Miscellany #3: "Crossword Puzzles as Puzzles"

This is the first of a three-part series of essays on crossword puzzles.

I recently realized that I don't often think about crossword puzzles as puzzles: as problems to solve. When I picture a crossword, I think of the beautiful completed grid, the pattern of interlocking words and black squares. Perhaps because I've been focusing a bit more on construction, I haven't thought of crosswords much as an experience from the solver's perspective. So, here are some observations that might be trite or obvious, but were new to me:

• A crossword puzzle is a series of questions.
• Questions are trivia (testing knowledge/memory) or riddles (with wordplay and misdirection), or both.
• At the start, you only know each answer's length in letters.
• The questions vary considerably in their difficulty. You may get some answers immediately, and others after some thought. However, even in an easy puzzle, many questions are initially difficult, and might truly be impossible, due to having multiple potential answers. (There are famous examples like ["Right now!"] cluing ASAP or STAT, but long entries with vague/misleading clues often have multiple solutions.)
• But, as you solve the easier questions, you get hints about the tougher ones! With each answer, you place some cross-letters into a few other answers. Which answers intersect with each other is mostly arbitrary: you receive hints basically at random.
• With each cross-letter, the previously unsolved clues get a little easier. Seeing an answer with some letters in it might jog your memory for a trivia question, or enable some wordplay to click into place. Clues that were too difficult slowly come within your grasp.
  

This is... a really good progression system for a game! A lot of casual mental games analogous to crosswords have emerged in the past few years, and I feel like designers of those puzzles would kill for a difficulty curve this satisfying and intuitive. To explain what I mean, let's contrast with some other games:

I enjoy trivia, and have had a lot of fun this past year competing in the online LearnedLeague, answering six trivia questions per day. However, trivia has a known issue: it's not very fun if a question comes down to "you either know it or you don't." It's always frustrating to get a trivia question you know nothing about, stare at it blankly, and admit defeat; conversely, if you immediately know the answer to a question... that might satisfy your competitive spirit, but isn't exactly fun, either.

A satisfying trivia question tests your knowledge and recall: you struggle to remember, and just barely get it. A well-written trivia question often includes a couple "entry points" that might jog your memory. I particularly liked this one, from a recent LearnedLeague MiniLeague on Eponyms and Namesakes:

“What cocktail with a partially geographical name was invented in the early 20th century by Ngiam Tong Boon, a bartender at the Raffles hotel?”

I didn't know the answer at first, but by trying to think of "geographically named" cocktails, roughly placing the language of the bartender's name, and vaguely recalling why the word "Raffles" was familiar, it came to me in a sudden flash of insight. (ROT13: Fvatncber Fyvat) This is the best kind of experience you can have with trivia: a few different thoughts swirl around in your subconscious, and just barely coalesce into the right answer.

But, of course, that particular question just happened to be fun for me, based on my specific knowledge. Someone who knew a little more about cocktails might have gotten it immediately; someone who knew a little less might have stared at it fruitlessly. You can't guarantee a satisfying experience for everyone, and each trivia question will always be too easy or too difficult for someone.

Often, trivia games include an extra step in which the player assigns scores to questions before the answers are revealed: in bar trivia, you usually choose your own scores, distributing more points to the answers you're more surer of, while in LearnedLeague you assign your opponent's scores, giving fewer points to the questions you think they'd get. This introduces an additional level of gradation, some finer control: besides the binary question of whether you get an answer or not, you have the subtler task of assessing how hard the question was. It's a smart addition to the idea of trivia, but it feels a little inelegant compared to the experience of trivia in a crossword.

