Kominers’s Conundrums: The best puzzles are made out of words

By Scott Duke Kominers, Bloomberg Opinion

DURING these recent weeks of lockdown, we’ve solved logic puzzles based around household objects — light switches and chessboards.* Now it’s time to try another genre, one of my personal favorites: wordplay.

Making games out of words is literally ancient. Even the Romans had a precursor of our modern crossword. And, of course, wordplay comes naturally to everyone in the form of puns, tongue twisters, and spoonerisms.** Wordplay puzzles take things to the next level by seeking surprising relationships between words, such as the ability to convert one into another by shuffling letters — otherwise known as an anagram. Here’s a famous one: https://wordsmith.org/anagram/hof.html

One of the best sources for these sorts of puzzles is the National Puzzlers’ League. They publish a monthly compilation in a journal called The Enigma — mostly in a versical form called “flats.”

In flats — which predate the crossword — a short poem is presented with some words conspicuously missing, along with a clue about how those words are related. The goal is to fill in the blanks.

I published one in The Enigma just over a decade ago:

HETERONYM (9, 2 *4-3)

(*4 = not MW)

I’m NINE that any hunter

Would want to TWO FOUR-THREE.

In rabbit or duck season,

It’s a bad plan, you see.

The verse itself is the puzzle, and lines at the top tell you a bit about the words you’re looking for:

The Basics: A “HETERONYM” is a classic form of wordplay. It means you’re looking to fill in the verse with two words or phrases that have the same spelling but different meanings. “Object” pronounced one way means “a thing”; pronounced another way, it means “to disapprove.” Meanwhile, “contract” could mean either shrinking something or a legal document. “Sake” is a rice wine, but it’s also the reason you take an action. You get even more heteronymic opportunities if you allow changes in capitalization (“August” vs. “august”; “Polish” vs. “polish”) or spacing (“mustache” becomes “must ache”).

The Clues: The numbers “(9, 2 *4-3)” indicate the lengths of the two parts of the answer: One of them is a single word that’s nine letters long; the other is a three-word phrase consisting of a two-letter word, a four-letter word, and a three-letter word (with a hyphen). The “*” before the 4 means that the four-letter word is actually a proper noun. And, naturally, these answer words fit into the analogous spaces in the verse (“NINE” and “TWO FOUR-THREE,” respectively).

The Advanced Clue: “(*4 = not MW)” further explains that the four-letter word isn’t just a proper noun — it’s an unusual one. In particular, it doesn’t appear in “MW,” better known as Merriam-Webster’s dictionary.

So give it a try: Can you think of a nine-letter word that fits where the “NINE” appears in the poem, and which you can break up into a three-word phrase with the proper word lengths to fit “TWO FOUR-THREE”?

Are you puzzled — befuddled, even?

There are multiple angles to try out: First, you might examine the verse, and focus on the words that seem most specific, or most unusual. Those are likely to be clues. “Rabbit or duck season?”: Why those animals specifically? Do they remind you of anything in particular?

And then you can think about the words themselves: How many nine-letter words would fit into the first line? It seems like the verse is suggesting a word like “SURPRISED.” That has nine letters, but when you break them up into the prescribed pattern it turns into gobbledygook.

So what else could the nine-letter word be?

Here’s another hint: I’ve actually used the word in my discussion of this puzzle already. Can you find it, figure out how it fits the verse, and then work out the wordplay? If so, then you’ve succeeded in stretching a different part of your brain than the one used for the light-switch and chessboard conundrums. Instead of logical reasoning, you’re deploying your brain’s language faculties, perhaps with a bit of assist from the part that processes humor.

And here’s another puzzle for more practice:

HETERONYM (7, 7)

Stuck at home another week:

a child past SEVEN?

“Not at all,” he said to me,

“I’ve got my game SEVEN!”

Here you’re looking for a single word with seven letters that means different things in the two contexts.*** And if you’ve really enjoyed solving these flats, check out this mini-issue of The Enigma, which gives a more detailed introduction to the form — .

THE BONUS ROUND
Try this 100% online “escape room” developed by Nick and Spike Huntington-Klein (). Or read and solve one of these interactive puzzle stories (). Get yourself a new virtual conference background (), or just rate your competition (; hat tip: Josh Krieger). Also: “Math Bridge Extended Beyond Fermat’s Last Theorem” (); RIP John Conway (). Quarantine-themed picture puzzles (); a cool take on the quadratic formula (); a coffee-pouring problem () that apparently broke the Internet (). And inquiring minds want to know: Real or Cake? ()

* Last week I suggested that we may not be able to tell when an arbitrary modified chessboard has a domino covering. But my student Alex Wei has managed to prove that one can quickly verify whether a domino covering is possible, by converting the problem into an example of what is called “bipartite matching.” So if you have a modified chessboard and are curious, you can send it to him :). Or if you’ve got a bit of graph theory under your belt, you can try to work out the algorithm yourself.

**And don’t forget the name game, which features prominently in “Glinky” perhaps the strangest short story I’ve ever read.

***Experienced flat aficionados will notice I’ve taken a bit of liberty with format here in order to make the puzzle more accessible to readers who’ve never solved them before.