Sunday 4 October 2020

What once was lost, now is found...

Calvin O. Brown and Setko.

Setko reproduction courtesy of the Puzzlemad Workshop, Hawaii Branch.
Hi guys, at this very moment, I will be working anaesthetising the elderly old ladies of Sheffield who have broken their hips ot the young crazy ones who have gone out in the pouring rain on their motorbikes and lost control at high speed. There's always someone who needs putting back together...even on a Sunday. Luckily for me, my good friend and PuzzleMad foreign correspondent (pretty soon in this strange world we won't be allowed to use the word foreign) has stepped in at exactly the right time with a fantastic exposition on a puzzle and story I have never come across before. Thank you Mike, over to you...

Aloha Kākou Puzzlers,

The last few foreign office submissions have been rather light fare. It was fun writing those, but in all honesty, it was mostly procrastination when I should have been working on this present post (Ed - I really enjoyed them!). I’ve been “working” on this post for well over a year, and I’m sure by the end you will be wondering why, to which I can only reply that you’ve probably never tried to write something interesting and half-intelligent for an international audience containing an abnormally high proportion of geniuses. It’s a little intimidating. Let me just say this: Kevin and I don’t intend to metagrobologise (Ed - is that a real word?) indiscriminately all over your computer, if it can at all be helped. Hopefully the long lead time has led, in some small way, to a better post.

We return, once again, to the less-traveled realm of the vintage mid-century puzzle. As you know by now, I have a particular attraction to this under-appreciated period. Many of its mechanical puzzles clearly benefited from the broader design aesthetic of the period. This is pleasing to those of us who believe that a great puzzle should also strive to be a beautiful puzzle. Those that follow, I think, achieved that end.

Zig-Zag, a Calvin O. Brown original.
First up is Zig-Zag. Zig-Zag is the invention of little-known puzzle designer Calvin O. Brown (1907-1970). Mr Brown was president (and founder) of Set Screw and Manufacturing Company, originally based in Bartlett, Illinois. Set Screw was established by Mr Brown in 1935 and remains in operation today, still family owned and operated. Moreover, one of Calvin’s granddaughters runs Setko, an offshoot company and direct descendant of the original Set Screw. The current Setko does not make puzzles, but rather various specialty screws and fasteners. The Setko name, however, was originally established by Mr Brown for his puzzle line, once it had developed into a marketable commodity. You’ll see it in that context for anything pre-1972. Fellow (and far superior) collector Rob Stegmann has a very complete collection of Setko puzzles. I am nearly there, only one more to go I think. Rob and I also have one Setko that you will never find. More about that further down.

Detail from the Zig-Zag patent, showing goal state.
Calvin O. Brown was an innovator in his field and was awarded a number of patents throughout the 1950s for various set screw innovations, including both the screws themselves and their manufacturing process. At precisely the same time, he also patented four puzzles, mostly of the peg-jumping transpositional type. One of these was Zig-Zag, filed in 1955 and awarded in 1957. You can check out the full patent here.

Zig-Zag with box and instructions.
Tannins in the walnut clearly affecting the box, except where shielded by pegs (top) and the price tag (bottom).
Zig-Zag is really a very fascinating puzzle, and I think that had it been introduced during the golden age of puzzling, it might be counted as one of our classics. Like the best of the early puzzles, its superficial simplicity belies a confounding complexity. Let looks at how it works.

Zig-Zag consists of two types of peg and the puzzle board consists of 15 holes and a trough. The pegs need to be arranged in the trough in such a manner that, following the placement rule, the receiving holes are filled in an alternating, or zig-zag, pattern. The placement rule is where the action is, of course. And it’s quite simple. For a given arrangement in the trough, you must alternately 1) place a peg in a hole, then 2) place the next peg at the end of the trough. Repeat, placing the third peg in the next adjacent hole, then the fourth peg to the end of the trough.