To be fair, trivia is often controversial in crosswords, for the same reason: it feels like you either know it or you don't. But I'm often struck by how, with a few cross-letters, an answer shifts from being completely out of reach to vaguely familiar. You often know more than you think you know! In David Karp's LA Times puzzle of September 9, 2023, 16-Across is:

[Brazilian steakhouse fare] (9 letters)

On it's own, that's not a trivia question I would get. (I don't think I've ever been to a Brazilian steakhouse.) Even with an R in the fourth position, it felt entirely unfamiliar; even with an O in the last... But with an H placed second, some vague memories drifted up from the unconscious, my brain's pattern-matching machinery tried its hardest, and I suddnely thought Wait, isn't CHURRASCO a thing? Haven't I seen that word, somewhere, on a menu, mentioned in conversation, in a half-remembered movie?

I got that satisfying trivia experience of stretching one's memory to its limits, because the cross-letters were drip-fed slowly enough that I got the answer only when I had just enough information. Someone else might have gotten that answer with fewer letters, or with more, but each of us would have had the same experience: right when you hit the minimum number of letters you need to figure out an answer, it just barely comes to mind.

By its design, a crossword puzzle maximizes the satisfying solving experience. It maximizes the number of questions that are answered when they're just barely solvable.

This applies just as well to riddles, although there aren't as many wordplay-based games to compare to. John Martz's New York Times puzzle of December 25, 2022 includes one of my favorite clues:

[Cut with a letter opener?] (10 letters)

Seeing a question mark, a solver's mind immediately starts racing to think of other meanings for each word: Cut, like an incision, or to divide something, or to reduce it, like "cut down," or remove something... Letter, like a note, or individual letter, or someone renting... Opener, like a can opener, or the first in a series, a letter opener like the word "Dear" might open a letter, or...

Solving a clue like this means holding all these potential meanings somewhere in mind, until a combination that makes sense emerges. I can't speak for others, but rarely are these solved by me consciously matching each potential meaning together; instead, I try to hold every potential meaning somewhere in mind, and each cross-letter hint also joins them in the unconscious, until in the proverbial "aha" moment, everything clicks. It's a cut of meat that opens with a letter: a TBONESTEAK.

Without some cross-letters, I would never have made it to that satisfying resolution! Most games simply don't have this elegant, built-in system of providing hints. Take the New York Times' Spelling Bee, in which players make as many words as they can from a set of seven letters.

This has a much simpler system for ensuring the game is somewhat satisfying. Answers (words) vary in difficulty, and you can find them in any order, so the solver's experience is one of steadily ramping up difficulty. You notice some words immediately; then, when you've exhausted the easy answers, you reach  deeper into your memory, stretching your powers of recognition to find more words. This is the satisfying, fun phase of the game! But for most solvers, you then reach a point where it simply becomes too difficult: the last few words are too obscure for you, and you eventually give up.

I don't want to knock Spelling Bee, which is a fun, popular game for a reason! It has a smart design that encourages the idea that you don't need to find every word (there are different "tiers" of complimentary titles you get for finding certain numbers of words.) Unlike the crossword's binary distinction of completion or not, you're meant to try your best at the Spelling Bee, and shoot for a high score. But... obviously, there's an element of personal preference here, but I'm always frustrated by a puzzle intended to end when the solver gives up. No matter how fun it is to notice words, it sours the mood that the last action you take in the puzzle is generally admitting defeat.

And on days when I do "beat" the Spelling Bee, I can't shake the feeling that that day was a little too easy. The Spelling Bee is most enjoyable if the puzzle lines up perfectly with your skill level, so that it's a fun challenge that ends with you successfully finding every word; but that's just as arbitrary as getting a trivia question that happens to meet your knowledge base. Playing the Spelling Bee feels to me like running on an ever-quickening treadmill; there is a period of time when the challenge is fun, but only because it's inexorably moving from too easy to too hard. A crossword puzzle provides hints for harder answers as you get easier ones: without such a mechanism, the Spelling Bee just gets harder.

