Stewart Coffin’s #167 “Cruiser”

As I mentioned in my October post, I’ve been having fun making puzzles using designs I found on the web and one of them is Stewart Coffin’s 2D packing puzzle, #167, a.k.a. “Cruiser”. I’ve shown it to friends and family and it’s been a big hit so I reached out to Stewart about selling them. We exchanged some emails and met so I could show him the finished product:

He agreed! I have his permission to sell them and if you’re interested, you can buy one at my Etsy store.


Model #360

I’ve been plugging away at my next puzzle, Model #360, for some time now. I made the first prototype out of wood, oak I think, back in the late 1990’s and it was pretty bulky. It sat in a box until I found a machinist to make me some slimmer models from delrin. Then I changed jobs and other interests and responsibilities consumed my time so it sat on a metaphorical shelf for another couple of years. Anyhow, after I built my 3D printer I decided to revisit the design, print some new versions, and eventually refined it to the point where it made sense to have some SLS prototypes made. Here is the family portrait:

The leftmost one is oak, the next two are delrin, the white one on its side in front is white nylon (SLS), the blue one is off of my 3D printer, the black short one is a dyed nylon version (also SLS) from Shapeways, the purple one is from my 3D printer, and the rightmost one is the latest version.

Most of the changes from version to version are internal and I can’t talk about them without giving away the solution. But I can give you this close-up of the final version:

My plan is to have it made of nickel-plated aluminum which I think will look pretty slick. Those of you who solved Model #808 may remember the red disc inside, the “proof of work”! Well, Model #360 has a bigger prize, a turquoise sphere which you can see in the picture. I’m a little worried that variation in their diameter may mean that some won’t fit but they should arrive today and then I’ll be able to check.

Like Model #808 this one will also be made on a limited edition basis. There will only be about a 100 and yours truly will be assembling, numbering, and initialing each of them by hand. I had hoped they would be ready before Christmas but that’s looking mighty unlikely; I think late January is more realistic at this point.

That’s it for today. Now I just need to put the quote out to bid and pick a machine shop to make them!

Some Fun DIY Puzzles

I was wandering around the web recently, looking at various websites devoted to puzzle collections, puzzle designs, puzzle math, etc., and found several that were simple enough for me to fabricate myself.

The first one I’ll talk about is the “Blossom” puzzle by Bernhard Wiezorke and here’s a link to a description of it on John Rausch’s amazing website: As John put it, “Unbelievably, the four ‘L’ shaped pieces hold together after the last piece is snapped into place.” I was thinking of modeling an .STL file for this by hand but, not surprisingly, someone else already had: I scaled it down, had it printed in sintered nylon (which gives a much better finish than my FDM printer can), and dyed it:

And here it is in its disassembled state:

They’re about the same color, size, and texture as Trix breakfast cereal (and probably as nutritious).

The second is a well-known Stewart Coffin puzzle, design #167, also known as “Cruiser”. The “Math Forum” website holds a fantastic trove of math puzzles and analyzes them in depth. Here’s their page on Coffin’s “Cruiser”. Some years ago I made some dissection puzzles with laser-cut acrylic and I thought I’d try that approach on this one. Here’s the result (shown in a semi-jumbled unsolved state):

On the whole, I’m pretty happy with how it turned out although it’s smaller than I would have liked (about four inches on a side). I have inflicted it on non-puzzler friends and family and it’s a big hit – it appears simple enough to invite and then sustain prolonged effort. One of my victims called it “annoying fun”.

Third up is another Stewart Coffin design, the “Pennyhedron”, which I read about it in Stewart Coffin’s 1990 book, “The Puzzling World of Polyhedral Dissections”. It’s a rhombic dodecahedron and here’s a picture of the one I made:

My initial plan was to OpenSCAD a model for the underlying rhombic shape, print twelve, and then glue / assemble them into a puzzle. Then a neuron fired inside my brain (life is full of surprises) and it said, “if you thought of it, someone else already has.” It’s not my favorite neuron but it’s right too often to ignore. Sure enough, I found this: It has holes in the side for magnets which I shrank down so that I could use spare bits of printing filament to line up the edges accurately. It worked out beautifully although I did have to do some sanding on the sides to ensure their flatness. I’ve included a picture of it disassembled at the end of this post after the spoiler warning.

