Authoring Knossos Games: Timeline

You may be curious as to what goes into making a puzzle before it appears in the magazine and, ultimately, on the Knossos Games website. In this series of occasional posts, I hope to give some insight into the process.

Imagine is published five times a year, roughly following the U.S. academic calendar. At the beginning of each summer, my editor e-mails me the topics chosen for the year’s issues. The puzzles for my column are typically due six weeks before the start of an issue’s publication window, and I wait to post a puzzle (and its solution) to the website until after the solution is published in the following issue.

For example, I started working on the puzzle that will appear in the next issue of Imagine (v22.n4, the March/April 2015 issue) back in December 2014. I mulled over a few possible ideas related to the theme of the issue (writing) during the holidays, then worked on a couple of specific concepts in early January. By mid-January, one puzzle idea had emerged as my clear favorite, so I focused my efforts there.

Since the puzzle hasn’t been published yet 1, I can’t give too many details. However, I can say that it has something to do with writing, and was tricky to create. It required charting out a lot of possibilities, and writing up a detailed solution to be certain that the puzzle worked the way I intended it to. I submitted a draft on January 25th, then discussed the puzzle with my editor, and by the 31st had submitted a revision to both my editor and the layout designer that will be the final puzzle seen in the magazine.

Depending on how the rest of the issue is shaping up, the March/April issue could be out any time between mid-March and mid-April. But the puzzle won’t be posted to the website until the following issue is out (with the March/April puzzle’s solution), most likely in June. Check back then for a much more insightful description of how that puzzle came to be.

There is another way that we can look at this, though, and that’s to focus on what I’m accomplishing right now. I’m currently between deadlines. As I said before, the puzzle that will appear in Imagine v22.n4 (the March/April 2015 issue) was submitted a couple of weeks ago, and now I’m working on the puzzle that will appear in v22.n5 (the May/June 2015 issue), which is due in mid-March.

At the same time, I’ve been working on a couple of big website updates for puzzles that were published in the past few months. I just completed a major overhaul on the Space Pods puzzles, one of which appeared in Imagine v22.n1 (the September/October 2014 issue). Work continues on an even larger update for the Logic puzzles, one of which appeared in Imagine v22.n2 (the November/December 2014 issue).

Thus, every puzzle typically covers a multi-month time span from start to finish, and several of these overlap at any one point in time. Since this requires switching off between puzzles, I keep a lot of notes to remind myself of what my ideas are and where I am in the process of creating, editing, submitting, and posting each puzzle. The most difficult part tends to be correctly prioritizing what needs to be done when. Even after many years of creating puzzles, it is still not obvious beforehand how long it will take to complete each step of the process.

Site updates: January 2015

An ongoing catalogue of Knossos Games website issues and minor updates.

Updated to WordPress 4.1.

Fixed: Mixing large and small puzzle images

Problem: In laying out the website, puzzle images are supposed to be centered horizontally within the column of text. However, if there is an image that is larger than the width of the text column, all of the images would be recentered so that they would be centered with the largest image instead of the text. This was ok if one large image dominated the layout and the other images should accompany it, but was inappropriate if one large image was simply mixed in with a lot of text and other smaller images.

Solution: By creating a separate div class, which relegates these large images to their own blocks, smaller images will center normally.

.content-graphic-big {
    display: block;
    width: 509px;

I still have an HTML5 problem, however, as the standard suggestion for centering images using the following just does not work for my layout, and I’m not completely sure why.

 img {
    display: block;
    margin: 0 auto;

Some images are centered using this technique, but most are misaligned left or right. Thus, I am still using the depreciated text-align hack.

.content-graphic {
    position: relative;
    text-align: center;

Here is an example of the original behavior, where all images are centered to the largest image width, which in this case I feel is still appropriate. Here is an example of the new, more appropriate centering of mixed image sizes. This problem was tackled now because it was causing many problems in re-editing the logic puzzle web pages.

I am a puzzlemaker, sometimes.

Knossos Games isn’t my day job. But it’s the part of my all-around occupation that I’ve been doing the longest. Let me try to explain.

I spend most of my time, quite enjoyably, being an educational psychologist. Basically, I study how people learn, specifically, mathematics. I have an undergraduate degree in mathematics from the University of Chicago, plus a Masters degree in mathematics and a PhD in educational psychology from the University of Wisconsin-Madison. I currently spend a lot of my time working with undergraduates who want to become teachers, to help them understand how their future students will think about math. But before all of this, I doodled on graph paper a lot.

I grew up making puzzles. I remember my very first puzzle that I made in kindergarten – a giant maze on packing newsprint. The teacher hung it on the blackboard near the door, so that my classmates could try it when we lined up for recess. Discovering graph paper soon after was a revelation. I went through reams of it in elementary and middle school. I became a member of the Study of Exceptional Talent (under the larger umbrella of the Center for Talented Youth at Johns Hopkins University) in the eighth grade, and the summer before my junior year I sent in some puzzles with a here’s-what-I-did-on-my-summer-vacation letter. One of those puzzles became my first publication in the SET newsletter, which a year later transformed into Imagine magazine. They asked me if they could publish more of my puzzles. Twenty-two years goes by really fast: college, grad school, now professor.

My primary job as a mathematics educator is to better understand how people think about mathematical concepts. I can then use that understanding to build better classroom experiences for my own students (and in the case of future teachers, their own students). How can I help them navigate a tricky concept most successfully? What will be the most common pitfalls for them? How can I ask just the right question to get them to think about an idea in just the right way? How can I pose the best activity so that the underlying reasoning of the concept they’re studying is self-evident? While the field is still young, there has been a considerable amount of research in this area that people like me can utilize in classrooms and pass on to other educators. And because there are still many unanswered questions, I help contribute to that body of knowledge by doing my own research.

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 that defies explanation.

Really, making puzzles and being a math educator are different sides of the same coin. During my professional formative years, I learned a lot about learning. Theories of cognition. How people solve problems. What makes a problem hard. When I’m in my classroom with my students (or really, when I’m in my office before class deciding what we’re going to do), I’m using all of that knowledge to help make things easier for them. But when I’m designing a puzzle, I’m using all of that knowledge to make things harder for everyone.

For example, when designing the gerrymandering puzzles, I expect newbie solvers to bump around a bit before discovering the two main principles for gerrymandering: packing and diluting votes. When diluting votes, you only have so many districts to distribute heavy yes-voting precincts in to so they don’t overpower the collective no votes. With this realization, the puzzle then morphs into a pentominos-tiling problem (or septominos for the 7×7 puzzles). Don’t kid yourself – there’s a lot of mental work that needs to happen to just get this far. But the game’s not over. In designing each puzzle, I charted out all the different ways to consolidate precincts into districts, and then intentionally picked what cognitive science tells me is the least obvious way as the solution.

The same expertise that makes me a good educator also makes me a dastardly puzzlemaker. All the knowledge that helps me clear away hurdles inside my classroom allows me to throw them right in your path in a puzzle. All of the hair-pulling and teeth-gnashing that’s avoided by my students, well, you get the idea.

The interest in making puzzles came about early. I don’t know why. The understanding of what makes for a good, challenging puzzle ended up being an offshoot of my occupational journey. While I am only a puzzlemaker sometimes, I’m thankful that I can spend most of my time thinking about thinking, both as an educational psychologist and as a puzzlemaker.