First release of revised edition, December 2000
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The spring of 1968 found me busily engaged in the design and manufacture of fiberglass canoes, kayaks, and related equipment, which I had been doing since 1961 after quitting electrical engineering. I was finding the noxious fumes of the fiberglass resins increasingly unpleasant. One fateful day, recalling an illustration I had seen in the marvelous book Mathematical Snapshots by Hugo Steinhaus, which my father had given to me way back in 1950, I started playing around with a cluster of 12 triangular sticks. I have always been keenly interested in mathematical and geometrical recreations. This soon led to a variation with notched hexagonal rods that made an intriguing interlocking assembly.
Back then I was much more adept with fiberglass resins rather than woodworking, so I decided to cast a few of these novelties in epoxy. By the way, the original pattern for molding these pieces was machined accurately from steel by our neighbor, Fred Wilfert, an expert machinist. Our three daughters, then ages 6, 7, and 9, took an interest, especially Abbie, the oldest. Evidently she took one of these novelties to school one day to show her friends, and somehow it also came to the attention of the Town of Lincoln children's librarian Heddie Kent. That led in turn, through a complicated series of connections now forgotten, to my being put in touch with a man in the neighboring town of Concord, Thomas Atwater, whose unusual profession was as business agent for puzzle and game inventors.
Soon, through the efforts of my newfound business agent, 3M Company indicated an interest in adding my Hectix (#25) to the new line of puzzles in their stationery division, and a contract was drawn up for them to be manufactured in injection molded styrene. On the strength of this, and especially the generous advance royalty, I decided to liquidate my stinky fiberglass boat business and embark on this new enterprise of inventing geometrical recreations.
I spent most of 1970 experimenting with other geometrical models and casting them in epoxy. Some of these are described and illustrated later in this publication. My agent had almost no success in licensing any of them, and in looking back at them now I am struck by how poorly conceived most of them really were. One exception was my Snowflake (#3) puzzle, which had limited success. A version of it was cast in polyester resin (with badly misshapen pieces) by the Sam Span Company. It came with a molded styrene base and 10-page instruction booklet. About 500 of these were sold by the Museum of Modern Art in New York. The only other exceptions were my Frantix (#9-A) and the Geo-Logic series, both of which are described in Part 2.
An amusing situation occurred in the summer of 1970. The Hectix (#25) Puzzle was being manufactured by Nylon Products in nearby Clinton, Mass. The individual pieces were spewing out of their high speed injection molding machines by the tens of thousands, but then they had to be assembled, and doing this with union chemical workers proved to be not only slow but very expensive. An emergency meeting was called in Clinton. After much head-scratching, I told them to ship all parts to my plant in Lincoln and we would assemble them for 4 cents each. Unknown to them, my plant was to consist of benches set up on our lawn, with our three children doing the assembly. I paid them 2 cents per puzzle and pocketed the difference. Soon some of their neighborhood playmates also got in on this bonanza. Some of them assembled about 100 units per hour. Abbie, then age 10, was clocked at 11 seconds. We assembled 20,000 puzzles in about two weeks until our contract sadly came to an end. I don't know where they were assembled after that.
There is an interesting sequel to this story. I noticed that some of our better assemblers, Abbie especially, were after a while doing the assembly more by feel without even looking. Later that year we were invited to do a puzzle program on the Tom Colton Show, Channel 22, West Springfield. For the finale of our half-hour show, Abbie was to assemble the Hectix blindfolded. This, by the way, was back when such shows were live, not tape recorded as they are these days. So we practiced until she could do it consistently in one minute. On the actual show we allowed two minutes with our fingers crossed, but she came though with time to spare. I wish now that we had a recording.
I am sometimes asked if I have patented any of my designs. I do not think that puzzle patents are a very good idea, and the following experience may help to explain why. I hold two puzzle patents, and the only reason for this is that they were licensed for mass production, and the manufacturer insisted on the patents (and paid for them). They were drawn up by patent lawyers and written in such convoluted language that I hardly recognized my own designs. (It was explained to me that this was done deliberately, but don't ask me why!) After the Hectix (#25) puzzle had been on the market for a while, I learned through my agent that we were being threatened with a lawsuit for patent infringement. I had already conducted my own patent search, and on the basis of that we concluded that the patent in question was probably of Sanson, 1968 - a more complicated assembly of 24 notched hexagonal rods. After we prepared all sorts of arguments why my Hectix (#25) was different, we learned that the threat was instead coming from a professor of architecture whose patent on structural members did not even mention puzzles. I was told that this was common practice among patent attorneys just fishing for a settlement, and we ignored it. Ironically, later I discovered that the basic idea for the Hectix (#25) puzzle had been discovered a few years earlier and independently by Bill Cutler, a very capable mathematician and puzzle designer, but unfortunately for him he never carried it through to successful production.
