About Those 2339 Solutions...On the introduction page of my pentominoes website I mention the very first set of pentominoes I ever owned: a toy called "Hexed" produced by the Gabriel toy company. I got this puzzle sometime in the early 80s and I was immediately entranced by the fact that the lid of the box stated that there were exactly 2339 different ways to fit the twelve pieces into the box (which formed a 6x10 rectangle). The exact text read, "A Computer Confirms There Are 2339 Ways To Fit These Shapes Into A [6x10] Rectangle."
Recently I was contacted by an individual, Rod Fletcher, who was one person who calculated that 2339 number. He might have been the first individual to figure out how many distinct 6x10 rectangular configurations there were, and he subsequently notified the Gabriel toy company of the calculation. He still has copies of the correspondence to prove it.
During the 70s Mr. Fletcher was a graduate student in electrical engineering at the University of Illinois. In April of 1975 he wrote the solving program on a Dec System 10 computer ("a roomful of racks with lots of blinking lights," as he put it). The program was written in the Macro-10 Assembly Language, and for every five solutions it found it printed out another row of diagrams (here is a scan of the first forty solutions found as sent to me by Rod -- note that the diagrams are depicted using 1s and underscore characters...).
Several hours later (after using "2 hours 31 minutes of CPU time" and fifty-nine printed pages), all 2339 solutions were found. Mr. Fletcher shrunk these pages down on a photocopier and mailed them to Kohner Bros., Inc (a subsidiary of Gabriel Toy Industries) as seen in this scan of that correspondence. He received a reply (on Gabriel letterhead) on 13 June of that year, thanking him for the information. His follow-up letter goes into more detail about his motivations for writing the program as well as an argument as to how the 2339 solutions can be verified as distinct and exhaustive. In lieu of any financial reimbursement, Mr. Fletcher simply asked that some copies of the puzzle be sent to him.
By the time those copies of the puzzles were received, the puzzle's packaging had been updated to include the "2339" number on the lid. This was the edition of the puzzle I eventually owned.
There many reasons why I was thrilled to be contacted by Mr. Fletcher. Obviously, this was an account that I could strongly relate to. I still own that original puzzle and the box it came in, and as a child I always wondered how a computer could count up the solutions (these days, after a lifetime of writing programs myself, I have a much better idea of how that was accomplished).
It's also a chance to appreciate the advancements in computer power during the past fifty years (as if we aren't often reminded of that already). Back in 1975 it took Mr. Fletcher's program just over two and a half hours to compile all of the 6x10 pentomino solutions. Today, using a copy of Burr Tools, that roomful of blinks lights is replaced by a fancy graphical user interface that can analyze polyform puzzles of all types of shapes and configurations. It can also find all 2339 6x10 pentomino solutions in about 4 seconds' time.
But beyond the topic of pentominoes, Mr. Fletcher's correspondence with me about all of this reminded me of a "simpler time" with the World Wide Web. A time when people (often geeky programmers on some level) would search the web for esoteric topics, and maybe, just maybe, they would find someone out there who had written information about such topics. "Personal webpages" are harder and harder to find these days on the web. The few that seem to remain from the late 90s and early 00s are so easily drowned out by the social networks, news aggregate websites, pop-up cookie warnings, advertisements, and AI-written-generic miasma that dominate the internet. Too often I feel like there may no longer actually be any "information" on the Web, just pages of links that refer to other links, but no one actually linking to real "content" (can the reader tell how disenchanted I've become with the industry that treated me so well decades ago?).
I still have my personal webpages (written in rough HTML, by hand, using 'vi' text editor). I don't update them very much these days. Many of the links no longer work. But occasionally, every now and then, somebody out there stumbles across them and finds someting of interest. And that can lead to an enlightening correspondence.
Mr. Fletcher's emails to me were one such correspondence, and I'm glad to have learned a bit more about the history of one of my favorite puzzles.
(Above is pictured hand-colored graph paper from my childhood... I still have this document upon which I was trying to record all 2339 6x10 solutions as I found more and more by hand.)
- Eric Harshbarger, 1 October 2021