Bermuda Hexagon, 4L Bin, Punch Cards, Nested Cubes,
Ship in a Bottle, Hoffman Packing & Inelegant Series
Bill Cutler (Bermuda)
Dean Hoffman (Hoffman)
Haym Hirsh (Inelegant Series)
Pit Khiam Goh (4L Bin & Ship in a Bottle)
Tom Lensch (Punch Cards & Nested Cubes)
All copies produced by Tom Lensch
Life got in the way of my puzzling these last few weeks, causing a few weeks to go by without any puzzle posts (aside from my recent post on Rob Yarger’s One Hand Puzzlebox); somehow, dear reader, you survived this lull and I am happy to be back to doing what I love – rambling and ranting about puzzles. To make up for this soul-sucking abyss that went almost entirely unnoticed, I shall pack several puzzles into the present post (see what I did there?).
This post collects several puzzles from different designers; all copies in my possession were produced at various times over the last several years by the incomparable Tom Lensch: master craftsman, puzzler and all-around-good-guy. Some designs are his and some are by others: all are amazing puzzles that bring a nuanced and original perspective to packing puzzles, stretching the term beyond our assumptions of what this might mean.
Please note that these are all older productions from Tom and are not available from him. Tom produces puzzles in fairly limited quantities and does not generally keep stock on hand, instead selling directly to collectors.
At the first Gathering for Gardner in 1993, OG puzzle designer, author, analyst and collector, Bill Cutler, shared his design for a challenging, three layer packing puzzle with the excellent puzzle craftsman, Tom Lensch. Since then, Tom has released three limited runs of this extremely challenging puzzle, most recently (a year or two ago) in an absolutely beautiful Kentucky Coffee-Tree with a Walnut frame. He offered two grains, and I opted for the narrower, medium grain. The puzzle is a good size at 3 cm x 13 cm; big enough to be appreciated aesthetically as well as comfortable manipulated but not so big as to take up an unnecessary amount of space.
Originally, the 12 pieces of Bill’s design were composed of one large triangle glued in various configurations to two smaller ones (a total of 12 large and 24 small), the whole puzzle consisting of 3 layers fitted perfectly into a hexagonal tray. The design provided a fairly significant clue, as the top layer showed 6 large triangles.
Following the dark grains of the Coffee-Tree, Tom elected to eliminate the large triangles, instead making them out of 4 small triangles, with the puzzle now using a total of 72 small triangles glued into 12 pieces; each piece is composed of 6 small triangles, but they are all quite different from one another. This design allowed the pattern to be consistent across its three layers, making the puzzle more of a challenge – considering that this was not an easy puzzle to begin with, Tom’s most recent release is, simply put, damn difficult.
I have not managed to solve this puzzle despite spending a good amount of hours spread out over a year or so: as with many great packing designs, you feel confident that you are onto something when you are nearing the end, only to find that one or two final pieces insist on poking out above the frame’s top or simply will not fit. While the use of multiple layers in most pieces limits the possible configurations, the triangles can nonetheless seemingly fit in so many different ways that the correct solution continues to elude me. However, the excellent woods and unique design are enough to keep me coming back, hoping that I will eventually find myself worthy of a happy dance when that last piece slides perfectly in.
This design by Pit Khiam Goh may share a name with other puzzles (4L by Yasuhiro Hashimoto and 4L Basket by Koichi Miura) but the similarities end there: this is an amazingly fun puzzle that has you searching for that perfect dance of pieces that must be inserted into its box in a way I’ve not seen elsewhere.
The box resembles that of Eric Fuller’s Pin Block Case , the opening severely restricted to no more than the center of one quarter – the box does leave open a strip on the back and bottom of the puzzle to assist with manipulating the oddly shaped pieces. Tom’s release uses brass pins along the edges of the right and left side of the box for a unique aesthetic, lending some color to the light woods used. When solved, the open quarter of the puzzle will be filled, apparent-cube style (the apparent cubeness belied by the gaps seen when looking through the open strips), some contrasting woods exposed asymmetrically yet beautifully at its main opening.
The four pieces are of the same general size and shape, their dimensions equal to two lengths of the square, fitted at a right angle. The challenge is based on the narrow protrusions placed along the pieces. The edge pieces are easily discerned as they only feature protrusions along a single side, lending you a much needed starting point. At 9.5 cm, the box is sizable, allowing the pieces to fit well in your hands and be easily manipulated via the access points at the back.
When first confronted with the puzzle, I was pretty intimidated; it seemed like something that would require a lot of trial and error to make any progress. However, after a bit of playing around, I saw that there was a clear logic to how the pieces must fit – before too long, I’d found the most likely configuration of pieces to be inserted for the solve and turned to determining how to get them in there.
