And… Repeat


[Image courtesy of Pinterest.]

I’ve had repetition on the brain lately. Repeatedly. How apropos.

I was talking about plagiarism with a friend of mine recently — a teacher who has dealt with her fair share of plagiarized essays from students — and I quickly summarized the USA Today/Universal Uclick crossword plagiarism scandal from 2016 for her.

She was understandably surprised that plagiarism was a thing in the crossword world — a thankfully rare one — and it got me thinking about intentional repetition vs. unintentional repetition.

When it comes to the Uclick scandal, it was pretty obviously intentional repetition.


But unintentional repetition happens more often than you’d think. The very rules for creating a traditional themed crossword lend themselves toward duplication, unintentional and otherwise.

Grid layouts, for instance, get reused all the time. When I started constructing, I actually assembled a stack of different grid patterns for 13x and 15x puzzles that I could use, organized by how the theme entries were arranged on the page: 9-13-9, 11-15-11, etc.

Despite the virtually infinite number of ways you could build a 15x grid, you see, when it comes to theme entries — particularly grids with diagonal symmetry and theme entries of matching length — there’s a finite number of ways to build a functioning grid.

So, we know that grids can easily be similar, but what about themes?

There are all sorts of ways that wordplay can inspire crossword themes — anagrams, sound-alike puns, entries reading backwards or being mixed up in a grid, portmanteaus, letters being removed from common phrases (and sometimes placed elsewhere in the grid), etc. — and if more than one constructor comes up with the same idea, you could have repeated entries with no malice or plagiarism involved.

Let’s say multiple constructors are working on puzzles with a similar theme, as they would for some of the tournaments hosted throughout the year, like Lollapuzzoola or the Indie 500. If the tournament had a time theme, it’s reasonable that more than one constructor could come up with a hook like “Time Flies” and look for entries that combine travel and time, coming up with NONSTOPWATCH or LAYOVERDUE.


[Image courtesy of DnD Beyond.]

Constructor Matt Gaffney actually wrote about a case of unintentional theme repetition for Slate years ago, discussing how he and Mike Shenk independently came up with puzzles where the word RAVEN was hidden in longer entries, and four of the five theme entries in the puzzles were the same AND placed similarly in the grid.

It’s a fascinating read that reveals a lot about grid construction, theme design, and puzzle mechanics. It’s the ultimate puzzly example of “great minds think alike.”

So, how do you avoid repeating a theme? Well, a little due diligence can go a long way. Sites like Xwordinfo and Crossword Fiend are great resources for searching theme answers to see if they’ve been done before.

Constructor Patrick Blindauer also offered some advice for coming up with new themes: solve more puzzles. He said, “Solving other puzzles is a good source of theme ideas for me. I try to guess the theme early, sometimes based only on the title; if I turn out to be wrong, I’ve got a new idea to play with.”

In this case, he avoids repetition through imagination. It’s a cool idea, one that will no doubt lead to some terrific new puzzles.

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Pizza puzzling!

I ordered pizza the other night, and being a puzzly guy, I couldn’t help but find a puzzle hiding beneath the lid of that pizza box.

The pizza was cut into eight slices, as you’d expect, all of roughly equal size. And I started to wonder: what if you had more than eight people sharing one pizza?

The simple solution would be to cut those pieces down the middle into long, thin pieces. But were there other solutions out there, other shapes that would allow more people equal access to a shared pizza?

So I did a little research, and I stumbled upon this recent Gizmodo article, which discussed a mathematical paper titled “Infinite families of monohedral disk tilings.”

I don’t know about you, but I’m definitely going to start calling pizza slices “monohedral disk tilings.”

Anyway, mathematicians had apparently tackled the pizza problem before, and they believe the solution rests with tessellation, the use of the same shape or symmetrical shapes repeated over and over to fill a given space.

When you think about symmetry and tessellation, you tend to think of straight lines.

But the amazing thing about these solutions to the pizza problem? They all abandon straight lines.

As you can see, there are numerous variations that work from this shield patterning. Since the shields are the same, dividing the shields up into equal parts in different forms yields other solutions.

And that use of arcs (curved lines) instead of straight lines makes patterns that would normally only work in squares, pentagons, and other shapes work for circles, like your friendly neighborhood pizza.

But there are more solutions for the pizza problem lurking out there if you abandon the three-sided piece and try more exotic shapes. Check out these patterns:

Granted, the average pizza slicer isn’t going to be dicing up a pie into 28 or 36 pieces… but it’s nice to know there are options out there, in case a few dozen friends stop by unexpectedly on pizza night.

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