That’s sounds pretty simple, but what you soon learn is that the pegs placed at the end of the line come to the front very quickly, and they must be in the correct sequence to maintain the alternating zig-zag above. Did you pay attention to this second order arrangement when you placed the pegs? Perhaps. But soon you also find that you will encounter a third order arrangement that must also work currently. The puzzle is to find this deeply nested ordering. At least for me personally, the third and fourth order was at the very periphery of what my brain could keep track of. It required work, analysis, and a modicum of trial and error. I spent a solid 20 minutes, as I recall, in deep thought, homing in on the solution. I was quite ecstatic when I solved it (Ed - I think that this sort of thing may be beyond me - I am terrible at sequential move puzzles). The correct starting sequence of pegs in the trough, once you find it, does not look like it should produce any kind of ordering whatsoever, but by following the simple replacement rule, the alternating zig-zag pattern materializes.

The solved state.
Although this entire puzzle is based on one exceedingly simple rule, its potential complexity goes up dramatically as you add more pegs to the line-up. Observe that you hit the second arrangement (the pegs you put at the end) after working through the first run (15 pegs). The second arrangement is half as long (7 pegs). Following that, you have a third tier that is half again as along (3 pegs). Then a fourth, which is extremely short, but since it is so deeply nested, it is anything but trivial. If there were 24 pegs, you would go yet another tier deep. If there were 100 pegs, you would be nested seven deep. That is nearly unfathomable. Mr Brown chose exactly the right peg count, in my opinion, at 15. It is just right to deeply stimulate the mind, yet is solvable in a reasonable amount of time. There is also a very satisfying balance between deductive analysis and trial and error. Few puzzles hit this mark so squarely. If you read the full patent, Kevin, you will find that Mr Brown describes another possible version which consists of 18 pegs in three different colors. This sounds very interesting and I am surely going to give it a try at some point. But all things considered, the Zig-Zag version that he ultimately produced was undoubtedly the right choice, especially for public consumption. (Ed - it also helps that it looks beautifully made)

After about here, you really need to think.
How far will this arrangement get you?
I am fond of sequential-type puzzles and have played with many, but Calvin Brown’s Zig-Zag was a truly new experience for me. It seems to exercise a different part of the brain than most other puzzles in this diverse branch. Researching my modest puzzle library, I could find no prior example of this puzzle. That, plus the fact that Mr Brown took the time and effort to patent it, suggests that it truly is something new and original. It certainly was for me, and that tends to happen less and less for me these days. To my thinking, this puzzle is not a variation on a theme, it represents a new theme. That gets me very excited. It’s the whole reason I do this. (Ed - and this excitement comes through and keeps me interested in stuff I don't have myself)

In the US, you can find Zig-Zag on Ebay semi-regularly. There are plenty of copies out there, so don’t overpay. But know also that this is a very high-quality puzzle. I have a lot of peg puzzles from this period and I can tell you that they do not come any better. Having pegs made by a machine shop that produces high precision set screws is clearly the way to go. Calvin knew this only too well and he originally used his puzzles as a marketing tool for his screws. If you get your hands on one of the Setko advertising puzzles, you will find that they use actual hex cap screws. More on that aspect in another post. The playing board is solid American Black Walnut, "Prince of Woods". Let me qualify that for my wood-enthralled editor, Prince of “North American” Woods (Ed - hahaha!). If you are ever honoured to behold the use-worn black walnut stock of an eighteenth-century colonial flintlock rifle, you would understand my bias (Ed - I am not likely to come across one of those in 21st century Sheffield!).

The back, with original tag. The collector side of me loves these details.
So that is Zig-Zag. Now we turn to a much different Calvin O. Brown design. This one is lovingly referred to by Rob Stegmann and myself as the “Lost Setko.” Why? Because this puzzle was never actually produced, as far as either of us can tell. It is the only puzzle that Calvin patented by did not see fit to add to his Setko line. That is unfortunate, but I have an idea why he made that decision. 