Some puzzles make asking for hints a part of the game, and the goal is to solve the puzzle with as few hints as possible. That's the basic mechanism of Wheel of Fortune, possibly the most similar word game to the crossword. Contestants guess a phrase based on an increasing number of letters, but here, the contestants choose between asking for more letters or guessing. This presents its own interesting challenge, gauging how confident you are in your guess vs. how helpful you expect more letters would be. But it works much better in the competitive format, where you're disincentivized to ask for hints because they also benefit your opponents. I've played some solo games that incorporate this mechanic, like Thematik from the Puzzle Society, but it's just too tempting to ask for hints. Sure, I have the goal of solving the puzzle with as few hints as possible, but my primary goal is to solve the puzzle. If I get stuck, even for a moment, it's hard to try to power through and get an answer rather than just take another hint! If you get stuck during a crossword puzzle, the only way out is through. You get cross-letters only as a result of finding answers, so you're always motivated to do the primary task of the puzzle: parsing clues.

I've found this to be the issue with a number of open-ended or score-based games: they don't incentivize you to actually tackle the puzzle. SpellTower from Puzzmo and Hex 10 from the Puzzle Society are similar puzzles which ask you to find the longest words you can in a grid of letters. But because each word you select limits your future choices (in SpellTower, letters you use disappear, while Hex 10 limits the number of words you can choose) the optimal choice for maximizing your score isn't to get started clicking on words, but to plan an optimal set of words in advance. In fact, you're incentivized to almost never start selecting words: to get the highest score, it's best to stare at the puzzle for as long as you possibly can before starting, since you always might discover an even higher-scoring set of words. 

Obviously, no one actually does this: in practice, at some point a solver just tries to select a word. But there's something inelegant about these misaligned incentives. If the puzzle gives you a goal (like getting the highest score) it shouldn't rely on you accepting that you aren't going to optimize that goal to get going. When presented with a crossword, your only goal is to solve the puzzle, and the best way to solve the puzzle is to get started tackling clues right away: even a wild guess might provide useful information, if some of its letters jog your memory to another answer.

To be clear: I regularly play all the other puzzles I've mentioned here (except Wheel of Fortune.) I think they're interesting and fun, and I enjoy stretching my brain doing things other than crosswords. I don't mean any disrespect to the designers of these puzzles, and I'm glad we're in a time when there's so much development of these kinds of games! I also recognize that I'm bringing a lot of personal biases into this: the difficulty curve doesn't always work as neatly as I've described, and I probably view crossword puzzles as more satisfying because I can generally complete them. The binary nature of solving vs. not solving a crossword can be off-putting to new solvers in a way that more open-ended aren't. There are also puzzles with a similar natural difficulty curve to crosswords, that I just happen to prefer less: word searches and Sudoku also give you more information as you complete them, but I don't enjoy the core activity of spotting words or number patterns as much fun as the trivia and riddles of crosswords.

But I do think that as puzzles go, the crossword is a remarkably good one! The humble diversion developed in the '20s more than holds its own against the best of modern, well-designed puzzles. It's hard to make a simple, intuitive puzzle that also automatically adjusts its difficulty to stay engaging throughout the solve. The crossword's beautiful little mechanism—every answer giving a few hints toward future answers—makes sense, doesn't require any extra instructions or software to implement, and makes the crossword fun for a variety of skill levels, from the beginning of the puzzle to the end.

And it's all the more impressive because this mechanism wasn't really designed at all. Crosswords originated from patterns of words and letters, from "word squares" and similar amusements. The trick that makes them so enjoyable is an incidental result of their nature: no one sat down to create a satisfying puzzle, and decided on a trivia game where each correct answer gave subtle hints to the harder questions. It's just an emergent property of a grid of intersecting words. The only element of human design here is that the mechanism does rely on there being no "unchecked" squares in a grid, so some credit is due (who else?) Margaret Farrar, for promoting that as a rule.

That said: I don't think people would enjoy solving crosswords as much if they were presented as a series of unconnected clues and answers (and not just because they'd be harder without seeing which answers intersected.) I do think that part of the joy of solving is seeing the completed grid, as well as some of Margaret Farrar's other innovations: the symmetry, the minimum answer length of three letters, the themes, the symmetric placement of theme answers, and so on. Which brings me to...

Part II: "Crossword Puzzles as a Craft" is coming soon-ish.