Jigsaws!

Jigsaws!

Four of my favorite puzzles from the past year have been jigsaw puzzles! I'm surprised to hear myself say that, as I've always had mild contempt for jigsaws, regarding them as formulaic, repetitive, and unimaginative. That disdain is shared by others: none other than Stewart Coffin wrote, dryly perhaps, that "most jigsaw puzzles are not designed to exercise or perplex the mind." But these four really breathe new life into the genre, and they give a sense of tremendous, unexplored possibilities. Each of them has been a joy to solve.

Framed Jigsaw by Hajime Katsumoto

The most elegant, and in my opinion most brilliant, is Hajime Katsumoto's masterful Framed Jigsaw, crafted by Jean-Claude Constantin out of laser-cut wood and acrylic. It has sixteen pieces, already a rather small number; but there are only four distinct types - and any two of them can be fit together, since all the connectors are identical! The catch is that the pieces must be carefully maneuvered into a 4x4 frame with a square 2x2 opening in the center.

It seemed rather daunting at first, and my initial trial-and-error experiments went nowhere. With a bit of logical thought, though, I was able to narrow down the possibilities considerably - always the sign of a great puzzle! - and execute the intricate series of movements necessary to fit all the pieces snugly into the frame. Ultimately I found it only moderately difficult, but with a very satisfying solution. Each of Katsumoto's puzzles is a gem, and this one is no exception.

Jigsaw Puzzle 29 by Yuu Asaka

Next up is Jigsaw Puzzle 29, so named because it has twenty-nine pieces (a rather odd number, given that they tile a rectangle). It was designed and made out of laser-cut acrylic by Yuu Asaka, and it has been widely popular, receiving a Jury Honorable Mention at the International Puzzle Party 38 in 2018.

Jigsaw Puzzle 29 has the most "traditional" appearance of the puzzles mentioned here - at first glance, the pieces look nearly indistinguishable in shape from those in, say, an ordinary Ravensburger puzzle, and they must be fit into an unassuming rectangular tray. Unlike traditional jigsaw pieces, however, they are completely blank, and it is not clear which side is "up".

Closer inspection reveals other differences as well. There are five corners (!), and the pieces vary slightly in dimension, so that it is not obvious at all into which orientation they belong. It took me quite a bit of (thoroughly enjoyable) trial and error and head-scratching to solve, and it was a challenge practically right up until the end.

Asaka has also released a simpler variant, Jigsaw Puzzle 19, which I haven't tried. I found Jigsaw Puzzle 29 perfectly approachable without having done its baby sibling, though, so it isn't necessary to attempt Jigsaw Puzzle 19 as a stepping stone. Here's hoping for a Jigsaw Puzzle 39 (or larger) in the future!

Cornered: The Logical Jigsaw by Portponky

The third, somewhat less publicized, design is Cornered: the Logical Jigsaw by Portponky, a designer I hadn't previously encountered. It's made out of laser-cut acryclic by Pavel Curtis, who describes it as an exercise in pure logic: "This is a challenging, but super satisfying solve, involving no backtracking or guessing: every single time you place a piece, it's because you know that it's correct!"

I might quibble philosophically with the latter statement; on some level, backtracking is just an iterative application of logical thought, and where you draw the line really boils down to how many steps you're able to keep in your head, a rather vague consideration. But it absolutely is challenging and super satisfying, and it's hard for me to envision solving it without first reasoning through the underlying logic of the design.

Cornered consists of twenty-five identically sized pieces, and the challenge is to arrange them into a 5x5 grid - somewhat reminiscent of Framed Jigsaw, but this time without a tray. And it has five corner pieces - somewhat reminiscent of Jigsaw Puzzle 29! But the bizarre assortment of connector types - one of them "androgynous" - gives it a unique flavor.

I can't say too much without dropping spoilers, so I'll just reiterate that it's as much logic puzzle as jigsaw, and if you've enjoyed Framed Jigsaw or Jigsaw Puzzle 29, I can certainly recommend Cornered as well.

Hills of San Francisco by Liberty Puzzles - a daunting box of beautiful laser-cut wood!

The final puzzle is really more of a traditional jigsaw puzzle, but it's so beautifully made that I feel compelled to mention it here. Boulder, Colorado-based Liberty Puzzles offers traditional, artisan jigsaw puzzles in over 600 designs. The one I chose is titled "Hills of San Francisco."

Those are some gorgeous and high-quality pieces!

In one respect, they are fairly ordinary: hundreds of 2D shapes interlock to create an image - in this case, an artist's rendition of the city of San Francisco. What sets them apart is that the piece shapes are very inventive and unusual; each one is unique, and among them one will find a variety of spirals, jagged edges, and odd angles. Each puzzle also contains a few dozen "whimsy pieces" - figurative shapes that cleverly relate to the parts of the image where they appear in the solution, often exhibiting a creative interplay between the patterns on the image and the shape of the puzzle pieces.