The patent was filed in 1953, making it one of Mr Brown’s earlier puzzles. The full patent is here, if you want to have a gander. The patent actually includes two distinct, but related, puzzle designs. We will be dealing with the simple circular example on the right (see below).

Illustrations from “Lost Setko” patent.
Puzzles that were patented but never produced are a mysterious breed. In order to fully experience these puzzles, you generally have to make them yourself. Given my deep appreciation for Mr Brown’s work, it was inevitable that I was going to make myself a copy of this puzzle. I’m no master craftsman, Kevin will attest (Ed - you are a whole lot better than me!), but if it can be made with a wobbly table saw, rusty drill press, and some sandpaper, then I can manage (Ed - I only have sandpaper!). Peg puzzles are squarely in my boathouse.

To keep my reproduction (I realise an unproduced puzzle can’t be reproduced, but just go with it please) authentic I used a nice scrap of Black Walnut. I then bought a cheap Setko puzzle and harvested the pegs. My version is probably as close as one can get to what Calvin would have produced. My only innovation was to mark the special holes with small brass inlays. Setko typically brands a circle around special holes, as shown in the patent drawing.

Calvin O. Brown Patent No. 2,778,641.
Beautifully turned pegs from Mr. Brown’s shop
The Lost Setko is comprised of a circular arrangement of 11 holes and five pegs; four of one colour and the fifth a different colour. Probably the most enjoyable part of the manufacturing process, apart from inhaling wood dust, was figuring out how to make the 11-sided regular polygon, or hendecagon. And guess what Kevin? You can’t! Not mathematically exactly, at least, since the internal angles of a hendecagon are an infinitely repeating decimal (147.27272727272... ad nauseum). But you can make something close enough. I used the method illustrated by Anton Ernst Burkhard in 1698, courtesy of the Wikipedia page linked above. This gave me the perfect excuse to buy a new protractor and compass (Ed - I cannot resist a bit of maths). To the right is Anton Ernst Burkhard’s 1698 copper engraving showing a handy technique for approximating a hendecagon. It works.

On the playing board, two of the 11 holes are marked. These marks denote the starting and finishing positions for the odd-coloured peg. Let’s call it brass, since that’s what I used on my reproduction. The brass peg starts in one of the marked holes, with two silver pegs on either side. Using conventional peg-jumping, one solves the puzzle by forming the exact same arrangement centered on the opposite marked hole. It’s a clever idea. Like Zig-Zag, this sequential movement puzzle was new to me.

A single simple circuit will obviously not be enough, but it's a good place to start.
The first time I tried to solve this puzzle, I futzed around for quite a while trying to out-think it. I assumed there was some hidden-in-plain-sight trans-configuration necessary. In a way I was right, but I was really over-thinking it and got nowhere on the first try. During my next session, I figured it out rather quickly, using a more straightforward process. I suspect Mr Brown didn’t move forward with this puzzle because, upon reflection, he considered it too simple. A significant number of people would surely discover the solution on the first try, I agree. This would tend to discourage production. Also, unlike every other puzzle Setko produced, the lost Setko has almost zero replay value once solved.

Although interesting and original, this puzzle is simply not on the level of Zig-Zag or the two transposition puzzles he also patented (and eventually produced). That said, I had great fun with it. I’ll also freely admit that it got the better of me the first time around. I think Rob solved it much more quickly, unsurprisingly. I sent Rob an early, more rudimentary reproduction in mahogany a few years ago. Rob, if you are listening, I have a copy of the improved version with your name on it. (Ed - Rob deserves this for the huge contribution to our community. His site is a constant source of information and enlightenment to me).

