Packing It In 4: Live Free or Pack Hard

First, there was Packing It In: Pack Hard.

Next, there was Packing It In 2: Pack Harder.

The puzzles returned in Packing It In 3: Pack Hard with a Vengeance

Now it’s time to make a decision:

Live Free? Or Pack Hard…

Bermuda Hexagon, 4L Bin, Punch Cards, Nested Cubes,

Ship in a Bottle, Hoffman Packing & Inelegant Series


Designers:
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

(Not Available)

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.


Bermuda Hexagon

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.


4L Bin

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.

The pieces feature two arrangements of protrusions, each comprising three sides with one mirrored.

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

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).


Nested Cubes

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…


Packing it in 3: Pack Hard with a Vengeance

First, there was Packing It In: Pack Hard.

Then. there was Packing It In 2: Pack Harder.

Now, it’s time for Vengeance.


(The order of these posts do not indicate relative levels of difficulty. Please puzzle accordingly).

Squary Packs, Quadro, Snake Pit, Mushkila

Yavuz Demirhan (check out his Etsy store)

In case you haven’t noticed, there are a lot of puzzles out there. A lot. Within the various subgenres of mechanical puzzle-dom, therein lies nearly infinite possibilities – who would have thought that even “just” a 4×4 cube could contain so many possibilities as to continuously bring us more TICs and Somas and so on…

Squary Packs

Some puzzles push out into their own territory, their movements and solution sitting somewhere amidst or between those that already exist. Yavuz Demirhan’s Squary Pack series is a great example of such a design: they are 2D/3D packing sliders that require you to navigate four dual-leveled pieces through a restricted one-piece-size opening at the center of the space to cover the bottom of the square box. The pieces are all flat-bottomed, with various voxels of different dimensions further complicating the solution, requiring you to slide your pieces around as you attempt to find a way to insert whichever piece needs to go in last; some of the series are further encumbered by blocks affixed to the box. You need to get all pieces in with the blocks facing up and you will find varying degrees of difficulty identifying where and when in the dance of pieces you can insert the final pieces.

The result can be quite tricky and is most definitely fun. I initially got #2 and 4 (knowing as I did that I would almost certainly end up wishing I had just gotten them all – my recent delivery of #1, 5, 7, and 8 shows I was most definitely right in thinking I had been wrong). My first impression was that they are quite attractive looking puzzles: his work is always wonderful looking and these are no exception. Dark wenge boxes with a reddish sappeli for those with blocks attached, which cover one of the two levels and protrude above the acrylic top for half that height. The pieces match the boxes with the same wenge contrasted by light ash blocks atop them. On the bottom of the box he has his logo/initials engraved above the name and # of the puzzle. Interestingly, they range considerably in the square’s dimensions (while all sharing a height of 3.5 cm): 1 & 2 are 7.5 cm, 3-5 are 9.5 cm, 6 is 11.5 cm, and 7 & 8 are 13.5 cm (ranging in price for a reasonable $30 – $50 depending on size). I’m happy to say that Yavuz is designing additional Packs, extending the series to (at least, I believe) 15.

Sitting down with the Packs, it took a minute to orient myself to what exactly I needed to do – initially, I solved my first two incorrectly by placing one of the pieces upside down (which was itself a non-trivial solve). I later learned that this was not correct and proceeded to attempt to (re)solve them correctly. It is necessary to find a way to get three of the pieces into the Pack such that there remains room for the 4th to be inserted and slid into the existing space – oftentimes requiring that the remaining pieces dance around before this becomes possible. This is complicated further in those Packs that contain internal pieces blocking the way. Each solution is unique and while these puzzles share a pleasantly consistent aesthetic, they are quite diverse. They range in difficulty: all the feedback I have heard from our fellow puzzlers has been most definitely positive, although some have felt that a couple of them were a bit easy. Regardless, I found them all to be challenging, with some being quite difficult (particularly #2 & 4). The coming versions are apparently a further step up in difficulty, and I look forward to getting them once available.

Yavuz has been making puzzles for a while and has a LOT more interlocking and packing puzzle designs out there (he has a few hundred on PWBP); while he produces his own works from time to time, it is not at all uncommon to find his works included in the puzzle releases of others (including one design set to come out in this week’s CubicDissection release). While I have a few of his designs that were made by other puzzle-makers, I also have the pleasure of owning a few more that he made himself – also 3D packing puzzles with restricted openings. His work is all wonderfully precise, using quality woods that look and feel great.

