The first Pathogen puzzle was created in November, 2008 for the public health issue (16.3 – Jan/Feb 2009) of Imagine, but for various reasons, never made it to the website around that time. When the magazine returned to the topic of public health (23.3 – Jan/Feb 2016), it not only made sense to design another Pathogen puzzle, but also to prepare both puzzles for the website.
While I’ve forgotten some of the details about how I first came up with the idea of a puzzle based on a disease, I do recall that this was a time when bird flu (H5N1) was in the news. I knew immediately that a puzzle about public health was going to focus on, in some form, the mathematics of disease transmission. It did take some creative effort, however, to take those ideas and form a puzzle with them.
If you think about it, the structure of the puzzle scenario does not make a whole lot of sense. If you know who is infected, the contact chart, and how many days the pathogen has had to spread, it really strains credibility that you wouldn’t already know who patient zero is or (in particular) who is vaccinated against the pathogen. The more realistic problem is: knowing who is infected and some idea of the contact chart, figuring out who else might be infected. But I couldn’t figure out how to make a puzzle from that situation which was still well-defined and not trivial. In other words, if the contact chart is completely defined, then determining who would be infected is easy. If the contact chart is not completely defined, then it’s impossible to completely determine who would be infected. This mirrors reality, but isn’t very compelling as a puzzle, since puzzles are supposed to have solutions.
The Pathogen puzzles as created aren’t that difficult, since you can figure them out through brute force if necessary: trying out every infected person as patient zero and seeing what happens. There are faster ways to solve the puzzle, of course, but even each detailed solution basically makes good guesses as to whom patient zero might be, then simply tries them all. I needed to explore the sensible possibilities to create and test out each puzzle, and while there is typically a different method used to create versus solve one of my puzzles, in this case I couldn’t think of an alternative.
Finally, I’ve met experts in a wide variety of fields through my years as a student and now as a professor, and those connections definitely come in handy when writing a new puzzle in an area which I have no expertise. The instructions were vetted by people both on my end and at the magazine, and their most important suggestion was to use “vaccinate” instead of “inoculate”, as the latter can mean to deliberately introduce a pathogen but not necessarily to produce immunity (such as for a culture or as a treatment). Even though the scientific situation of the puzzle may not be realistic, I still want to get these educating details right.
Even though this is the first time the Pathogen puzzles have appeared on the website, they still went through several design refinements. It took a while to get the right look for the contact chart and accompanying solution labels.
Forming the seamless shape that encapsulates the contacts between circles/people was accomplished by merging shapes together (left column above), instead of trying to draw the shape from scratch. Unfortunately, there is a bug (I think) in the SVG rendering engine inside of Adobe Illustrator, as these complex shapes are not perfectly displayed on the website, regardless of browser. It’s a problem that I’m going to have to live with for the moment, as I can’t read the raw SVG code and mentally translate it into the visual shape to determine where the problem is.
An additional complication was the fact that different sizes of graphics would be necessary for what appeared in print versus on the website. This is something I try to avoid, as it creates twice the number of images that need to be produced, but occasionally it makes sense. Here, the print images needed to be smaller to fit on the page, while larger web images were more legible on the screen. The print images are scaled by 150% with further adjustments to lighten the stroke weights.
The firstGreek Temple puzzle coincided with the first time that I tried to align the content of my puzzle column to the content of the magazine. Prior to the fall of 2004, I basically just created whatever puzzles I wanted to. Starting with Issue 12 of Imagine, I began creating puzzles that matched the theme of each issue. With the first issue being Archaeology & Paleobiology, this provided an opportunity to publish a new type of puzzle I had been working on for a while.
Unfortunately, back then I didn’t consistently keep very good notes about creating puzzles, so I don’t know exactly when I created the first Greek Temple puzzle. I do know that, prior to the fall of 2004, I had made an entire set of smaller Greek Temple puzzles based on the idea of linking the four possible state changes for the gateways (open, close, change, same) to the four possible options of moving between two tiles (alpha to alpha, alpha to beta, beta to alpha, beta to beta). While the graphical style of the puzzle has remained remarkably consistent over the years, I don’t remember how I came up with that original idea. The set of smaller puzzles has never been published, as they really belong together as a complete set; instead, each time a history or archeology issue comes around, I’ve chosen to create a new Greek Temple puzzle.
I did create a backstory for the puzzles to help me with some of the design details: A couple of archeologists have recently unearthed these ancient yet pristinely preserved structures. They accidentally realize that, with the introduction of a source of water, stepping on certain tiles at the entryway opens each temple’s doors via some sort of hydraulic mechanism. Yet they do not know why these structures are here, what they are for, or why they are the first to discover them in regions that have been thoroughly explored before.
Finally, each puzzle thus far has used a different pairing of gateway state changes and tile jumping options (see above). There are only a finite number of these, so I’ll necessarily need to start repeating, but some of the possible combinations keep the gateways open more often and some keep them closed more often. I’ve tried to stick to combinations that strike a balance. Regardless, it has been an interesting aspect of the design challenge to see how these combinations affect movement within the puzzle space.
Note: this blog entry shows some parts of Greek Temple puzzle solutions. Go back and solve the puzzles first!
Before this update, I had only ever posted to the website the first two Greek Temple puzzles (12.1 from 2004 and 13.2 from 2005). Subsequent Greek Temple puzzles (18.2 from 2010 and 19.2 from 2011) published in the magazine fell at a time when website updates were sporadic at best. With the most recent puzzle, it was time for a major update.
Most of the graphics have remained the same since my initial conception of the Greek Temple puzzles. For this update, I did, however, adjust the positioning of the alpha and beta labels on each tile.
This realignment was necessary to accommodate the biggest part of the current update: new, detailed diagrams that indicate solution steps though open and filled circles on each tile. Solutions were originally posted (and will continue to be posted in the magazine for compactness) as text through cardinal directions (N, S, E, W). This solution representation isn’t optimal, since it requires the reader to move through the solution one step at a time, going back and forth between the text of the solution and the puzzle diagram.
Thus, I’ve created these solution diagrams that show the path of the solution on the puzzle diagram itself, grouping several steps together at a time (using the same slideshow technique used with the Space Pod puzzles). It isn’t typically possible to show the entire solution at once, since this type of puzzle often relies on moving back and forth between tiles in order to change the state of the gateways.
Working out how to represent the overlapping parts of the solution path was one of the hardest aspects of designing clear, useful solution diagrams. Another challenge was that the solution path needed to represent two simultaneous pieces of information: your physical position in the puzzle, as well as the orientation of the gateways. This was resolved with using the open and filled circles.
One benefit of these new diagrams is that it also allows me to point out important parts of the puzzle space, so that I can describe why the solution must go the way that it does. While it is possible to represent the problem space of each puzzle as a tree diagram, I think it is more useful (for similar reasons described above) to show the loops, dead ends, and traps in the actual puzzle space.
One final conundrum involved describing these pathways through words as your orientation to the puzzle space changes as you move through it. I decided to give directions for turns (left and right) based on your current position, but to describe parts of the temple (front and back) with respect to facing the entrance. This seemed to be the least confusing out of many bad options.