MGWCC #435

crossword 5:37 
meta DNF 


mgwcc435hello and welcome to episode #435 of matt gaffney’s weekly crossword contest, “Six of One”. for this week 5 puzzle, matt challenges us to find a two-word, 11-letter phrase found in mathematics. okay. what are the theme answers? … uh, good question. there are no especially long answers in the 17×17 grid; a fistful of 9s, a handful of 8s, a whole bunch of 7s, etc.

i’m just going to tell you up front that i haven’t solved this meta and i’m not going to figure it out. there is just nothing at all to go on and i’m too frustrated to give it a real write-up. i worked on this some with andy last night and we got nowhere. here is an incomplete list of things we noticed/tried:

  • {It starts with a new moon} TET crosses the first T of {7th-largest city in Washington} EVERETT. this was striking to me because it seems clear that SET/EVEREST would be better fill. it was striking to andy because he actually solved the crossword incorrectly, with an S in that square. anyway, this suggests that either EVERETT or TET is important thematically.
  • there are a handful of entries that are members of a canonical set, in many cases a canonical ordered set. APR(il), IOTA, UNIFORM (NATO alphabet), MARS, BLAZERS, NATS, ERATO, HELIUM. arguably NEIL (armstrong, the first of 12 moonwalkers) and ANNE (boleyn, the second of six wives of henry viii), but those are stretchier. there’s also INKY (CAP), the blue pacman ghost, which is only part of an entry. and CUATRO is a member of an ordered but infinite set.
  • there is a pretty outrageous dupe in the grid, with {Passes carefully} EASES BY and {High anxiety} UNEASE. i don’t know if this is related to the meta or just an oversight.
  • speaking of which, {Mistake} OVERSIGHT is in the grid and it’s an autoantonym (it can mean watching over something, or failing to watch over something). didn’t see any others, though.
  • the usual list of things people notice that have nothing to do with the meta: words that can take another letter to make a different word, words that have homophones, double letters in the grid, etc. i don’t think there’s any particular reason to look at these this week, but andy did because he suggested that the title might be hinting at equivalence or duplication of two things.
  • speaking of equivalence, {Tot preceder} TATER is a synonym for {Shot over the wall} HOME RUN. like everything else we tried, though, this went nowhere.
  • we tried thinking of sets of 6 things. the one math-related one that occurred to me was PEMDAS, the order of operations (parentheses, exponentiation, multiplication, division, addition, subtraction). strikingly, the unusual clue {Bc3+, e6#, or Kg7!!} for CHESS MOVE contains a + sign, and there are parentheses in other clues. a few stray hyphens could possibly be mistaken for minus signs, but not so much with the other three.
  • {Obtain via deception} COZEN is only one letter off from DOZEN, and the title suggests “half-dozen”. (it’s also a homophone of COUSIN, but that did not seem to matter.)
  • four different clues start with {One}. this would be more striking if there were six.

so here’s where i am right now: i think there are a whole bunch of theme entries in this grid, not necessarily the long ones. i think they are related to each other not directly, but because they can be transformed in some consistent way to members of some set (perhaps of six things, perhaps eleven). i think EVERE(S/T)T or (S/T)ET is among them.

i could be wrong about all of this, but … i have nothing. did i mention i’m frustrated?

i am going to submit MIXED NUMBER, because it is 11 letters, two words, a math term, and it suggests a kind of wordplay. (admittedly, a kind wordplay i don’t see in this puzzle, but hey. picky picky.) somebody let me know what i missed.

[Added solution graphic with Mobius Strip — Matt]mobius

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46 Responses to MGWCC #435

  1. pgw says:

    sneakily hidden meta this week. it turns out there are several clues doing double-duty, all making a looping sequence: authority clues manager but can also clue oversight; mistake clues oversight but can also clue boo-boo; injury clues boo-boo but can also clue insult; jibing clues insult but can also clue uniform; ensemble clues uniform but can also clue suit; and honcho clues suit but can also clue manager, so we are back where we started! for each of these six clues it’s six of one, half dozen of the other, and the first letters of the six entries, in the order given above, spell out mobius. not only that but those letters are placed symmetrically in the grid such that tracing the paths between them resembles a mobius strip!

    before i noticed the symmetry and the resultant image, i was sure i had the right answer but i wasn’t convinced i had the complete solution and spent a lot of time searching for a way to spell out strip as well. i convinced myself of a few tenuous connections, but there was just no way to get the r and i to work. but the really interesting thing about my solve was that the first of these “this clue can work for different entry” connections i noticed was home run / tater, which isn’t even involved in the meta!

