnar entered this design in the 2015 Nob Yoshigahara Puzzle Design Competition. I had a bash at it in the Design Competition room in Ottawa and from memory
it kicked my backside.

The premise is fairly simple: pack the pieces of a 3*3*3
cube into a box where the only potential issue is that a pair of opposite
corners are blocked… the pieces are interesting in that there are an increasing
number of cubies on each piece – from 2 up to 7 cubies – start from the largest
piece, remove one cubie to form the next in the series – repeat until you’re
left with a simple 2-cubie piece.

So, what’s it like as a puzzle – pretty damn good! Those two
blocked corners in the box turn out to be really well-chosen! In theory there
are three ways to assemble those pieces into a cube… and then each face could
be uppermost, and oriented one of two ways, so I reckon there are 36 possible permutations
for those pieces inside the box… and while I’ve no way of telling whether I’m
right or not, I suspect that Laszlo has reduced that to a single possible solution
(allowing for reflections).

I’m just happy to have found

**solution!***a*
Next up is L-I-Vator II that uses the same shaped box and introduces
a different set of six pieces – these pieces only go together to assemble a
cube in one way… ! … so while it might be a little harder to find a potential solution
outside of the box, you know that’s how it must look inside of the box (allowing
for arbitrary orientation of the cube) when you do find an assembly.

Actually, no, it doesn’t… :-)

There is a lot of tricksiness involved here too… more tricksiness
than the original, IMHO.

At this point I need to interrupt myself and talk a little
about Brian’s work on these puzzles – terrific! I’m a sucker for good-looking
hardwoods – and the canarywood – particularly the bits with the spalting on
them are just lovely… they look the business… and the fit is exactly what you
want for a packing puzzle: the solution rattles, but nowhere along the way will
you be tempted into doing something that you shouldn’t be allowed to – it’s
obvious what you can and can’t do in terms of any tricksiness… :-) Nice work,
Brian!

OK, back to the solve – this one took me a while longer than
the first one… spread over a couple of evenings – ending with a wonderful
moment of triumph at the end of a series of deductions – yes, dear reader –
this one rewards Think©ing and deducting.

The third in my little Wood Wonders set is BDSM – and I’m
sure there’s a PG-rated explanation for the name out there somewhere, although I
suspect that the less PC version is a lot more descriptive!

Once again there’s a set of pieces to build a size 3 cube but
this time the “box” is more of a diagonal cubic bandage – picture a box with
two of its opposite corners sliced off on the diagonal… or just look at the photo!

My friendly well-worn copy of BurrTools tells me that the
pieces will assemble into a cube in 11 different ways… which makes finding
assemblies a bit like shooting fish in a barrel… however, and it’s a big
HOWEVER, finding one that will assemble inside the confines of that blocky wooden
ring is tough!

If L-I-Vator II kept me busy for a bit longer than the original,
this one kept me thoroughly amused for several evenings! I’d been working on some
puzzle hunt problems with some mates via t’internet and been making very little
progress on those puzzles so found myself fiddling with BDSM while trying to
work out some phonetic anagrams (it’s harder than it sounds!) when I finally
managed to find a useful way of getting the bits inside the bondage… YAY!

(Sadly my success on BDSM didn’t translate into great
encouragement and breakthroughs on the puzzle hunt… that was not a spectacular success!
Fun, but not a spectacular success!)

Thoughts on solving – I found it easiest to attack these head-on
– play with the pieces directly inside their boxes from the get-go… establish
if there are any real constraints on where some of the pieces can go and work
around those… and then experiment, invariably coming up with assemblies that
almost worked and then bashing through all of the possible variations on
ordering, orientation and tricksiness before discarding and trying another
assembly… fun puzzles to play with and even more fun to solve!

The two L-I-Vators are both brilliant designs, with the progressions of adding voxels/cubies from smallest to largest pieces. Very satisfying, as the choice of pieces is not merely random, but is a complete study. (As a mathematician, I see a contest problem in there.) As for the puzzle solution process: gee, I must have gotten lucky, since I was able to solve both in about 30 minutes each. The same cannot be said about the BDSM puzzle, as this has taken me a few hours to solve. There is absolutely no doubt about it: BDSM is wicked!

ReplyDelete-Tyler

...yup, evil! In a good kinda way... :-)

DeleteTyler, Allard.

ReplyDeleteHow would one go about developing an appreciation for interlocking/burr type puzzles as exemplified in the L-I-Vators post? My cognitive blindness sees them as primarily exercises in trial & error. However with able guides (Kate Jones, George Hart, Doug Engel), blogs (Rob's, Jaap's), and books I've begun to glimpse the logical & mathematical elegance within many categories of puzzles. So for a few years I have been amassing & vetting a collection (625+) of mechanical puzzles and abstract games which we make available to K-12 student/teachers through our "student-curated" inquiry-based learning" resource center here in Virginia/USA.

I could "cut my losses" and maintain a prejudice against interlocking/burr puzzles -- shunning their mere "aesthetic" appeal when I visit Wood Wonders, Cubicdissection, and Pelikan, but as an adherent of the Allardian Creed "I'm not a quitter!"

BTW, if you would like to see pictures of our physical space in all of its "blinged out" glory, click the "Google Docs' link below -- which also leads to a teacher's guide to the Geometry-related puzzles, games, and references our Curiosity Shoppe has to offer: https://goo.gl/1i5pF9

What a fantastic trove of resources and a great idea to get grow the next generation of problem solvers (and puzzlers!) - Nice work, Bob!

DeleteEssentially there's alsways going to be some element of trial and error with these sort of puzzles - the really good ones allow you to figure our sort of method for removing a significant number of the possibilities and keep it in the "fun" realm befroe it goes into the "brute-force exploration of every single possible combination" realm. (Or at least that's my theory!)

Hi, Bob,

DeleteI have learned several solving hints for such puzzles, but one that I find to be most effective is a 4-colour assignment for 3x3x3 cubes. I could never explain it as effectively as Conway, Berblekamp, and Guy in their landmark compendium . Once colours are added to the cubies of the pieces, then only certain solutions exist, or one can prove that certain colour combinations have no solutions. Once a 3x3x3 solution is found outside the box, the second puzzle is to insert the pieces in the restricted opening of the box. Some of these are straightforward, while others require a rotation of a piece or two within the box. (Good Luck!)

I do not recommend trying to solve the 3x3x3 cube within the box without first solving ALL possible 3x3x3 solutions outside the box.

So, for me, the solution process reduces to the elimination of contradictory cases, thus leaving just a few valid solutions to try to insert in the box.

The bonus for me with such puzzles is, as I stated earlier, that the pieces themselves form a progression. This is mathematically very beautiful. Such puzzles are apex puzzles for me.

Hmm, it appears that the "landmark compendium" didn't come up, as I used angled brackets. Silly me. The missing title is "Winning Ways for your Mathematical Plays." I am fortunate to have both the 1982 two-volume original edition as well as the 2001-2004 four-volume second edition. A terrific wealth of information!

Delete