Evidently, a lot of care and artistry goes into these designs, and they're beautifully made from 1/4" thick laser-cut wood - just the weight of the pieces in your hand reminds you that this is no ordinary jigsaw. The publisher describes them as a tribute to a bygone era in puzzle history:

The golden age of jigsaw puzzles was approximately the 1930s. This was before the advent of die-cut (stamped) cardboard puzzles. Most puzzles were made of wood, and hand-cut using a scroll saw.... By the early 40s, the craze had died down.... The art and popularity of the hand-cut puzzle subsequently waned significantly. Liberty Puzzles are a throwback to the golden age of jigsaw puzzles!

I've done a few other Liberty Puzzles designs as well, and they're all beautifully made and just plain fun. They make for a great communal solve, and I've particularly enjoyed working on them with friends and family.

At the time of this writing (November 2019), all four puzzles are in print and available! Framed Jigsaw is in stock at Mr. Puzzle Australia, Jigsaw Puzzle 29 at Puzzlemaster, Cornered at Pavel's Puzzles, and Hills of San Francisco at Liberty Puzzles.

Let's hope we can look forward to more innovations in this genre in the next few years!

Adventures in 3D Puzzle Printing

Figure 1. Jeff Namkung - Slow Waltz (left); Janus (right)

Adventures in 3D Puzzle Printing

The past fifteen years have been a fruitful period for interlocking mechanical puzzles, with the online archive Puzzle Will Be Played now indexing over five thousand published designs. Unfortunately, the sheer breadth of the puzzle catalog ensures that only a tiny minority of designs are commercially available at any given time. This can be quite frustrating to the casual collector, or to those seeking out a specific puzzle, which (if it has been produced at all) may be quite difficult to obtain.

Over the past six months I've been exploring 3D printing as a solution to this problem, and found (somewhat to my surprise) that a vast range of puzzle designs - fully functional, and even aesthetically attractive - can be successfully realized with home 3D printers.

Figure 2. Yavuz Demirhan -
Nembus 2 (left); Knotty 6 (right)

What has most surprised me is the quality of output. No one will mistake 3D printed puzzles for artisan-made wood creations, but they are not throwaway prototypes either: they are smooth and precise, and a joy to play with. Best of all, they are fast and inexpensive to manufacture, and require no special skill to produce other than a basic understanding of 3D printer operation.

In this post, I'll discuss some of the challenges with 3D puzzle printing, and I'll introduce puzzlecad, a software library that streamlines the creation of 3D printable puzzle models. Along the way, I'll showcase some of the puzzles I've successfully printed. All of the models pictured in this post were printed by me, at home, on a Prusa i3 MK3. I hope that this work will inspire more people with the realization that printing high-quality interlocking puzzles - even fairly complex ones - is fun and accessible to everyone.

Anything (Rectilinear) Can Be Made Printable

Figure 3. Two pieces from Coffin's Quartet.
The piece on the left has an overhang;
the one on the right is simply printable.

The idea of 3D printed interlocking puzzles is not a new one. Frans de Vreugd's Gordian Knot was posted to thingiverse, one of the leading sites for printable models, as early as 2011. Richard Gain has designed several puzzles specifically to be amenable to 3D printing, and he has made many more (by a variety of designers) available for purchase in his Shapeways shop. Recently, Lee Krasnow of Pacific Puzzle Works, already renown for his accomplished wood and metal puzzlecraft, has made a number of new and classic puzzle designs available on his thingiverse page and in his etsy shop.

However, 3D puzzle printing has historically been encumbered by several challenges. A significant obstacle arises when printing puzzle pieces with overhangs. Figure 3 shows two pieces from Stewart Coffin's "Coffin's Quartet". Let's call the piece on the right "simply printable" - it can be easily printed, in the orientation shown, on essentially any 3D printer. But the piece on the left poses more of a challenge: no matter how it is rotated, some part of it will have empty space underneath. Because 3D printers build up objects in layers, with each layer supported by the ones beneath it, pieces with overhangs are more difficult to print.

Figure 4. More simply printable puzzles:
Bruce Love - Love's Dozen (left);
Andrey Ustjuzhanin - Boxes and Frames (right)

Many great puzzles consist entirely of simply printable pieces. The Demirhan puzzles in Figure 2 are simply printable; a few more examples are shown in Figure 4. But many other puzzles contain one or more pieces with overhangs, so to capture the full breadth of interlocking puzzle designs, some mechanism for handling more complicated puzzle pieces is essential.