Incidentally, when my Hectix (#25) design was later copied and manufactured by other puzzle companies without permission, I asked 3M Company if they intended to enforce our patent. I was told that this was almost never done because of the cost of litigation, which could run as high as half a million dollars. It seems that only the lawyers come out ahead in this game. By late 1970, it was becoming clear that the only sure way to earn a living in this business was to start making and selling my own products. I wasted much effort trying to find some practical way to cast the pieces in epoxy. When I finally came to the realization that this was a bad idea, I switched to woodworking.
In the fall of 1970, I had the good fortune to be invited to participate in an arts and crafts festival at the DeCordova Museum, located nearby in my hometown of Lincoln, Mass. It was here that the term AP-ART originated. It seems that one of the other exhibitors at the show took his work very seriously. When he found my children and me, purveyors of wooden "toys" setting up right next to his exhibit of abstract sculpture, he displayed his strong displeasure and asked, "What's that!" That was back in the days when Op Art and Pop Art were in vogue, so I jokingly replied AP-ART. He found it not very funny and objected to our being even in the same room with him. So, to our good fortune, we were banished to the more folksy and friendly outdoor craft area, which happily introduced us to other craftsmen and marked the beginning of our craft fair years. That memorable phase of our family enterprise, all too brief as it was, kept us all entertained and was a valuable experience for our three little helpers. It also brought us in direct contact with the public and served as a valuable learning experience for me.
By early 1971 I was beginning to make and sell my unique line of geometrical woodcraft products. Describing to others what I did for work always was a problem. If I said that I created puzzles, they would usually ask "jigsaw or crossword?" I soon learned not to follow that up with any attempt to describe them as three-dimensional puzzles because I dreaded being asked almost invariably, "Oh, do you make Rubik's Cube?" It hurt every time I was asked that. (And I still am asked!) Consequently, for a long time I deliberately avoided the use of the word puzzle in describing my work. Never again will I use it in the title of a book. Hence the renewed emphasis on my fanciful but fitting slogan "AP-ART, the sculptural art that comes apart."
From 1971 to 1975, most of my sales were at craft fairs. Usually our whole family was involved - my wife Jane and our three little girls, Abbie, Tammy, and Margie. The most important of these was the annual American Crafts Council fair, first in Bennington and later Rhinebeck, which was both wholesale and retail. Soon I had more business that I could possibly handle and was turning customers away. The main reason for this was that practically no one else was in this line of woodcraft, and certainly not as a full-time business. Even many years later this was still the case.
The wholesale business was more profitable of course because of the volume, but I much preferred the retail sales because it brought us into direct contact with the public. I recall many amusing incidents. One passer-by, probably a psychiatrist, stared at our large display of perplexing polyhedral dissections and asked, "Did you have an unhappy childhood?" Later that was used as the name for one of my more puzzling creations. More than one customer asked if I had a puzzle that would drive someone completely out of their mind. I assumed they were targeting their spouse, and I would remark to Jane that perhaps we should check our liability insurance.
We had one act that we used over and over. Usually my Jupiter (#7) puzzle served as the centerpiece of our display. It looks a lot more confusing than it really is. If you toss it up with a slight spin it flies apart into a jumbled heap of 12 pieces. I would remark that anyone who could put it back together could have it. No adults would ever try. In the meantime, our youngest, Margie, would be planted in the gathering crowd and would work her way to the front. You can guess the rest. The audience loved it.
Most of our retail sales at craft fairs were to customers who were buying gifts for someone else, and I knew that they were nearly always for adults. I always regretted that so few were for children, but the cost was a factor. We did have one low priced novelty that we called the Buttonhole Puzzle (#45). Not my idea but an old favorite, it is just a stick and loop of cord that you attach to someone's clothing like a price tag. We made them from wood scrap using about 50 different kinds of exotic woods. My kids sold them for 25 cents each, often after attaching them to the victim's clothing. Sometimes we would be told years later that they were still on!
In another attempt to come up with a low cost product that children could afford, in 1972 I turned my attention to topological puzzles, which typically use beads and cord with no close tolerances required. One of these was my Sleeper Stopper (#44) puzzle. Since I could not find any supply of high quality wooden beads, I decided to make my own. The machine that I devised to make them was basically a rapidly rotating 8-inch abrasive disk at the bottom of a round drum. Three-quarter-inch rosewood cubes with holes already drilled were loaded into it 100 at a time, and the abrasive was progressed from coarse to fine, and finally to buffing with wax. They came out rounded and shining like gemstones.
Soon customers began asking if they could buy just the beads. I made a larger bead mill with 12-inch disk and we turned them out by the thousands in various exotic hardwoods. The demand was phenomenal. At craft fairs we filled large wooden bowls with beads. People couldn't resist the urge to run their fingers through them, much the same way you play with sand at the beach. I devised a semi-automatic machine for drilling the holes, and turned over much of the operation to my kids. We added buttons to the line, and then pendants and earrings made with colorful laminated woods.