My fourth DIY puzzle is Dic Sonneveld’s “4 Piece Cube”. I don’t remember how I found the “Puzzle Will be Played” website but it is also an incredible goldmine of puzzles, some of which are insanely hard. Here is the link for Sonneveld’s 4 Piece Cube and here is how mine came out:

I used OpenSCAD to model the two pieces and then had Shapeways print them in sintered nylon (and I let them do the dyeing.) The assembled puzzle is about 1 1/2″ on a side. If the color pattern looks familiar, it’s because Microsoft uses it for their logo. (If you’re reading this, Microsoft, you should talk to Dic Sonneveld about making these for trade-show give-aways – they would be a huge hit!) Anyhow, I really like this puzzle because of its simple appearance and elegant design: it consists of just four pieces, two each of only two different shapes.

OK, so here’s the SPOILER ALERT. I’m about to show pictures of Coffin’s “Pennyhedron” and Sonneveld’s “4 Piece Cube” in their disassembled states, which will give away their solution. Even though the Pennyhedron is almost two decades old and is shown disassembled on John Rausch’s Pennyhedron page, I wanted to give fair warning.

When assembled the seam between the pieces is invisible and the only way to solve it is by trial and error. I think it turned out really well and if you have a 3D printer, I encourage you to give it a try.

And here is the “4 Piece Cube” puzzle disassembled:

Unfortunately, I miscalculated some of the dimensions and had to do a fair amount of sanding to get the pieces to fit; that’s why you can see the white nylon showing through the dye in several areas. But now it fits together perfectly.

That’s it for today. Puzzle on, Wayne! Puzzle on, Garth!

Update on Model #808

I have a couple of things to report about my Model #808 puzzle. First of all, I’m sold out (!). I’m kind of in shock because I had expected to sell two or three of them a month for the next couple of years, not all 106 of them in eleven weeks.

Second, if you’re trying to find one, I would suggest checking with these fantastic puzzle stores who have the #808 for sale:

Eureka! Puzzles in the U.S.

Puzzle Master in Canada

Oy Sloyd Ab in Finland

Third, I wanted to alert everyone that when you open the puzzle you will find two items inside that you probably don’t want to lose. One is a small red disc with the Pyrigan logo on it – it’s a token of my appreciation and tangible proof that you solved the puzzle! The other is a small metal piece that is part of the puzzle’s mechanism. I won’t describe it in any more detail because I don’t want to spoil the puzzle but if you lose that piece, the puzzle becomes much easier to solve. Normally the piece rests in a small cavity and won’t get away from you but if the puzzle were to be bumped while it is opened or if the lighting is poor and you don’t notice it, it might escape. If that happens, let me know and I will send you a replacement.

Fourth, here are some reviews:

PuzzleMad – Mike Desilets has been keeping an eye on my progress with #808 for some time and and I am incredibly flattered by his patience (3 years!) and his positive review. His review includes some pictures which look a lot better than the ones I took. Thanks, Mike!

Extremely Puzzling – Goetz Schwandtner has been reviewing puzzles on his blog since 2008 and his August 25th, 2017 post gives a review of #808 along with a picture. Goetz, it was a pleasure meeting you at IPP – see you next year I hope!

That’s it for now. Time to get cracking on Model #360!


Puzzler in Paradise

I attended my first IPP earlier this month and had a terrific time. First and foremost, the people are just fantastic: generous, imaginative, super smart, just great people. The huge support and welcome I received as a newbie just floored me with outright puzzle gifts, advice on how to get the most out of the event, suggestions on who to talk to for help on my puzzle ideas, encouragement to participate in the Puzzle Exchange (more on that in a bit). What a wonderful way to be introduced to a whole new level of puzzling!

