Tuesday, July 18, 2023

Two for the Price of One: (spoiler-filled) behind-the-scenes

For a long time, I assumed that it would be impossible to make a 15x15 crossword with two equally good solutions to the same set of clues - it was a sort of Holy Grail, as I imagine it has been for many constructors. But as it turns out, someone had already written such a crossword, and not even a professional constructor!

OK, not at the 15x15 scale, but the philosopher Dan Dennett, in an appendix to his book Breaking the Spell*, includes a 4x4 crossword with two distinct solutions as a way of illustrating the indeterminacy of radical interpretation. Building on W. V. O. Quine's idea of the indeterminacy of radical translation (in principle, there could be two equally good ways of translating from one language to another, with no possible evidence that would adjudicate between the two), he proposes the indeterminacy of radical interpretation - imagining that two people could observe Kim Philby extremely closely but come to totally different conclusions based on the same evidence (one concluding that Philby is a loyal Brit, the other that Philby is a loyal Soviet). As a simple illustration, he provides this mini crossword:

He doesn't give the solutions, but I take it that they're SLOP/LOVE/EVEN/DERN and SMUT/HOPE/IRON/PENN. It's far from perfect (the first one duplicates LOVE, which is a complete no-no, and clues as vague as [Movie actor] certainly aren't in vogue), but it got me (hubristically) thinking. Sure, Dennett is a guy who thinks for a living so he's probably pretty smart, but he's also probably never constructed another crossword in his life. If he can do it in a 4x4 grid, surely I, a professional crossword constructor, can do it in a 15x15 grid?

Naturally, I started with a 4x4 corner, the top left. I wanted to pick a 1-Across pair that would have two clear answers, so that solvers would have an obvious starting point and they'd know which answer to put in which grid if I told them that they were ordered alphabetically. So I settled on CALC and TRIG, which I liked because 3-Down in grid 2 could be IDLE, leaving three synonymous options for grid 1 (LOLL, LOAF, LAZE). My optimism quickly started to fade - after toiling away for a while, I found that I had to add some helper squares to get a corner that seemed remotely workable. I couldn't even manage a measly 4x4! But when I did manage to pull off the corner, it seemed like a promising proof of concept - there were plenty of pairs that had very specific, uncontrived clues, like [Starchy Indian food] and ["Spider-Man: Across the Spider-Verse" voice actor].

(At the above point in construction, I didn't have the full grid pattern yet, but I'm including it in the image for simplicity's sake.)

Now an obvious problem arose. There are very few entries that start with EE, and I needed to find one that could be paired with one of the same length starting with FE. I found EERIE/FERAL, which then immediately confronted me with the same problem at 30/35-Down, but this time with IR and AR as the starts. Again, it didn't take me long to find those crossword stalwarts, IRA and ARI, but if every pair I made immediately forced another toughie, it was going to be rough going. But of course, this was only the beginning. In a stairstep area like that, things are relatively easy - once I got backed into a corner or otherwise blocked-off section, I'd have nowhere to hide. I traveled down the staircase starting from FERAL/EERIE and soon found myself at the first blocked-off section, where 80/81/82-Down are. I was confident that if I could finish that section, I could manage the whole grid. 

Already, though, I was unhappy about having to use ESTOP (which I wouldn't normally put in a grid), especially crossing PURLIEU (a word that I like and definitely would put in a grid, but which is pretty tricky). But the fact that NEA/PTA was a natural pair for 72/76-Down, giving promising beginnings for the intersecting acrosses, was very encouraging. Despite the promising beginnings, this section involved a lot of false starts and do-overs.

The usual way things went with these blocked-off sections was that I'd find a fill where close to half of the pairs had very natural cluing options - but that still left at least three or four pairs where I had to pull a workable clue out of my ass. And sometimes, I'd be able to do it for all but one or two of those pairs, which would be tantalizing, but not good enough. Sometimes I'd spent ages trying to get those last two pairs work, knowing that I'd probably have to settle for some stretchy stuff. For the below fill, EGOT/TO_O was the sticking point. Grid 2 could have TOTO/ANT or TOGO/ANG in addition to TO-DO/ANT. ANT is a much more promising partner for LOO than AND is, because they're both nouns, but TOTO/EGOT seemed impossible. (I attempted a lot of absurd connections - "Well, Quincy Jones has an EGOT, even though it includes a non-competitive Oscar, and he worked on The Wiz, which is based on The Wizard of Oz, which features TOTO, so maybe there's something there" - that went nowhere.) Both TOGO and ANG spelled trouble, since they're proper nouns without a ton of variety in cluing angles. So it had to be EGOT/TO-DO - I eventually came up with a clue I liked for that pair, so I really wanted LOO/AND to work. I really didn't want to have to settle for clues like [Word found in "floor sander"], which would be an exceedingly cheap solution, but I was comforted to know that option was in my back pocket. While it's not ideal, a clue that's only a hidden-word clue for one of the two solutions, like [Andy Murray's head?] for LOO/AND, is a godsend in desperate circumstances.

