Sadly, I received word in April 2018 that The Center for Talented Youth at Johns Hopkins University decided to cease publication of Imagine magazine. May/June ’18 was the final issue. That summer, I also left UIC to start a new job at The University of Maine. With the normal demands of the publication cycle gone, and a big mathematics education project awaiting me at UMaine, I haven’t been able to devote much time to puzzlemaking and updating the website.
But that doesn’t mean that Knossos Games is no more. I’ve kept the website up and running, because I knew how many people enjoy the puzzles here. There are still parts of the website that need to be updated. There are puzzles that were published in Imagine that I’ve never had time to post on the website. And there are puzzles that I had been saving up for Imagine that never saw the light of day.
A year before Imagine magazine began, back in 1992, my very first published puzzle was in the pages of the Study of Exceptional Talent Precollege Newsletter. Since Imagineceased publication a couple of years ago, the people at SET thought that their newest members might be unaware of Knossos Games. This past January, I spoke with Carol Blackburn, a research psychologist, SET staff member, founding editor of Imagine, and longtime enthusiast of my puzzle column. The following is reprinted from the SET Precollege Newsletter with their gracious permission.
SET alumnus Tim Boester has been making puzzles for nearly as long as he can remember. He began publishing puzzles in Imagine magazine when he was in high school, and continued to do so throughout college, graduate school, and into his professional life as an educational psychologist and mathematics professor. Puzzles by Tim appeared in all but six of the 125 issues of Imagine. You can visit Tim’s wonderful online archive—a treasure trove of puzzles—which includes thoughtful explanations of how to solve his puzzles at knossosgames.com. In this spread, we showcase just a few of the puzzles he created over the years, and hear about his journey from a boy who loved puzzles to a professor who studies how students learn advanced mathematical concepts.
When did you start making puzzles?
My interest in making puzzles started early. I don’t know why. I remember drawing my first puzzle in kindergarten—a giant maze on packing paper. The teacher hung it on the blackboard near the door, so that my classmates could try it. Discovering graph paper soon after was a revelation. I went through reams of it in elementary and middle school. I grew up making puzzles.
For years, pencil and paper were the only tools I had. Even today, I still start by jotting down notes and sketches on graph paper. It helps me clarify my preliminary thoughts about a new puzzle idea. However, using the computerized tools we have now has definitely influenced my process in creating puzzles. For example, being able to rapidly prototype puzzles and print out several copies enables me to test different versions quickly. I can explore many more options than I could before. At times I wonder how I was able to create some puzzles as a kid when I had to do everything by hand.
Many of my early puzzles were simply variations of puzzles I had seen and liked. Creating my own puzzles inspired by ones I enjoyed helped me better understand how puzzles work and how they are constructed.
When did you start publishing your puzzles?
I became a member of SET in eighth grade, and the summer before my junior year, I sent some puzzles with my SET Update. You and your colleagues liked them and asked to publish one in the SET Precollege Newsletter. Then you asked to print one in the very first issue of Imagine magazine, on the Creative Minds Imagine page. Then another. By volume five of Imagine, I was a regular contributor with my own column, Knossos Games.
Where did the name Knossos Games come from?
I wanted a title that communicated the long history of puzzles, but also felt modern and fun. Knossos is the city on the island of Crete where King Minos, according to Greek mythology, built the labyrinth holding the Minotaur. Knossos Games hopefully evokes the notion of puzzles inspired by this tradition.
Your range as a puzzlemaker—the types of puzzles you created and their settings—really grew over time. I still remember when you sent us a puzzle inspired by something you learned in a biology class.
Yes, the professor was talking about how a particular cellular transport system works, and I thought, this could make a good puzzle. There were some channels that allowed molecules to move alone (uniport), others that required co-transport with another molecule (symport), and still others that required transport of another molecule in the opposite direction (antiport). It took some thinking before I decided how to use those channels in a puzzle, but eventually I came up with the right structure. Instead of having a traditional finish line, the goal of the puzzle was to use the channel-based passageways to move objects through the puzzle until all the objects had been moved to receptors scattered throughout the puzzle.
Puzzles are always based on rules. Coming up with new puzzle ideas means coming up with new sets of rules. So I’m constantly on the lookout for real-world situations that contain some inherent rules or structure that I could build upon or transform into a puzzle.
That biology puzzle was the first of your “themed” puzzles, where your Knossos Games puzzle related in some way to the theme of the issue of Imagine in which the puzzle would appear. You came up with some wonderfully creative ideas, like the archaeology puzzles with the Indiana Jones-like booby-trapped squares in a maze.