    anyhow, this puzzle is pretty great. the title is a perfect fit, and the idea is subtle and well-executed (the only clue that was really pretty weird in retrospect was jibing for injury, but to me it didn’t stand out enough to tip me off.) the large grid had me thinking the puzzle would be dense with theme (or that somehow the number 17 would be important), but in the end i guess it was just necessary to give six theme entries room to be placed where they needed to be without running into one another.

    i had several math-related ideas that seemed to be going somewhere but didn’t. from the title i noticed that there are 6 entries of length 9, and if you count moth and eaten as separate words, there are 11 words in those 6 entries. i tried over and over to figure out a way to extract the answer from that. there were also 6 6-letter across entries and 6 6-letter down entries so i was thinking maybe the idea was “six of the acrosses, half dozen of the downs” – but of course this didn’t go anywhere. i also noticed that [grid size] – [number in title] = [length of meta answer], which was intriguing but didn’t spawn any brilliant ideas. finally, i noticed the grid contained 6 lone black squares so i spent some time looking at the surrounding letters.

  2. Matt says:

    Thanks, Joon — 40 correct answers this week.

    The “Six of One” in the title refers to the six one-word clues, each of which can define both its own answer but also one of the other members of that set:

    [Authority] can be MANAGER or OVERSIGHT
    [Mistake] can be OVERSIGHT or BOO-BOO
    [Injury] can be BOO-BOO or INSULT
    [Jibing] can be INSULT or UNIFORM (i.e. “consistent”)
    [Ensemble] can be UNIFORM or SUIT
    [Honcho] can be SUIT or MANAGER

    The first letters of that loop spell out MOBIUS, and connecting those six letters in the grid in order forms a contest answer MOBIUS STRIP.

    • pgw says:

      oh wow – i didn’t even see that the 6 theme clues are the only one-word clues. neat.

      • That was actually the only way I got this one — the shortcut. I saw the six one-word clues, circled the first letters of their answers, saw that they were symmetrical, and figured that could not be a coincidence. A minute later I saw MOBIUS and played connect-the-dots.

        I never saw how two answers could work for each clue …. well, that was one of my suspicions early on since I thought MANAGER and SUIT could be related, but I didn’t see the other pairs.

        • Maggie W. says:

          I saw the six one-word clues, figured out the chain of clues/answers, drew the strip connecting their first letters on the grid in the right order…and still took another 24 hours to see MOBIUS, instead thinking, “SUIBOM? What’s SUIBOM?” Ah, me.

  3. Jim Curran says:

    I tried many angles like Joon did, but got nowhere. My answer MAGIC SQUARES was a mathematical wild guess from all the 11-letter mathematical phrases I could think of (Golden Ratio, Least Square, etc.). AND I almost answered MOBIUS STRIP after I saw a recent reference to Mobius in Matt’s Twitter feed. Should have gone with that gut feeling.

    • Matt says:

      Whoa, total coincidence on that retweet. I would certainly never put a hint to a meta on my Twitter feed.

      • Jim Curran says:

        Matt, I didn’t see it as a “hint”. I just wondered if that tweet got you thinking and was a germ of an idea. I hope people don’t start to scour your Twitter feed for hints now!

      • Katie M. says:

        That’s why I didn’t use Mobius Strip for my wild guess, – because it was in your Twitter feed!

  4. Tyler Hinman says:

    Fun fact: There are exactly six Cs in the grid, that’s the only letter that appears exactly six times, and two are in the same row, another two are in the same column, and the last two are in the same diagonal.

    So yeah, not even friggin’ close.

    • pgw says:

      I think there are also exactly 6 P’s. Another rabbit hole I went down.

    • sharkicicles says:

      I too got stuck on the 6 Cs. I went with golden ratio since the Cs are in the grid roughly in the shape of a lowercase phi.

    • Justin Weinbaum says:

      That’s true, and I was just as successful using that to solve the puzzle. #TeamNope with alot of company this week.

    • Dave C says:

      That was the rabbit hole I went down as well. I drew all kinds of connecting lines to the Cs, but all they resembled were crappy attempts at helping my kids with folding paper art projects when they were in elementary school. Still, there was a little bit of a pyramid look about it, so I entered Cube Pyramid.

    • Paul Coulter says:

      I also worked heavily on the 6 Cs. One interesting result was that 6 of the clues had a C in them and 6 did not, but this went nowhere. The other interesting thing I noticed were the palindromes at 9, 16, and 36. I thought I was on to something with squared numbers when I saw Tot in the clue for 4, but this fizzled, too.

      My Hail Mary was “chaos theory,” since it seemed like something Matt would do for a hard meta that produced chaos across our papers. I got a laugh out of Katie’s #MGWCC tweet that said something like, my sheet is starting to look like a serial killer’s bedroom wall.

    • Magoo says:

      I got hung up on the six C’s too. Also not close. Lovely idea for a tough Week-5-of-5. Hats off to the correct answers, especially Jangler, and to Matt.

