Tag Archives: behind the scenes

Imagine 24.4 puzzle…

Work has kept me very busy this spring, so I’m still working on updates for the If Then City Blocks and Cell Wall Transport System puzzles. But it was long overdue to switch off the winter theme and remove the direct link to the holiday puzzles, although they can still be found here.

Origin Stories: Christmas Trees

My mom loves Christmas decorations. She decorates every available space in the house with garlands, greens, candles, wreaths, and lights. Her navity scene was hand-carved in Germany and was a gift from my dad on their honeymoon. But nothing compares to her collection of Christmas tree ornaments.

Every Thanksgiving, dozens and dozens of boxes descend from the attic to decorate the Christmas trees. Yes, trees. We started with one in the living room, but with so many ornaments, she became a museum curator, only able to display a small fraction of the continuously growing collection on any one holiday. For years, my dad refused to put up a second tree, knowing this would be the path to extreme self-indulgent holiday cheer.

And he was right. When a neighbor brought over a used artificial tree one year, the barrier holding back unrelenting twinkle and sparkle had been breeched. She’s now up to four trees: a live tree we get every year from a local Christmas tree farm, a small driftwood tree for displaying ornaments made from natural materials, a half-size artificial tree for the small ornaments, and the aforementioned full-size artificial tree that stays up all year. (The excuse: it’s too difficult to take apart and haul into the attic. Sure.)

In the sprit of her unrelenting passion for Christmas tree ornaments, the latest holiday logic problem celebrates the yearly chaos of choosing which ornaments should go where. This puzzle was modified from one originally posted in 2005. It is an homage to the holiday-themed grid-based logic problems I made as a kid, but which have been entirely lost. I updated the puzzle text and clues (including changing some of the ornaments and tree locations), added new graphics and a detailed solution.

Origin Stories: Reindeer Games

I started writing holiday-themed logic problems as a kid. I really liked solving grid-based logic problems, and once I figured out how they worked, I started creating my own. Unfortunately, I can’t find any copies of those original puzzles I made. But those early puzzles inspired me to start writing holiday-themed logic problems again once I got serious about the Knossos Games website in the mid-2000’s. As these puzzles aren’t published in the magazine (or anywhere else), they are a special bonus to my website visitors.

Even though my earliest logic problems were of the grid-based variety (both solving and creating), I have avoided that type of puzzle when writing for the magazine. In fact, I refrained from writing logic problems for the magazine altogether for the first five years. It was only when I found an interesting though flawed logic problem that I published my own improved version in the magazine. The following year I wrote the two-year garden logic problem and have written about one per year every year since.

When writing a logic problem, you want to situate or structure the puzzle using a natural order or pre-existing rules. This helps solvers initially engage with the puzzle, as they can utilize their prior knowledge to gain an entry point and start solving. The order of Santa’s reindeer, memorialized in story and song, made for an obvious choice. I used the L-shaped arrangements of the two-year garden logic problem as the basic structure for this new puzzle.

Top: L-shaped example from two-year garden logic problem.  Bottom: L-shaped example from reindeer games holiday logic problem.

This puzzle was originally posted to an older version of the website in 2004, then resurrected as part of the newest version of the website in 2015. When I decided I wanted to restart the holiday logic problem tradition, I found a copy of the clues to this puzzle, but no solution! I had to go back and solve the puzzle myself to remember how it worked. I rewrote the entire prologue to the puzzle, utilizing actual proclamations found on the internet as a basis for the language used. The new version of the puzzle added graphics and a detailed solution.

Welcome Logic Fans

If you’re here because you read the article I wrote on logic and puzzlemaking in the recent issue of Imagine, you might want to check out the following:

There are “origin story” blog entries for some of the logic puzzles I’ve written: the Coin Box problem, the Two-Year Garden problem, and the Castaway (Part 1) problem. I’m working on more.

I also wrote about the updates (part 1, part 2) of the logic puzzles for the most recent version of the web site.

Finally, here’s the blog entry that started it all, where I discuss how making puzzles and my job as an educational psychologist are really two sides to the same coin.

Fall ’16 Updates Just Around the Corner

It was an active summer here at Knossos Games HQ, with two warm-weather themed updates (Park Trails and Park Cleanup Logic puzzle). But the big news was that Tim moved to Chicago to start his new job as the Director of the Mathematical Sciences Learning Center at the University of Illinois at Chicago.

As always, the Knossos Games summer hiatus was spent preparing updates and puzzles for the magazine and website (as well as packing and unpacking a lot of boxes!). As I’ve commented before, several things are always going on at once, and the summer was spent writing puzzles, preparing site updates, and generally getting things organized. There are a lot of exciting updates coming!

Update: DNA Transposition

Note: this entry contains minor spoilers about the solutions to the two DNA Transposition puzzles. Go solve them first!

Back when the first DNA Transposition puzzle was printed in Imagine, we were concerned that readers would not completely understand how to solve the puzzle given the abbreviated instructions printed in the available space. In situations like this, the website comes in handy: we can post detailed instructions and examples and print a link in the magazine in case readers want more information. So that’s what we did, but I never got around to posting the actual puzzle (or the second one) until now.