This is what really makes the puzzle fun – rather than getting bogged down by too many possible configurations, a bit of early analysis allows you to focus your efforts on the dance, forcing you to examine the possible entries and movements to determine the order of insertion, and the needed back and forth steps to allow each to get where they need to go. The final solution relies mostly on this logic, combined with the careful planning necessitated by the restrictive nature of the puzzle.
After finding the correct configuration, I eventually found the correct order of insertion; I then needed to find the proper dance moves to follow this order, finally spending a good amount of time trying to realize these moves, forcing me to not only have a good grasp of its choreography, but to discover the kind of great aha moment that is the mark of a really cool packing puzzle. This is not the kind of puzzle that you will solve without realizing you were about to do so – you need to know what needs to happen going in and really think about how to put this into action. The solution really is elegant – turning down some dead ends, I found my failed attempts to be a bit fiddly at times and was impressed by how graceful the actual solution felt.
The puzzle fell into that sweet spot of puzzling time (not you, MQ) – I was able to solve it in just a couple sittings, well beyond anything resembling easy but well short of reaching the point of frustration (let alone boredom). This is the kind of puzzle that begs to be solved, its unique challenge playful despite being difficult.
Punch Cards was Tom’s entry at IPP23 in Chicago. Consisting of a 3.25″ X 2.75 ” X 1.7″ frame, it comes with 5 acrylic squares with a number of circles cut out in unique and asymmetric patterns. Inside its walnut frame, you can see 6 dowels of differing lengths, obstructing the ability to fit the acrylic pieces inside.
The frame has a unique, fidget-friendly feature basic to the puzzle (which is to say it isn’t a spoiler). Solving the puzzle with a static frame would clearly be impossible – the pieces simply cannot be inserted with the dowels where they are. As such, one side of the frame can be lifted a quarter of an inch or so, lifting a couple dowels from one side of the puzzle, leaving you with only those on the frame’s other side to restrict entry. Of course, placement of the acrylic pieces must allow the frame to be closed in order to find the solution.
Examining the pieces allows you to dismiss some potential entries, leaving you to try various orientations and orders to determine where each piece might fit; some amount of trial and error allows for progress with a good amount of logic to bring you home.
Solving Punch is really quite fun – each little aha combining to produce that final sense of earned satisfaction that comes when the frame snaps perfectly closed, leaving the acrylic pieces jutting out of one side, displaying its unique design wonderfully and temptingly. I’ve found it to be fun to just fidget with it, the frame snapping shut satisfyingly; while re-solving is fairly straightforward (assuming you haven’t mixed the pieces up), there is something about sliding each piece in and dropping the frame closed, securing the pieces perfectly within, that I find gratifying (I’ve done it about 5 times just while writing this).
This is a design that I have been hunting for since reading about it in some of the great puzzle blogs out there (as opposed to the mediocre one here). Originally entered into the 2012 Nob Yoshigahara Puzzle Design Competition, the puzzle consists of five nested cubes (you can see where the name comes from), the outermost a respectable 7.5 cm.
All but the smallest cube (which is so perfect as to seem to consist of a single piece of wood) has a lid that fits with the absolute precision found in all of Tom’s work. They rest perfectly atop each cube with an airtight feel that is stable and secure while being easy enough to remove. The largest cube features a brass pin at its bottom, protruding straight ups bit less than half the length of the cube. Each of the other four cubes feature a small hole on multiple sides, placed slightly off-center in an inconsistent manner that is the main challenge of the puzzle.
The fit of the various cubes is absolutely perfect; as they slide slowly into one another, you can actually feel the air being displaced by the precise fit. Of course, it is not a simple matter to get each in completely: the brass pin prevents this until you find the correct orientation of each successive piece.
I worked my way in, starting with the largest of the cubes, soon falling into the familiar state of puzzling zen that accompanies some puzzles. The puzzle has a conceptually similar experience to Punch Cards while feeling totally unique in practice: the reliance upon a mixture of close examination and trial & error, with a nice dose of logic bringing it all together. Each success was progressively more satisfying until all four inner cubes sat perfectly one within the other, the combined piece sliding wonderfully into the outermost cube so precisely that any puzzler would find it impossible not to smile. Having accomplished this challenging feat, I placed that final lid atop the box, the seemingly simple wooden cube subtly belying the trickiness contained within.
Ship in a Bottle
Ship in a Bottle is another design by Pit Khiam Goh; I am constantly impressed by the diversity and uniqueness of his designs that rely on a broad range of mechanisms that oftentimes use a genuinely original approach to puzzle genres, resulting in a puzzle that is pretty much impossible to resist.