As I became more experienced, I was ready to take on greater challenges and wanted to focus on creating puzzles that are unique. About ten years into creating puzzles for Imagine, I decided that I wanted each puzzle to relate to the theme of each issue. That self-imposed constraint was difficult but inspired some of my best puzzles. It was a real struggle at times to fit each issue, with topics as diverse as “energy” to “service and leadership” to “medicine.” I never would have thought to base a puzzle on fish ladders if I hadn’t been given the topic of “marine biology.”
The archaeology puzzles were made for a history issue. I had to make a bunch of them because there were many ways to set up the rules, and I had to try out various rules and see what would work. Often, I don’t know before I create a puzzle what the solution will be. The final form of the puzzle emerges only after trying out different rules and combinations of rules, following them to their logical conclusion, and examining the results. Writing puzzles is a great way to practice and solidify your abilities in deductive reasoning.
What was one of your favorite puzzles?
One of my favorites was actually suggested by you, Carol. For a political issue, you suggested creating a puzzle about gerrymandering, and it was an intriguing suggestion. Here again, I knew the idea could be used to make a puzzle, but it took a while to figure out exactly how. I searched to see if puzzles based on gerrymandering had been made, and I found some, but they didn’t hinge on how gerrymandering works. I thought, they are missing the point of what a gerrymandering puzzle could be.
In the puzzle I finally created, the nefarious task is to gerrymander local districts so that your side wins a majority of districts (seats) even if it does not win the majority of votes. These puzzles hopefully enlighten solvers about how incredibly influential districting can be on election results. By doing the puzzle, the solver really sees how gerrymandering works, why it is so politically powerful, and why it needs to be stopped. Later I made a few other puzzles about real-world topics, where working through the puzzle gives you a better understanding of the way a system works, like the puzzles about where to position windmills in a wind farm to maximize the energy capture, or tracking the spread of a pathogen in a population.
The mathematical discipline of logic has existed since the time of Aristotle, but logic puzzles are a much more recent phenomenon. The mathematician Raymond Smullyan galvanized the field with his creation of “knights and knaves” logic puzzles, in which all knights tell the truth and all knaves lie. Given a set of statements from different people, one can deduce who is telling the truth and who isn’t.
At first I avoided making logic puzzles, because I didn’t think I had anything to add to the genre. Eventually, I came up with a “knights and knaves” puzzle inspired by the TV show Survivor. In my version, the first few people kicked off the island would always tell the truth, the middle people would tell one true statement and one false statement, and the last people would all lie. The puzzle presents you with a collection of statements by various people, and you have no idea which ones are true and which are false, and you have to logically sort through them. Logic puzzles are a place where I can ramp up the difficulty, and the Survivor puzzles (1, 2) are really tough. With an overwhelming number of clues, a big part of the challenge is just figuring out where to start.
Have you watched many people solve your puzzles? I wonder if you are sometimes surprised at the strategies they use.
I haven’t done as much of that as I would have liked. I had more opportunity when I was a graduate student in educational psychology. Back then, it was easy to find students willing to test-drive a puzzle. It was always interesting to see if my cleverly laid traps actually tripped them up, or if they just sailed on by, not taken in by the snares I had planned.
In my work, I certainly spend a lot of time watching my students solve math problems, and I read lots of professional papers about others who have watched students solve problems. I am always looking at how people approach problems. I’ve been doing this for a while, but I am still surprised sometimes at the thinking that people put in to solving a problem—right or wrong.
How does puzzlemaking relate to your career?
Some of my colleagues over the years haven’t known what to make of my puzzle hobby. To them, it doesn’t have a clear connection to my occupation. Sure, some of the puzzles are math-related and sort of learning-related, but to them it’s a weird remnant of my origin story.
Really, being an educational psychologist and making puzzles are two sides of the same coin. During my professional education, I learned a lot about how people solve problems. As a professor, I am trying to understand how people are thinking through mathematical concepts; and in my classroom I’m trying to use that knowledge to make those concepts as accessible as possible. Maybe not easy, but accessible. How can I help students navigate a tricky concept most successfully? What will be the most common pitfalls for them?
But when I’m designing a puzzle, I’m using all that knowledge to make things harder for the puzzle solver. I’m trying to understand how people are thinking, but then I’m trying to throw obstacles in their path. The same expertise that makes me a good educator also makes me a dastardly puzzlemaker.
I want to thank you for all the dastardly and delightful fun you created for us. Imagine would not have been the same without you and Knossos Games.
It was a pleasure. Puzzlemaking has always been an excellent creative outlet. And now that I am a teacher, it’s been fun to be able to write problems for Knossos Games that I could never put on a test because my students would kill me.