As I mentioned, once I finished that section, I was very confident that I could finish the job. But this is the point at which I started to run into another difficulty: the two solutions combined have 180 words, including 60 three-letter words. It's hard enough to avoid dupes in a Sunday grid, which has around 140 words. I knew that the 3s would become increasingly hard to wrangle as the possibilities diminished. In the top-right corner, where I headed next, I ended up with A LA - already, the ALI option was foreclosed to me. Soon after, in the middle left, I'd find myself experimenting with fills that had AL_ at 70/74-Down, needing a vowel in the third slot - ALE and ALO were the only possibilities I hadn't already used, and neither of those panned out.

The top-right section had one of the most satisfying breakthrough moments of the whole process. ALA/ORO was the last clue to fill, and I nearly despaired of it being possible. I very much didn't want to use something like [Palindromic foreign term often used in crosswords]. I'm fine with [Palindromic name] at 6/17-Down, because at least that's a clue that you might see in a regular crossword, even though it would ideally be more specific. But for ALA/ORO, that would have really felt like a cheat. So I was incredibly happy when I realized that both could be tied to "Au" (the masculine form of A LA in French, and the chemical symbol for ORO in Spanish). Clues that work very straightforwardly for both solutions in the same way (like TOME/SAGA or ORG/NET) are great in their own way, but clues that work in radically different ways in the two solutions feel more special.

The other most satisfying breakthrough came in the next section I did, the middle left. I had ABACI/AMISH locked in place pretty early, because once I stuck PURLIEU/REACHES in, I wanted to make sure there would be a viable pair at 97/102-Across, given the paucity of A___I and A___H entries. This really constrained the 89/92-Across slot because the nearby 69/73-Across spot also had very limited options due to the I at the end of 73-Across. The particular difficulty of 69/73-Across is that one of the ending letters was a consonant and the other was a vowel - it's much easier when the corresponding entries have similar vowel-consonant patterns, because that means that, broadly speaking, they're going to be similar types of entries that might be amenable to cluing identically. So I actually came up with a couple of basically workable fills for the middle left section that floundered just because I couldn't manage to connect them to the lower section via 89/92-Across. So once I found a pair that seemed at least potentially doable, I stuck with it. That pair was DECAF/IONIC, which I noticed early on could be both clued as "orders." The problem was that those orders otherwise have seemingly nothing in common. I did know there was a famous McDonald's location with Greek architecture, but alas, it turned out to have Doric columns, so that was off the table. I spent all weekend turning it over in my brain. (The nice/horrible thing about this puzzle was that much of the work didn't require me to be looking at the grid, since it was all about just dreaming up connections between seemingly unrelated entries. Besides, I'd spent so much time with it that the grid was seared into my brain and I could even work on the fill in my head.) Finally, I reached a level of similarity that was so abstract (and yet still oddly specific) that it could link the two entries: [Order for when you want something to top things off, but you still want to be sensible].

The bottom-left corner was the next real sticking point - compared to it, the last two sections were a breeze. There just aren't a lot of options for __I/__F, which narrows the options right off the bat. I went through a lot of fill combinations for this corner, and the one I ended up with was the only one that came close to working. But I really struggled with cluing GIRDLE/LITTER. In principle, it shouldn't be that hard, since they're both nouns with a couple of different meanings and many different cluing angles. But I just wasn't getting anything I was happy with, so I left it and did the last couple of sections before circling back.

Fun side note: much like Dennett's puzzle, the last corner I finished here has EVEN clued as "(to) make smooth," though paired with EASE instead of IRON. This was a total coincidence: by the time I had gotten to this point in construction, I'd totally forgotten the specifics of Dennett's puzzle.