By 1975 we were filling so many orders for these that there was little time for making wooden puzzles. I began thinking that maybe it was time to return to more creative endeavors. But then an unemployed mechanical engineer named Laurie Grob who lived nearby, and whose wife was one of our button customers, came up with the idea of a key ring with a fancy wooden part that could be made using my bead machine. He had also located a company that was interested in purchasing them in very large quantity. We made an even larger mill using my wife's old washing machine, and we spent all of 1976 turning these out by the tens of thousands in various fancy woods. When that contract finally ran out, Laurie bought out my half of the business and moved to New Hampshire, where he improved the whole process and started a successful button business. Last I knew, he was still at it. I happily returned to making wooden puzzles.
Over the years, my associates and I have participated in a number of puzzle exhibits where the theme was just to display the various objects to be viewed by the public, usually in glass cases. The obvious objection to this is that mechanical puzzles are by definition designed to be manipulated. Take that away and what is left? Most polyhedral dissection puzzles do have the feature of being attractive to look at when assembled, especially when made with colorful exotic woods finely finished. But that can be both an advantage and disadvantage. I soon discovered that some customers were acquiring mine just to look at, without ever taking them apart. Sometimes I would even get a call from one of them exclaiming that some unruly visitor had taken one apart, and would I please send directions for putting it back together.
I will admit that when I first started making polyhedral dissection models, I too was fascinated by the way that geometrical solids fit together in space and the interesting shapes that resulted. Many of my early designs were little more than that - sculptural art that came apart. Later on, many other novel design aspects came into play, none of which could be appreciated or enjoyed by just admiring the assembled puzzle. I would often use plain hardwoods rather than colorful exotic woods in my work so that the sculptural features, which were really incidental, would detract less from all the other more important creative aspects that went into the design.
Again we come back to the limitations of puzzle exhibits. Some of us have tried hands-on puzzle shows with limited success. For the general public, the puzzles need to be very simple ones. Even so, you can soon end up with a pile of puzzle pieces unless there are many helpful hands around to reassemble them. Most museums don't have that kind of help available.
Given the limitations of puzzle exhibits or museum collections, and the impossibility of producing enough to supply the public demand, perhaps the next best alternative is to be found in illustrating and publishing. Such books are now coming out like never before.
My first book, Puzzle Craft, was begun in 1974 as a newsletter of limited circulation having to do with mechanical puzzles in general, especially those that could be made in the classroom or workshop. In 1978, the various issues were assembled into a booklet. Later, more chapters were added, and it was published as a book of sorts. A revised and improved edition was published in 1985. Minor revisions continued to be made until its final printing in November 1991. In all, about 2500 copies of Puzzle Craft 1985 were printed. In 1986, Oxford University Press became interested in publishing something along the lines of my Puzzle Craft to be included in their Recreations in Mathematics series. This involved a whole new approach and complete rewrite with much more material included. That book, The Puzzling World of Polyhedral Dissections, came out in hardcover in 1990 and in paperback in 1991. About 1800 of the hardcover were printed, and probably a few thousand of the paperback (I was never sure). They both sold out within months, never to be reprinted by Oxford, for reasons which to this day remain a complete mystery.
Since I continued to receive requests for my old Puzzle Craft (1985), and since there was much overlap between it and the Oxford book, in 1992 I came out with a completely new edition of Puzzle Craft in which the emphasis is on woodworking, whereas the Oxford book was more to do with geometrical recreations. In 1998, The Puzzling World of Polyhedral Dissections was made available at the Puzzle World web site. To save space and avoid duplication, they will be referred to frequently in this publication and abbreviated as PC'85, PWPD, and PC'92.
In addition to the above, I should mention some of the other related printed matter that I have disseminated:
From the start in 1968, I have kept records of my designs on file. Since names can be confusing (especially mine!), in 1970 I started numbering them as well. In 1985, I adopted a revised numbering system which I still use. In 1993, thanks to this amazing computer I'm using, I began making this list available as Serial Listing of AP-ART Puzzles Produced and Sold. It is updated yearly or sometimes even monthly. This present publication can be thought of as an expanded and much more detailed version of that list.
My numerical serial listings of designs described above is approximately chronological. However, since I have often used a letter suffix for a new modification of a previous design, therein is a departure from chronological. This could create a problem if loose-leaf additions to this publication are to be made. Therefore, henceforth I am revising my numbering of designs to make them strictly chronological as of January 1998.
Many of my designs are accompanied by an explanatory printed sheet which may also occasionally include the solution. Since 1993, an up-to-date listing of all these has been available as Serial List of AP-ART Instructions, Descriptions, and Other Printed Matter. The most recent version of this list is included in the appendix of this publication.
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