The Lost Setko in its (likely) native packaging.
What about the other ‘lost Setko’ described and illustrated in the patent, the one shaped like a figure 8? Great question. I hope to have some information to report on it in the near future. I have a piece of wood about the right size, so once I achieve critical-motivation, I’ll make a copy and give it a play. Yes, I could just analyse the patent diagram and probably figure it out, but where’s the fun in that? This is a mechanical puzzle blog, after all. Kevin would have my radish if I did something like that. Also, I really want to draft those intersecting heptagons. (Ed - Radish???? Why on earth would I have your radish? Where do you store it? I have a first class honours degree in anatomy as well as my medical degree so I know that you don't have a radish as part of you and I really don't fancy having to reach inside if you have inserted it somewhere!)
A few thoughts to conclude. Calvin O. Brown died quite young by modern standards at 62. This is unfortunate for many reasons, not the least of which is that he would likely have continued to give the world original puzzles, had he the time. There is a lot more to say about Mr Brown’s puzzle endeavours and their evolution, and I have only scratched the surface here. I’ll offer a minor teaser, though, and mention that his puzzles eventually went “national” and formed the backbone of Stancraft’s ‘Hoyle Bookshelf Games’ series. But despite commercial success, it is clear that puzzles were not just a business venture, they were a true passion. Based on the originality of his design work and his attention to quality craftsmanship, we can recognize in Calvin O. Brown a kindred spirit from another era.

Black walnut, among its many superior qualities, takes a high polish.
Progressive sanding down to 1500 grit followed by linseed oil does wonders.
(ED - OMG that's absolutely stunning! Well done.)

Ok, Kevin, that’s all for today. Give our fine readers their well-deserved sendoff!

Wow! Thank you so much - this was an amazing exposition on a fabulous vintage puzzle. I am so grateful for your help keeping me publishing when I get busy and providing an aspect of puzzling for the readers that I know next to nothing about. These look really amazing - both from a puzzling point of view as well as the beauty of lovely wood and polished metal. Once my bank balance has recovered from my recent splurge of purchases (Big Steve and Ali's Kong puzzle on Kickstarter and hopefully I will have got a copy of Juno's upcoming puzzle too) then I will have to have a look out for a nice copy of the Zig-zag puzzle on Ebay. Hopefully I will get home at a decent time to be able to advertise this on social media.

Keep safe everyone.


  1. Hi Kevin, Mike - Great article! Perhaps Brown will receive some well-deserved attention. The whole Setko series is very nice. And thanks for the shout out :-) Readers interested in peg solitaire may find George Bell's website worthwhile:
    Mike - I am still at my robspuzzlepage address, but your old email seems to have changed. Has it really been three years? Regards, Rob

  2. Hi rob! Three big ones, you are right, that's sure sobering. I'll drop u a line with my new (and final) email.

    Mike d

  3. Very interesting to hear the history of Setko! If you don't have any Setko pegs, these puzzles can be made using coins and a board drawn on a piece of paper. I wonder if there is a shorter solution to the Lost Setko?

    These kind of "no capture" variants are most closely related to a 1D Solitaire Army:

  4. I've been playing around with the Lost Setko (11 hole board). It might appear you have many choices about jumps, but in fact the board states you can reach are just a big (1D) maze with two possible paths to the exit. I believe the shortest solution has 150 jumps. Because it is a maze, there is no way to take a shortcut.

  5. Hi george, that was my though too, but wasn't sure. The two paths go in either direction right, one being slightly shorter?

    1. Yes, in one case all the jumps are clockwise, in the other, counterclockwise. You can also think of it as moving pairs of pieces in one direction or the other.

  6. Thanks for the solitaire army tip too. Good explanation on wikipedia under Conway's soldiers for anyone interested. Developed in 1961, similar time period. Very cool.

    1. In Conway's soldiers there are captures, when you eliminate captures you get something like Chinese Checkers (2D). Without captures you can advance an army as far as you like, but you can still minimize jumps. In 2007 I wrote a paper about the shortest game of Chinese Checkers, Lost Setko is kind of a 1D version of this.

  7. Very interesting. I’m trying to complete my collection of Hoyle Official Game Puzzler book shelf series with walnut basses an metal pegs similar to the one you have pictured. I’m curious if you know the complete list of them. I thought there were 11 but based on the model No. listed on each directions I have a gap. Let me know if you have any info. Thanks an your post very fascinating.