When I circled back to GIRDLE/LITTER, the most promising angle seemed to be that both are the names of products that conceal things. I ended up with something like [Product for concealing what goes on in the lower torso area], which technically works but is kind of a stretch, and landed with a thud for the testers. I mentioned to Kelsey another option that I'd been considering, which was an audio clue that could double as [Waist concealer] and [Waste concealer]. She was super into the idea, which helped convince me. I'd been on the fence about it because it's clearly a cheat, but on the other hand, it's a much better clue, and definitely improves the solver experience, which is the most important thing. (Plus, at the end of the day, I knew that I had come up with a functional text-based clue too, so it didn't diminish the accomplishment in my mind.)

Another big improvement to the puzzle came from another tester, Jake. For DELTA/MUSIC, I'd considered doing something like [Mouth output], which I didn't like because music doesn't always come from a mouth. [Word with "blues"] was another option, but again a bit unsatisfying. I ended up with [Alt-J output], which is wonderfully precise - the band Alt-J is named after a keyboard shortcut that produces the delta symbol. But it does rely on very specific trivia, which isn't ideal for this kind of puzzle. Jake almost immediately came up with [It carries through the air], which I love.

And then I had a complete puzzle! It took me about a month, dedicating some time to it every day. I'm glad I did it, and I will never, ever do it again.

*I should mention that I haven't actually read this book! I flipped through it at the library once and the crossword grid, naturally, caught my eye.


  1. amazing. i have also had this idea at some point in the past, but, well, "purely aspirational" pretty much describes it. i can't believe you made yourself actually do it.

  2. I'm very pleased that you've touched on all my favorite clue/answer trios here: ORO/ALA, TODO/TONY, DECAF/IONIC (which I didn't get until reading this), DELTA/MUSIC, and the audio clue. Regarding the last, I believe I've seen someone use IPA symbols in a clue to achieve a similar, homophonic-ambiguity type of effect. But I couldn't even begin to tell you where.

    1. I did think about using IPA! This isn't what you're thinking of, but I'm fond of the Tom McCoy crossword that is filled out entirely in IPA.

    2. For another IPA crossword (and I guess it's a mild spoiler that that's what's going on, but also, it's a 10+ year old hunt puzzle so... *shrug*) there's this diagramless from the 2014 MIT Mystery Hunt, written by my dear friend Quinn Mahoney: https://puzzles.mit.edu/2014/puzzle/uncommon_nonsense/

    3. Yes, the Tom McCoy puzzle is both not what I was thinking of and remains one of my favorite crosswords ever. I wish I could go back and solve it for the first time again

  3. Hi Will,

    Just felt the need to comment here to let you know this is my new favorite crossword I have ever done. I have never spent 2.5 hours on a crossword like I just did. I was completely transfixed by it, and determined to solve to completion. It was an insanely rewarding puzzle. I could recognize how much thought and time you put into the both the grid and, especially, the clues. You're amazing, and I'm truly thankful for this. I mumbled a lot of "oh my god"s and "fuck"s while solving this one. Particularly just floored by the ABACI/AMISH clue. I will remember that one. The ORO/ALA, STUDIOS/SPLIFFS, ARCING/PLANET clues were just incredible. Even the simplicity of the shorter clues like CEL/PET, DOCS/TUMS, and SAW/SAP really stuck with me too. The whole puzzle made my day. Thanks! -Pao

    1. Wow, thank you so much - certainly the kindest thing anyone's ever said about one of my puzzles!

  4. A commenter on the other post said it felt like a slog to solve... and it kind of did, but in the best most fulfilling way as, once I completed it, I really felt like I figured out something clever. I don't usually get that feeling with a regular crossword that I solve in less than 10 minutes. I also really appreciate the look behind the curtain at the construction process!

    The only entry I didn't really understand without looking up was DECAF/IONIC. (I had it as DECAF/TUNIC for the longest time!) I probably would have gone with "It might describe something with a neutralized charge" but I prefer chemistry to Greek architecture!

    Also, I was thinking more about the GIRDLE/LITTER pair... I do like your solution, but given the body part usage for girdle, specifically "pelvic girdle," I also came up with: "It may be found below a cat's spine."

    1. Ooh, I didn't know the body part meaning of girdle - cool angle!