Regardless, I discovered and fixed a few flaws in the original graphics before posting this update. Most of my attention focused on the solution graphics, both the path through the apparatus and the tree diagram showing the problem space. Finding the appropriate way to show a path that loops and doubles back on itself in a single diagram was tricky. I found that creating template path pieces worked best – these could be assembled then merged together to form one seamless, semi-transparent path.

path pieces

Representing loops in the problem space diagrams presented a similar challenge. I first charted out each problem space on paper, then created a digital version that could be rearranged so that loop connections would be close together (or as close together as possible). Several alignment issues were also corrected in the problem space diagrams.

Compounding all of this in the second puzzle was, in addition to an intended (shortest) solution, an additional solution that merited attention. This meant creating multiple solution path graphics, all of which needed to share the same visual language, and creating a single problem space chart that could highlight each solution separately while still being compact and coherent overall.

Origin Stories: DNA Transposition

I find the entire concept of genetic code fascinating. I’ve taken a few biology classes over the years, and every time we discussed DNA, I marveled at how something could simultaneously be so simple yet so complex. Thus, I had wanted for a long time to make a puzzle that relied on DNA.  I knew the opportunity for that puzzle had arrived in the summer of 2010, when I learned of the topic for one of the Volume 18 issues of Imagine: Biotechnology. The second puzzle was subsequently created in 2013, for the Frontiers in Medicine issue.

In the earliest brainstorming phases of creating a brand new type of puzzle, I usually start by writing down all the ideas that I have. No matter if they become part of the puzzle or not, I just want to make note of everything in my head, so that later thoughts or avenues I pursue don’t cloud my original ideas. Sometimes, those original ideas are changed significantly by the time the final puzzle is produced. (Sometimes the original ideas don’t produce anything of value whatsoever!) Remarkably, for the DNA transposition puzzles, much of my original ideas appear unchanged in the final puzzle.

Notes from July 22, 2010:

Going back to mazes with structure and rules1, the puzzle contains a set of connected paths. What governs which paths you can take at any intersection is a token that changes. (Instead of keeping track of this in the physical space, like in the Cell Wall Transport System puzzles, this puzzle uses an external item, more like the subway token puzzles2.)

You have a bit of DNA. Some intersections do nothing, but some rearrange bits of the DNA according to order. For example,


would move the first bit to between the third and fourth (making it the new third). So GATC would become ATGC.

Different paths have different restrictions. For example, a path could only let pass bits of DNA that have the sequence “GA”. The original piece of DNA could pass through this, but not the new rearranged piece (as it does not have “GA”).

The crucial idea of a “token” that you carried through the puzzle was essentially what made this puzzle different from my previous puzzles, and helped to clarify the instructions to others. The “intersections” became the bubbles in the final puzzle, while the “paths” became the connecting tubes. The diagram is meant to be an iconic representation of the prototypical chemistry lab apparatus.


The instructions took several passes, with the assistance of a few biologists called in by myself or my editor, adjusting the vocabulary to best fit what was happening in the puzzle. For example, I initially used the word translocation, which I found out typically refers to moving whole parts of a chromosome. Transposition is more appropriate when moving a shorter sequence or, in this case, individual nucleotides. Also, using the term DNA isn’t appropriate here, since DNA refers to the entire molecule, not a short sequence of nucleotides. The instructions therefore use the term genetic material, even though DNA is retained in the name of the puzzle.

The design of the puzzle took a while to finalize.  I needed to visually communicate how each bubble transformed the genetic material.


Early attempts directly translated what I had in my notes, using numbers to show the rearrangement of nucleotides. These needed to be large to clearly display the numbers, but were too large and too cluttered for the rest of the puzzle. Thankfully, I hit upon the idea of completely eliminating the numbers and letting greyscale boxes denote the positions of the nucleotides.

This type of puzzle necessitates charting all possible paths through the problem space in order to ensure the designated solution is the shortest. In other words, every pairing of position and genetic token that is possible by moving through the puzzle must be examined. Because of the cyclical nature of the puzzle (repetitively rearranging the nucleotides and moving back to the same physical position in the puzzle), loops are possible (moving around the puzzle and returning to the same location with the same order of nucleotides). This challenge of representing a problem space with these loops was resolved by using one-way arrows.

Problem space for example DNA Transposition puzzle, shown above

Moving up each arrow loops back to a position that could have been achieved using fewer moves (sometimes utilizing a very different path through the puzzle), while the most direct solution is highlighted in blue.

Origin Stories: Pathogen

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.

Pathogen example: two days to spread, one person vaccinated

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.

Testing each infected person as patient zero (solution bottom right)

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.

Update: Pathogen

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.

First row: initial attempt. Second row: larger circles, thinner connections. Third row: visual style used for first publication, medium connections between mid-sized circles, thicker boundary. Fourth row: final adjustments for second publication, thinner boundary, font and color changes.

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.

Left: print. Right: website.

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.