Sunday 25 February 2018

The McGenniss Transpose Puzzle

Garage-crafted version of David McGenniss’ 1899 transpose puzzle (U.S. Patent No. 639,602).
Just when I seem to be struggling to find something to write about, the Puzzlemad foreign correspondent (North America) steps in and takes the pressure off! I have been working on both the Popplock T11 and Hanayama Cast Trinity, and failing badly! This means that I have very little to write about myself just now. There might well have been a few new puzzles arrive as well as a bit more lock-picking paraphernalia arrive recently but very little solving has gone on. Have a quick look at the New additions page to keep up with my recent arrivals. In the meantime let me hand you over to Mike Desilets for a fascinating expose of a puzzle travesty! After reading, if any of you mathematicians out there can formally prove or disprove the travesty then please get in touch.

Aloha Kākou puzzlers,

If you are reading this, it means another of my dubious posts had passed the stringent Puzzlemad quality assurance process. Barely, I’m sure. (Ed - it is the QA which is dubious; the posts are fabulous). Fortunately for me, Kevin is required to complete a number of burdensome domestic chores each weekend (dispensed with a firm but fair hand by the lovely Mrs S, current) (Ed - she's all yours! Whack! Ouch!). This frees up space for my ramblings, for which I am very grateful. In this episode, we are going further into uncharted territory. How can that be, you ask? Has Puzzlemad not already covered every nook and cranny of the puzzle world? Sadly no, not yet. But this entry will get us one step closer. (Ed - remember I don't collect boxes)

Like you, I enjoy reading about, seeing, and playing with the latest and greatest puzzles. But I also have a soft spot for all things old-timey. You may have picked that up from the vintage puzzle articles. In this post, however, we are going beyond vintage to the antique. By my unscientific reckoning, that means stuff from before the twentieth century. (Ed - I think some auction houses define antique as being more than 100 years old)

Today’s offering is an early transposition puzzle invented by David McGenniss at the close of the nineteenth century. We’ll call it the McGenniss Transpose. A copy of the full patent specification is here. As you will read, the patent was applied for in April of 1899 and awarded in December of the same year. That’s an eight-month turn-around. Very fast! It was a simpler time in many ways. Today you can expect no less than a two-year wait, more likely three. In 2014 the average pendency period (before the US Patent Office would even glance at the application) was just over 18 months.

I came across this interesting puzzle while doing some other unrelated research and the design really struck me—nice symmetry and well proportioned. I’ll admit, I also figured it was well within my skill level to solve. It looked to be a straightforward transposition exercise. I filed the patent pdf for later study. Then, during the recent holidays, I returned to the McGenniss Transpose and tried to track down a physical copy of the puzzle, or at least something closely based on it. No success. Many puzzles from the Victorian period ring through history, either as reproductions made when patents expire or by spawning families of related puzzles. I had expected this to be the case for such an attractive and simple design, but it apparently wasn’t.

The McGenniss Transpose in isometric projection.
I thereupon retired to the Puzzlemad workshop (Ed - I have a workshop??? Why did no-one tell me?) and set about crafting (loosely defined) a copy for myself. Although no measurements are given in the patent, the specifications are very clear on how the puzzle is to operate and the proper spacing between elements. One trip to the hardware store for wood scraps and another to the craft shop for little wooden discs and I was all set. After nearly a full day of fiddling, I managed to kludge together something half respectable and wholly functional. (Ed - I have to say it looks pretty good)

Now things get interesting. It was time to sit down and play with the McGenniss Transpose. I began by shifting pieces around semi-systematically, as one tends to do with this type of puzzle, exploring the movement and especially the bypass routes. After a little while, I got serious and figured I’d have a go at a proper solve. I worked and worked, but could not seem to get the entire field transposed. Most of the pieces switched very easily using the offset containers, but there was always a specific piece that seemed impossible to move. Now, as a seasoned puzzler, I know that the seemingly impossible is just what good puzzles are about. So I kept at it, trying to find the secret manoeuvre. No luck. I reread the specifications, checked the patent drawing, checked my copy. Everything seemed in order.  After some more study, I began to think there was a design flaw. 

Sticky wicket?
Examine the image above and you will see the offending piece in purple. That particularly piece seemingly cannot escape its slot if there are only four ‘spaces’ (each the size of one disc) with which to manoeuvre. I couldn’t find any logical way to circumvent the basic geometry of the puzzle. The next step in such situations is to get a second opinion. I promptly took the McGenniss Transpose to my office and foisted it upon Amanda and the rest of my co-workers. Was I missing something obvious? It wouldn’t be the first time. Thankfully for my ego, everyone else had the same experience. The final piece, four deep in its slot, would not budge.

So as of this post, I am declaring the McGenniss Transpose puzzle unsolvable. If anyone can present a solution, I will immediately retract that statement and humbly lick my wounds. You will also become my personal hero (Ed - mine too). Just be sure to study the specs carefully and note the spacing of all elements. Use the patent drawing for reference, not my very low-tolerance reproduction. Mine gives the appearance of more space than should actually be present.