Second, the events were mind-bogglingly great: a puzzle competition, a puzzle exchange, and a puzzle “bazaar”. There were over five dozen puzzles in the puzzle competition and I had a chance to play with all of them. I liked one from VIN&CO so much that later I bought one. I will make a nice icosahedron out of these some day, I swear:

Next came the puzzle exchange in which one hundred participants all bring one hundred copies of a never-before released puzzle and exchange it with the other participants. I was blown away not just by the cleverness of the puzzles but also by the professional quality of their manufacture and finish. The craftsmanship was unbelievable and there were several I hope will reach the marketplace so I can buy them. Stan Isaacs’ was based on a tiling problem posed in the as-yet-unpublished Volume 4 of Donald Knuth’s “The Art of Computer Programming” series: “Find seven different rectangles of area 1/7 that can be assembled into a square of area 1, and prove that the answer is unique.” I was able to buy a copy of it later:

On the last day there’s a kind of puzzle “bazaar” in which puzzle sellers and puzzle buyers go completely nuts. Errm, I plead no contest. There were puzzles there that I’ve been looking for for ages, like Wil Strijbos’ Lotus Puzzle. (Even cooler than finally procuring the Lotus was having an extremely informative conversation with Wil about manufacturing puzzles and he gave me some very helpful advice – thanks Wil!) Here’s a picture of the puzzle along with the reason for its name:

At dinner, I had the amazing good fortune to sit at a table with Sven Baeck who runs Mallorca Puzzles and he had brought a super rare, super cool Roger D puzzle, “Gartenschlauch”. Given its rarity and its price I figured this was probably the last time I would actually be able to work on solving one so I got to work, dinner be damned! I have to admit, I’m pretty proud of this:

In summary: Pure. Puzzle. Euphoria.

Model #808 is Done!

Surf’s up! Dinner is served! Lift-off!

Well, the day has finally arrived and Model #808 is now available for purchase. There are only 106 of them – that’s all I made – so if you’re interested please head over to my Etsy store. And here it is:

I have to say, everything about this process took longer than I expected so it’s a great relief to have at last reached the finish line. I never would have guessed that I would go through fifteen design revisions and three machine shops over the course of almost three years. Well, I guess that just means Model #360 will be a cakewalk!

First Batch of Puzzle #808

Since my last post on Model #808, I have learned a lot about machining and manufacturing. For one, I realized I needed a professional mechanical engineer to do the tolerancing of my design and prepare proper design drawings. I had previously tried to get by with the .STL files generated by my 3D design tools. For another, I learned that cost is not the only factor to consider when choosing a machine shop. I am now working with J&J Machine Company and these guys are outstanding!

But here’s the important news: the first batch of puzzles came back last week and I have assembled two of them so far. Drum roll please! Ta Dum:


I have to admit, I am really pleased with how the engraved logo looks: red ink on the matte black (bead-blasted) anodized aluminum. The bottleneck will soon be me. Next week I expect the remaining puzzles to arrive of this limited edition run of 100. Once I get the machined pieces, I have several manual steps to go through: adding the red ink, adding the internal pieces (I won’t spoil the fun by saying what they are!), hand numbering and signing the puzzle, and doing the packaging.

It has taken a long time to reach this point but it won’t be much longer before Model #808 is ready for sale so check back soon!

The Partridge Puzzle

I recently stumbled across the Partridge Puzzle invented by mathematician Robert T. Wainwright. Consider a collection of square tiles, the smallest of which is 1 unit by 1 unit in size (and there is one of them) and the largest of which is N units by N units in size (and there are N of them). The total area of all the tiles would be 1x(1×1) + 2x(2×2) + … + Nx(NxN). That sum of cubes turns out to be [(N x (N+1) / 2]^2. This means that the area covered by the tiles is the same as the area of a single large square whose length and width are [N x (N+1)]/2. So wouldn’t it be cool if you could find an arrangement for all those tiles that allows them to fit inside that larger square? That’s the Partridge Puzzle.

