You also created some fiendishly difficult logic puzzles.
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.
After receiving a bachelor’s degree in mathematics from the University of Chicago, Tim Boester studied mathematics education at the University of Wisconsin-Madison. He received a Ph.D. in educational psychology and a Master’s degree in mathematics based on his research studying how students conceptualize limits in undergraduate calculus classrooms. He is now an Assistant Professor at the University of Maine.