The purple disc is four-deep in the hole. How can it escape? An n+1 situation, if you catch my meaning.
Insolvability is a very interesting development, assuming you accept my conclusion. It begs the question, why in the world would someone go through all the trouble and expense of applying for a patent on an unsolvable puzzle? The first possibility is that it was a complete mistake. David McGenniss thought he had invented a great puzzle but had not actually played with it or solved it himself, and therefore did not realize it was unsolvable. This seems unlikely, on the face of it. Would McGenniss, and also his co-patentee Oren Burt, really not know how their own invention functioned?

The second possibility is that there was an error in the specification and drawing. Perhaps some miscommunication between the inventor and the lawyer who drafted up the documents. If the offset box on the offending side were shifted down one position in the direction of the entrapped disc, for example, then the puzzle is solvable. Perhaps this is the answer. But then again, an inventor would probably know at a glance if the drawing were not correct. It’s hard to believe he didn’t check it before it went out the door. What kind of a man are we dealing with here anyway?

Let’s take a step back for a moment and look a little closer at our protagonists. What, did you think you were going to get away without a history lesson? Feel free to skip ahead if it’s not your thing. For me, puzzle people are as interesting as puzzles themselves. Even more so when they lived over 120 years ago. 

Like many of today’s puzzle designers, our heroes McGenniss and Burt had full-time day jobs. They were in the textile business. To be specific, they worked in undergarments - as does my editor (Ed - have you been looking through my computer webcam? I'd better get dressed!). Knit ribbed underwear, to be unnecessarily specific.

McGenniss worked for the Ionic Knitting Company in Easthampton Massachusetts, alongside his erstwhile companion Oren Burt. Burt was the manager of the company, McGenniss was superintendent. Reading between the lines of the source material, I take that to indicate that Burt took care of the boring but vital paperwork and McGenniss was the hands-on guy making sure the machines worked and things got done. Fiber and Fabric (1894, Vol. 20) reports that McGenniss was “setting up the machines.” Have you ever seen a textile machine? He was basically a mechanical engineer and an inventor as well. Prior to the Transpose puzzle patent, McGenniss had acquired three patents for improvements to textile manufacture machinery. One of these was filed prior to incorporation of the Ionic Knitting Company and it is likely that McGenniss and Burt started the company specifically to implement their patent ideas.

Early textile machines, mechanical puzzles of frightening complexity.

The Ionic Knitting Company started operations in 1894, an ambitious undertaking given the stiff regional competition and the still-fresh financial panic of 1893. Somehow they were able to secure credit and launch the business. Soon after starting, they went into production day and night, doubling the workforce in their first year of business. Within five years, however, they experienced serious financial difficulty and by 1899 the bank had seized the company’s assets. $15,000 was owed. Given that the operation was originally capitalized at $20,000, it seems that not a lot of progress had been made, profit-wise, in the intervening years. Now, don’t you wish you’d skipped ahead? (Ed - no! It's fascinating)

Admittedly, this isn’t a nineteenth-century textile industry blog, but it is important to get into the heads of our designers. At the very time that McGenniss and Burt applied for their transposition puzzle patent, they were in serious financial trouble with their company about to go belly up. I couldn’t find any clear end date for the Ionic Knitting Company, but I don’t think it survived beyond 1899. Certainly, a strange time to be investing time and effort in a puzzle patent, of all things. But then again, McGenniss and Burt had grown up during puzzling’s Golden Age. They had witnessed the 15 Puzzle craze, the Sam Loyd phenomenon, and all the other puzzle happenings of the late Victorian period. They knew that puzzles could be converted into money, and they were nothing if not entrepreneurs. So perhaps the McGenniss Transpose was a final gambit to become financially solvent. Or, more generously, perhaps McGenniss and Burt were just really into puzzles, and this was a way to keep their minds off a crumbling business and nasty bank letters. We won’t ever really know. 

That concludes the history portion of the post. Now back to the present. Having found the puzzle to be unsolvable, and knowing the historical context of the designer, let us revisit the initial question of whether or not the McGenniss Transpose had ever been produced. In fact, the question seems more urgent than ever. I made some inquiries with certain large puzzle collections and collectors to see if examples could be found. First stop was the Hordern-Dalgety Collection. Mr Dalgety was kind enough to weigh in on the topic. Although he understandably did not have time to conduct an intensive search of the collection, he was not aware of anything matching the description of the McGenniss Transpose. James noted a certain similarity with the Perplexity Puzzle, which came out a little later. Allard and Jerry both have reviews of the Perplexity puzzle which you should check out. It does make for an interesting comparison. Given the strictly two-dimensional nature of the McGenniss Transpose, however, a puzzler cannot take advantage of the tricky mechanics used in Perplexity. James also noted that the French use undersized discs, which apparently allows for otherwise impossible bypassing. This is clearly not the case with the McGenniss Transpose.