Now it turns out there are zero solutions for N=1 through N=7 and there are 18,656 solutions for N=8 (so far, solutions have been found for N=8 through N=33).  You can buy an N=8 one from Kadon Enterprises:

It’s really nicely made; here’s a picture of mine:

Although there are 18,656 solutions to this thing, after several frustrating days I was able to find precisely zero of them. So I wrote a program to solve it, which I suppose is either winning at the meta-level or cheating depending on how you want to look at it. I (or if you prefer, my program) found all the solutions to the N=8 puzzle and I let it run long enough to generate a solution or two for N=9 through N=13. Here’s my GitHub repository where I’ve parked my source code, solutions, and some analysis:

This was a fun diversion and gave me an excuse to learn Python, Java, GitHub, and AWS EC2 management. I will leave you with a picture of my favorite of the 18,656 solutions:

It’s my favorite because it is the most fragmented of all the solutions. That is, this solution has the fewest number of same-sized tiles touching each other. If you want to learn more, here are some excellent links to explore:


Constant Negative Curvature

One of my favorite events is the local annual Celebration of Mind gathering inspired by Martin Gardner’s immense contribution to recreational mathematics. I went to one last night in Brookline, MA sponsored by Eureka Puzzles and gave a short presentation on my interest in what I’m calling (probably incorrectly) a “unit hyperbola”. My talk was called “Horsing Around With Z=X*Y” and if this kind of thing interests you, you can download the PDF of it here.

Basically, I used OpenSCAD to model Z=X*Y for X and Y values ranging from -1 to 1. That generates a saddle-shaped half-cube (with Z value from -1 to 1). I found that you can take those half-cubes (or unit hyperbolae) and compose them into some very weird-looking shapes. Here are some examples:













I’ve convinced myself that every point on the curved surface sees constant negative curvature in all directions – hence the title of this post – but I’m no mathematician and it wouldn’t completely surprise me to learn I’m wrong. The basis of my conviction is empirical: I can slide the curved surface of one of the half-cubes over the curved surface of the more convoluted shapes while keeping the surfaces in full contact with each other at all times. Since I know the curvature is fixed for the half-cube, I conclude that the curvature must be fixed for the convoluted shapes too.

In any event, it’s clear that the “holey” shape repeats its pattern in all three dimensions so it should be relatively straightforward to define the minimal subset cube that “tiles” space accordingly – but I ran out of ideas when I was playing around in OpenSCAD. Now that I’ve had to organize my thoughts for the presentation, I think I’ll take another shot at it.


Puzzle Collection Extravaganza

I was recently asked how many puzzles I had in my collection and I realized I had no idea. So I figured if I was going to go to the trouble of taking them all out of their boxes and actually count them, I might as well take some pictures too.

Here’s my kitchen table over-run by puzzles:

Puzzle Collection

As you can see, there are some old classics in there, like an original 1980 Ernő Rubik cube and an IMP puzzle (now known as the “Fifteen Puzzle”) from the 1930’s. The most recent addition is Wil Stribos’ “First Box” puzzle – the blue cube in the upper left. That was a fun sequential discovery puzzle, beautifully made from anodized aluminum.

Strictly speaking, not all of those are puzzles. The three black and white toys on the bottom left are just fun to manipulate or make shapes with. And the white rectangular puzzle on the right, sitting next to the black calculator looking thing (a super cool Vulcan Electronics XL 25!), is a Rubik’s Magic puzzle that I modified. Normally, it has paper inserts printed with a pattern of rings; I replaced those with a pattern of semi-circles that I think makes it look more interesting even when it isn’t solved.

OK, coffee break’s over! Back to working on Model #808.