Ship consists of a bottle-shaped wooden frame with an acrylic front and back attached by rounded brass pins that helps give it a slightly nautical feel; its narrow sides are open, allowing for the easy manipulation of the pieces within. Inside, there are six maple blocks: two are one-voxel cubes and four are two-voxel rectangles. Engraved on the blocks is the image of what appears to be an Ancient Greek Trireme (or similar). The interior of the bottle is three by four voxels, with two left empty. Atop the bottle, there is a one-voxel opening at its center; the puzzle comes with a lid that protrudes into the bottle’s neck, its top extending outwards to plug the hole, one side featuring a magnet that holds it to the frame with a fidget-friendly click.
The puzzle has a unique goal: it arrives with the ship facing out towards the neck and you must remove the pieces and re-insert them so the ship has turned, facing in towards the bottle’s bottom. This makes for a fun puzzle that is perhaps equal parts slider and packing. Three of the rectangular pieces are oriented perpendicular to the neck, requiring you to find the room to pack them in properly, rotating each of the pieces after having inserted them sideways. But, in the words of the late, great Don Pardo: “That’s not all!” – remember, the goal is not just to get the pieces in, but to do so such that the image of the ship can be reversed.
This combination of puzzle genres makes for a truly fun experience; although I found it not too difficult to get all of the pieces in, the available order and placement of the inserted pieces severely limits their internal choreography, which must allow for sliding the pieces around one another so as to create the reversed image of the ship. Aha moments abound along the way: first you must find how you can get all the pieces in, then you must find how to do so to allow the solved state to be found. This progressed for me in phases, as I would find myself closer to each goal only to find myself backtracking as I realized I needed to tweak my method. For example, I eventually came across the correct dance, only to find that I had two pieces inserted in the wrong order, leaving the ship with an inverted side. I’d sort of missed how exactly I had gotten to this point, and found myself struggling to reverse the dance; this allowed for a better understanding of the puzzle’s solution, and I was then able to change the order of insertion to allow for the solved state to be reached.
The design is really quite amazing: resetting the puzzle to the original ship orientation is a fairly trivial and straightforward matter (largely due to the fact that you can put the square pieces in last, leaving plenty of room to get the rectangles in beforehand) – it is only when you try to reverse it that you run into the significant challenge of the design. After a couple of good puzzling sessions, I was able to find the solution; I left it solved for a while before resetting it to allow for a solid re-solve challenge when I inevitably forget how the hell I was able to solve the thing.
Hoffman Packing Puzzle
This is perhaps one of the most iconic packing puzzles out there, a classic design first described in 1978 by Dean Hoffman (not to be confused with the 19th Century puzzle godfather Professor Hoffman, author of Puzzles Old & New and other quintessential puzzle books). (Ed. This is perhaps the second best thing to come out of that year…… 😉
Hoffman’s Packing Puzzle is such a prototypical design as to deserve its own Wikipedia page; as such, I will not get into some of its interesting mathematical significance (because I am obviously totally capable of doing that…. cough cough). The puzzle consists of 27 identical pieces that will form a 3 x 3 cube that is internally imperfect (as its total volume is less than the internal space of the box) while having perfectly parallel sides.
Haym Hirsh has come out with a series of designs built off of this design, combining pieces so as to create puzzles with a single, unique solution as compared to the original’s 21 distinct solutions. Haym’s Inelegant Series begins with the puzzle formerly known as Hoffman Jr. (Inelegant 5 x 5), followed by Inelegant Soma, Inelegant Box, Inelegant Cube, Inelegant Snakes and Inelegant Fake, which have all been produced by Brian Menold of WoodWondersOnline (I have so far only managed to obtain copies of Soma and Snakes – he does re-release these from time to time so I may yet realize the impulses of my Hoffmania). These are really quite fun and challenging, riffing on the concepts behind the original Hoffman to create a series of aesthetically similar yet mostly practically unique experiences that feature added tweaks such as empty voxels or pieces fixed to the frame.
Tom produced an insanely cool run of Hoffman some years ago; not only did he use a different exotic wood for each for the 27 pieces, but he actually engraved the name of the species on each individual piece. Fitting perfectly into a two-tone wooden box (with a lovely, floating lid), the puzzle just looks fantastic. This makes for both a cool version of a classic puzzle as well as a fun way to check out samples of exotic woods – I’ve certainly pulled them out when trying to identify what type of wood a puzzle might be or to help choose which woods to get when presented with a choice.
Despite having multiple solutions, Hoffman is quite a challenge that is entertaining to solve, as you watch what at first appears to be nothing more than a rather chaotic jumble of blocks turn into a nice, smooth cube (eventually…… hopefully… maybe).
Welp. There ya go: my packing puzzle mega-review.
Stay tuned – one of these days just might be a Good Day to Pack Hard…