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.
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.
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.
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.
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.
A new edition of the absolutely authoritative and exhaustive guide to both classics: Alice’s Adventures in Wonderland and Through the Looking Glass. Extensive annotations concerning the background and influences of the work, the historical context, and how the works comment on the state of mathematics:
• Two logic puzzles were specifically styled after Raymond Smullyan’s “knights and knaves” or “truth tellers and liars” puzzles. The first Castaway puzzle (based on the reality television show Survivor), adds people who sometimes lie and sometimes tell the truth. Smullyan calls these people “normals”. The second Castaway puzzle, not mentioned in the article, defines different ways in which people might lie based on whom they are speaking to. I have not found a similar Smullyan puzzle (although by no means have I read them all).
The article also includes a sidebar of puzzle books. I’ve listed those in a separate blog post if you’re interested in details and links.
Again, I’d like to thank Imagine and my editor, Melissa Hartman, for giving me the opportunity to write an article like this, in addition to my continued puzzle contributions. If you like the article and Knossos Games in general, please consider subscribing.
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.
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.
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.
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.