  5. CFXK says:

    Yikes! :)

  6. Mike W says:

    The clue “Full of snark” was a tipoff to me to look at the one word clues – a coworker loves the word “snarky”. Also, is it a coincidence that Matt’s WSJ meta puzzle from last Friday was titled Lost in Translation with the answer German? A Mobius strip is non-orientable (causes one to lose perspective) and is named for a German mathematician.

  7. Lance says:

    Ugh. I’ll have to take a look at the grid again, now that I know how it works, to see what I think of the elegance, but my gut reaction is that that’s a huge amount of noise to a small amount of signal. (A 17×17 where only six clues/answers are relevant?) “Six of One” doesn’t feel like much of a pointer in the right direction, and there’s just so much other stuff going on.

    If I counted right, there are exactly eleven answers that are a letter change from a word in the clues–TATER (water) being one, COZEN (dozen) being a particularly prominent one, especially given the weirdness of the word and the “half a dozen” implication of the title.

    There are three three-letter words that appear in other answers (PER, ASH, EVE); there’s an odd sort of SEVEN at the center left, which combined with TWA (a letter off from TWO?) and COZEN (a letter off from DOZEN?), seems to…to…something. Probably just as well that I didn’t try to push any harder on the numbers in the clues (“one of 24”? does “ace” count, if it’s cards, and if it is, is “tray” indicating something?).

    All of which I guess is just to say again that there’s a whole lot of noise here to try to find the signal in.

    • Matt says:

      The Mobius Strip wouldn’t fit in a 15×15 at all. Even the 17×17 was a tight fit. I sent Joon a graphic but he’s AFK, but let me put it up myself so you can see.

      I thought the “Six of One” was enough of a hint, or even noticing how few one-word clues there are to begin with.

      • Lance says:

        Oh, I have no doubt that a 17×17 was necessary! I had no doubt even while solving that, whatever was going on, you weren’t able to fit it into a 15×15. It just meant there was 25% more surface area to contain noise. (And did I mention that 22A contained AREA? Notable math concept, that…)

        Noticing one-word clues, though, is exactly the sort of signal-in-the-noise that’s hard to find, IMHO. If you had a lot of one- and two-word clues and then a small number of ten-word clues, those long clues would stand out. But it’s not easy to skim a whole lot of clues and notice that some of them are particularly short, unless all of the other clues had been, like, five or more words. Or, maybe, to put it another way: Friday’s WSJ puzzle had eight one-word clues, and while that’s slightly more than this puzzle in a somewhat smaller grid, it wouldn’t surprise me to find that roughly within the margin of error. (I wonder what percentage of one-word clues you’d expect to find in an average crossword.)

  8. Joshua Kosman says:

    Weighing in with another red herring that totally derailed me: There are exactly six six-letter entries among the Acrosses, and exactly half a dozen Down entries that are half-a-dozen letters long. Could not believe that was sheer coincidence.

    • Vraal says:

      This had me for the LONGEST time too.

    • Matt Gaffney says:

      Man, that’s rough. Unintentional, though.

    • jps says:

      I was completely stuck on that too. And thought the 17×17 was needed to accommodate the 6-letter entries.

      Also, USHES/SENTTO was so bad when USHER/RENTTO would do, that I thought the S must be part of the answer and that somehow the 12 6-letter clues would each provide a letter (and a space in one case) for the 11-letter answer.

      • Matt says:

        Yeah sorry about that. The reason it happened was: originally what became SENT TO / WENT UP / COO / LOST IT was RENT TO / RENTER / TAO / POST IT, and the instructions asked for a famous mathematician. So RENT TO had to become SENT TO. But I saw that a random TAO in the center entry (because of Terence Tao) would be a too evil red herring across the middle with those instructions, so I wound up changing those entries without realizing that, with RENTER becoming WENT UP, I could have USHER after all.

  9. Evad says:

    Only two other puzzles in the (modern, since we automated the verification process) history of the MGWCC have had fewer correct solvers:

    # 252 had 29 solvers

    # 296 had 4 solvers

  10. Dan Seidman says:

    Did anyone else try to make something out of COZEN TWIG? Six of one is another way of saying 12:54.

    • kaes says:

      Yes! I thought of this, and thought I was onto something since COZEN seemed important to me from the beginning (so similar to dozen!). Gave up when it was only nine letters and didn’t anagram to anything…

      Also spent way too much time puzzling over the six P’s and half-dozen C’s in the puzzle before realizing there were actually seven P’s. Oh well.

  11. Norm H says:

    Yeah, it’s Week 5, so it’s supposed to be hard.

    Like some others, I got hung up on the six Cs. Nothing there. I thought of submitting PRIME NUMBER as a Hail Mary.