The Perplexity Puzzle. A real classic from the early twentieth century.
Patented in 1900 and produced in a variety of forms over the following two decades.
Next stop was the Slocum Collection, housed at the University of Indiana’s Lilly Library. Andrew Rhoda, Curator of Puzzles, was kind enough to conduct a thorough search of the puzzle database and could find no published version of the McGenniss Transpose. Andrew also searched the Slocum papers and found no evidence there either. He noted some other transposition/sequential movement puzzles of interest - the French Les Roues Du Char- 8 Discs, for example:

The Les Roues Du Char- 8 Discs, a nice-looking puzzle in the transpose family.
(Photo courtesy of The Lilly Library, Indiana University, Bloomington, Indiana.)
Based on these results, I conclude that it is unlikely that the McGenniss Transpose was ever produced commercially. This is not particularly unusual for patents, even puzzle patents. The fact that the puzzle is unsolvable was also likely a factor. This would certainly have become apparent to the designer at some point and would mean either producing a modified version not covered by a patent, or, humiliatingly, redesigning and submitting another patent application. With all the other things McGenniss and Burt had on their minds at this time, namely paying creditors and finding new employment, both options were probably equally unattractive.

Thus ends the story of the McGenniss Transpose, a puzzle that was not to be. Yet another odd footnote in puzzle history. I’m pretty sure I have the only copy in existence. I briefly considered modifying my reproduction to make it solvable, but I think I will leave it alone. It will be a good test for unsuspecting victims and gives me an excuse to launch into impromptu lectures about New England textile entrepreneurialism (Ed - that sounds riveting!).
“What, you can’t solve it? Well . . . funny story. How much time do to you have?” 
Ok, folks, that’s it for today. I know this brand of puzzle post isn’t for everyone, but I hope it is for someone. Regardless, if the Puzzlemad editorial board continues to let this stuff slip through, I will continue to produce it. Back over to you Kevin...

Thank you so much, Mike! I have to say that I was enthralled - even with the knitting machine history. You seem to have a real fascination with what I call sequential movement puzzles as well as the history. I am really awful at that type and only manage to solve them by random trial and error - I just don't have the ability to conduct a proper analysis of this sort of puzzle.

I am always open to something new as long as it is puzzle related and interesting to proper puzzlers. If you feel the urge to get your literary creativity out then feel free to contact me to discuss it.

[1] Clothiers' and Haberdashers' Weekly. Volume 14, No. 1. June 16, 1899.
[2] Fibre & Fabric: A Record of American Textile Industries in the Cotton and Woolen Trade. Volume 28, December 31, 1897 and Volume 28, December 31, 1894.
[3] The Annual Statistics of Manufactures. 1894. Public Document No. 36. Ninth Report. Published 1895, Wright& Potter Printing Co., State Printers: Boston. 

Finally, before you all go off and do the important things that you should have been doing before you got side-tracked by my blog and Mike's wonderful article, can I ask a question on behalf of a friend? He has been trying to complete his collection of Wil Strijbos puzzles and is desperate to obtain a copy of the Butterfly Lock box/Pleasure and Pain puzzle that I reviewed here. If you are willing to sell your copy then please contact me and I will put you in touch with him to negotiate a price. He has already managed to buy the Angel box and Washer cylinder recently and the transactions have gone through without hitch. I am sure he will be very grateful.


  1. If the exhaustive programming went right...

    The McGennis puzzle admits no solution!

    If you shorten the longest divider between the pieces from a length of 4 to a length of 3, still only allowing orthogonal slides, i.e. going from:

    X X X W X X X X
    W W W o o W W W
    - - - o - - - -
    B B B o o B B B
    X X X X B X X X


    X X X W X X X X
    W W W o o W W W
    - - - o o - - -
    B B B o o B B B
    X X X X B X X X

    then you have a solution in 82 moves.

    Funnily, if you shorten one of the 2 double rows of 3 pieces to 2, like this:

    X X X W X X X X
    W W W o o W W X
    - - - o - - - X
    B B B o o B B X
    X X X X B X X X

    then you have a solution in 88 moves.

    Another way to make the puzzle work is to lengthen the board in the following way:

    X X X W X X X X X
    W W W o o o W W W
    - - - o - - - - -
    B B B o o o B B B
    X X X X B X X X X

    and it will take you 118 moves to solve it.

    1. My goodness! That is a fantastic analysis! I'm seriously impressed.
      How did you do that? By hand? Or did you program a computer to do it?

      Thank you so much for that. I'm sure that Mike will also be very grateful.

  2. Just programming fun.

    A good, tricky one is:

    X X X W X X X X
    W W W o o W W X
    - - - o - - - -
    X B B o o B B B
    X X X X B X X X

    which takes 94 moves that look rather non-trivial.

    And by the way the simpler:

    X X X W X X X X
    X W W o o W W X
    X - - o - - - X
    X B B o o B B X
    X X X X B X X X

    is solvable and takes 68 moves.

  3. I am very grateful indeed! Its really great to have a second opinion, and a mathematical one at that. The Puzzlemad staff are a bit challenged in that area I'm afraid.

    I think I tried the 82 move version back when I was first playing with it. Seemed shorter at the time, but that could just be me. I'll try again and this time count the moves. Thanks very much for stepping up and contributing some much needed rigor.

  4. For the avoidance of doubt, one move is here defined by the sliding over a piece over one "square".

  5. Replies
    1. Got it. Will count accordingly when i play, Thanks.