One option is to print with "supports", temporary structures that are detachable once the print is completed. However, removal of supports leaves scars that are aesthetically unpleasant - and even interfere with puzzle operation by reducing the accuracy of the tolerances. High-end printers can print supports with a special material designed to minimize scarring, but that option is unavailable on many 3D printers, and it introduces additional cost and complexity in any event. Commercial printing services such as Shapeways are another option, but they can be quite expensive.

Figure 5. Example of a snap joint. Once locked in
place, the joint forms a permanent connection.

The ideal solution was suggested by Richard Gain: print overhanging pieces in several components that can then be snapped together. Figure 5 shows an example of such a "snap joint". Once locked together, the joint forms a strong, permanent connection.

Snap joints can be used to produce high-quality renditions of puzzles that are traditionally difficult to print. For example, Tim Alkema's Rift (Figure 6) can be printed using just a single joint each for the white and blue pieces (the yellow and green ones are simply printable). By using multiple snap joints when necessary, arbitrarily complex rectilinear puzzles may be constructed.

Figure 6. Tim Alkema - Rift

Puzzlecad: A CAD Library for Puzzles

Puzzlecad is a new software library that streamlines the specification of puzzles for 3D printing, including puzzles that require snap joints. It's implemented in OpenSCAD, a general-purpose open-source modeling platform. Puzzlecad translates the structure (voxels) of an interlocking puzzle into a 3D printable model, automating the work of laying out the puzzle components, beveling, and joints. A typical puzzlecad specification for a single piece looks like this:

burr_piece(["x..|xxx|x.x", "...|...|x.."]);

Those strings of x and . represent arrays of voxels; an x puts a cube at the relevant position and a . leaves it empty. The example just given, in fact, produces the piece on the right in Figure 3 above. Puzzlecad allows for a wide range of customization; for example,

burr_piece(["x..|xxx|x.x", "...|...|x.."],

    $burr_scale = 12, $burr_insets = 0.07, $burr_bevel = 0.5);

prints a piece with voxels 12mm on a side, 0.07mm tolerances, and 0.5mm beveling on the edges. (I've found that these particular settings work well for many puzzles.)

Snap joints can be easily modeled by annotating individual voxels within the puzzle specification. The following specifications give the two components of the jointed piece in Figure 5 above:

burr_piece(["..x|xxx|x{connect=mz+,clabel=Ay-}.."]);

burr_piece(["x|x", ".|x{connect=fz+,clabel=Ay-}"]);

Figure 7. Snap joint with the label "A"

The snap joints modeled by puzzlecad are rendered with an identifying label, such as the letter "A" on the male connector in Figure 7. The identical label is printed on the interior surface of the corresponding female connector. In this way, the correct joint pairings and orientations can be easily identified when preparing puzzles with large numbers of jointed pieces. Once the snap joints have been connected, the labels are permanently hidden from view.

In this way, essentially any rectilinear interlocking puzzle can be prepared for printing in just a few minutes. Puzzlecad ships with documented examples that provide more detailed usage information.

For more examples and information on Puzzlecad, or to download the library, please visit:

https://www.thingiverse.com/thing:3198014

Figure 8. Gregory Benedetti - Stand By Cubes 1, 2, & 3

The Future of Puzzles and 3D Printing

Figure 9. Clockwise from top left:
Oleg Smol'yakov - GELO-1234; Ken Irvine - Pink Ivory Ring;
Osanori Yamamoto (arr. Ishino) - Pig Nose 2

When I started collecting mechanical puzzles in earnest a few years ago, I was initially frustrated by the (at best) intermittent availability of even the most essential puzzles in the canon. Puzzle collecting takes patience - and also money: assembling a representative collection of interlocking puzzles requires an investment of many thousands of dollars, a barrier that is prohibitive to many.

3D printing offers a solution to both problems. Most of the puzzles in this blog post used roughly $2 worth of filament (the Stand By Cubes were the most expensive at around $4.50 each, partly because I used costlier "woodfill" filament for the bases). Decent printers are now available in the under-$400 price range. For a relatively modest investment, anyone can now select a puzzle from a vast menu in Puzzle Will Be Played, implement it in puzzlecad in a few minutes, and have a copy ready to play with the next day.

Figure 10. Stewart Coffin - Involute (left); Convolution (right)

In the coming years, 3D printers will become increasingly inexpensive and easy to use, and we can reasonably expect them to become commonplace in the not-too-distant future. The technology has the potential to completely change the equation for puzzle accessibility and availability - to introduce more people to the breadth and ingenuity of puzzle designs, and hopefully, to inspire and enable new designers.

Since acquiring a 3D printer, I've enjoyed acquainting myself with new puzzle designs, many of which would otherwise be difficult for me to obtain. I look forward to more puzzle exploration in the months and years ahead!