    Then, bumping up against the deadline, I stumbled onto something I was sure had relevance:
    — 12D: Change first letter to get DOZEN…another word for 12.
    — 28D: Change first letter to get DAYS…”28 Days” is a movie.
    — 52D: Change first letter to get CARDS…52 cards in a deck.
    — 39D: Change two consecutive letters to get STEPS…”The 39 Steps” is also a movie.

    Short on time, I figured there was some kind of “substitute A for B, B for C…” process that would eventually lead back to A, so I submitted CYCLIC ORDER. Never thought to check the one-word clues.

    Well done, Matt. Maybe what I really should have submitted was RANDOM GUESS.

  12. Jeff Louie says:

    The lack of obvious theme entries, the larger grid, and the fact that the first four across clues were 1, 4, 9, and 16 had me convinced that this HAD to have something to do with squares (e.g. “MAGIC SQUARE” or “LATIN SQUARE” or “SQUARE ROOTS”—I searched the grid in vain for hidden root vegetables forming squares). All the n^2 numbered squares (through 81) formed TTBOATUAE though, which was not helpful. The T on 36 was also the one that could’ve/should’ve been an S, as noted above, which had me even more convinced the n^2 thing had to have been part of the meta. Overall, I thought this meta was the most evil meta ever, due to these coincidences.

  13. LuckyGuest says:

    Argh! I had all those pairings of alternate entries where each satisfied one clue (and more — like TATER-HOMERUN, TWIG-STEM, RELAX-UNLASH, etc.) and even tried drawing lines in my transitions from clue–>alternative answer–>that answer’s clue–>alternative answer for that clue, etc., but all it was a chaotic mess (leading me to consider Chaos Theory and String Theory). I finally settled on “Markov Chain” — a sequence of transitions from clue-entry to alternative clue-alternative entry. But the worst of it is, in my list of 11-letter math terms, I had included Mobius Strip, and it was the only one I starred. Brilliant meta, brilliant solvers.

  14. Norm says:

    It was a moebius strip when I was growing up — but I would never have gotten it regardless.

    • Small Wave Dave says:

      Maybe we would have gotten it if Matt had included “with an umlaut” in the instructions!

  15. Garrett says:

    I was looking at the grid after I finished it and my first thought after not seeing any obvious theme fill was that the puzzle grid filling left me with a sense of there being a lot of letters U, so I counted them. Exactly twelve. Then I looked at the title, “Six of One.” After thinking about that for a moment, I recalled that old phrase, “Six of one, half a dozen of the other,” and I thought that Matt was giving us an indirect clue for the number 12. Suddenly, I got excited because in set theory the letter U means Union. And one way of showing Union graphically is with a Venn Diagram. So, that is what I submitted. It seemed perfect!

    Naturally, when I saw I was not on the leaderboard, I was crestfallen, and I spent the rest of the time left wondering what it could have been! Reading now the solution I must say I had wondered about some of the clue/answer pairs, especially Hashmark Units/Yards one, which made no sense to me at all.

    • PuzzleCraig says:

      I also submitted VENN DIAGRAM as my hail mary. Bits and pieces of it (VEN) and (GRAM) are in the grid, and the squares in the middle made me think that some obscure pattern of the letters might emerge to resemble a Venn diagram. I’m inclined to think that there might still be one there randomly. :)

  16. BarbaraK says:

    My wild guess was GOLDEN RATIO. My rationale was that four of the words had an A followed by a U (AU = gold) and the U was 1, 2, 3, and 5 letters after the A – Fibonacci numbers.

  17. slubduck says:

    As Lucky Guest said above, there were a whole host of entries which were pairs, not just the 6 in the solution or the 3 others LG mentioned, also

    ASYLA – YARDS (think both could be clued by ‘prisons’, or am i wrong?)

    some of these surely are weaker associations, but I had my list of 9 good pairs and kept trying to find the last 2
    my short list of guesses was Markov Chain, Ordered Pair, Golden Ratio
    oh well, fun to think I was maybe 40% down the correct road here on such a tough one.

    • LuckyGuest says:

      I also considered “Ordered Pair,” since I noticed so many double letters — 15 of them in 13 words — but couldn’t make it go anywhere. And as long as we’re making rabbit hole confessions, I noticed the “one” in the “Six of One” title, and the four occurrences of “One of” in the clues (including the first clue) and thought that had to have meant something.

  18. ajk says:

    As one who was absolutely nowhere (well, nowhere productive), I just want to say that it was IMO totally fair and clever. And also to say to my future self: remember to look at the clues. :)

  19. Kali says:

    Only six times in the grid is there an anagram of one in the answer. All, save one, are ordered as ‘oen’ (which means nincompoop or castrated donkey!!!!) The last is ‘eno’…. The Eno method is a thing .. just not an 11-letter thing… Too much time spent on that rabbit hole!!!!

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