Quadro

Quadro is a small-ish puzzle whose wooden box and acrylic top share an aesthetic with the Squary Packs (the puzzle’s name also etched into the bottom). It consists of 6 identical squares that must fill a rectangular box – while not interlocking, the solution will require a rather delicate dance to allow you the chance to drop that last block in with the satisfaction the comes with finally filling this up with those. This is one of those puzzles that is more complicated than it looks without being something insurmountable – I still managed to go in circles for quite a while, even asking other puzzlers if perhaps there was a “trick” that I was missing. Eventually I actually stopped and tried that thinking thing I’ve heard so much about, soon managing to find the right moves (leaving me wondering how I had managed to do everything but the one thing that would work).

Snake Pit

Snake Pit eschews the acrylic top for an attractive mix of light and dark woods with an opening that runs the length of the puzzle and is 1/2 as wide, leaving one voxel on either side. There are 4 pairs of mirrored pieces that must find their way inside for a fun solution that was just the right level of difficulty for me.

Mushkila

Mushkila is my newest acquisition, having received it along with my second order of Squary Packs. It uses a beautiful mix of woods with lovely grain patterns that play nicely with the mix of red and dark and light brown. Interestingly, the opening is not a regular shape: it runs the length of the box (similar to Snake Pit) to allow the single rectangular piece to go in and also adds a square cut-out to allow the five angled pieces to go in at any orientation. This gives it a bit of a deco look, which meshes well with his choice of woods. I have yet to solve it, but having spent a little bit of time on it, it is clearly a non-trivial solution that should provide a fun solve while looking great on my shelf.

All of these packing puzzles share a simplicity and elegance, both in terms of their aesthetic as well as their movement – I highly recommend following Yavuz’s Etsy page as I know that any time Yavuz has something available, I will happily say “yes, please” to whatever it is, sight unseen

Fun Grade: 5 Sinatras
Difficulty Grade: 3 to 4 Sinatras

Puzzle Oddity

Anti-Gravity Box

Frederic Boucher, 3D Packing Puzzle, 2.25″ x 2.25″ x 1.5″

A few months ago, I wrote to Frederic in the hopes that he might happen to have a few puzzles that were seemingly unavailable. Most were, but he did happen to have a last copy of Anti-Gravity Box, which I happily requested, along with a few other new puzzles that he had on hand.

I have solved several of Frederic’s puzzles in the past – 3D and 2D packing puzzles that offer a serious challenge, comparable to pieces by MINE or Osanori Yamamoto, featuring elements such as interlocking elements and restricted openings.

Anti-Gravity, however, adds new mechanics by introducing a number of magnets into the mix. This makes for a unique and novel puzzling experience; it is no longer “just” about finding a way to get the pieces into their frame, as the magnets throw one’s general approach out the window.

The box is a 3×2 voxel frame that features a removable, acrylic top, allowing you to easily reset the puzzle and view your progress. The box has two, single voxel openings at 90 degrees to one another; both are in the middle of the bottom level, allowing you to enter each axis, but offering no room for angles of any kind. You must fill it with 6 identical rectangular 3×1 blocks; 2 have two magnets on one side, 3 have magnets on one end, and one block has none.

There are rules, of course: you need to place it on a flat surface and you are not meant to pick it up or tilt it (of course, you may hold it while you insert other pieces); you cannot poke your finger into either of the openings to push the pieces; it goes without saying that you cannot just lift off the top and place them in. The removable top is a kind addition, as it avoids the need to struggle to remove pieces when you have eventually found you had made a mistake. The puzzle arrived with the pieces stacked neatly inside. It is kind of cool to have a puzzle so confident in its structure, that it can come fully solved without having spoiled anything.

While by no means simple, neither is it an overly difficult puzzle – in my experience, one of his other packing puzzles was more challenge than I could meet (I am admittedly not so great at packing or interlocking puzzles generally – my interest far exceeds my ability when it comes to these types of puzzles).

More importantly, this is a very fun puzzle, and one with which trial and error will not get you very far; knowing the pieces you can eventually figure your way through it.. After spending a few minutes playing with it, experimenting to get to know the pieces and what they can and can’t easily do, I had to stop and think. This led to the first big aha moment of a series of such moments, leading to the full solution. Each step is its own planned approach, each piece requires forethought once a workable order has been determined. Apparently, this has two approaches that lead to similar solutions; I have found one and will undoubtedly spend some more time to find the second.

TL;DR: Anti-Gravity Box by Frederic Boucher is an original approach to a 3D packing puzzle, with magnetic pieces needing to be stacked using entries that allow for little margin of error. While not Boucher’s hardest puzzle, each move must be planned and purposeful through thoughtful approach and not just trial and error. It features a convenient removable top to reset after you inevitably make a mistake, and is so confident in its own puzzling, that it can arrive solved without lessening its challenge.

Originality: 4 and a Half Sinatras

Difficulty: 3 and a Half Sinatras

Instructions Included