"Significant Digits" Oct. 13, 2023

[Nycerjohnnie]

Mathematics was going to be my Hail Mary. I didn’t submit because I didn’t want to win a mug (as if, right?), have people ask how I got it, and have my story be “I guessed an answer.”

As for the meta, I am extremely disappointed. I actually started this way and got “MAT”. I decided to stop because of course there is no 16th letter in the 16th answer. I convinced myself I was going down a rabbit hole trying to convince myself my Hail Mary was correct. IMHO this meta is very inelegant. It seems empirically to have been difficult, but when you look at the solution there isn’t really much substance.

Yes exactly. The first three are elegant. The Xth letter of X, it actually makes a square. It’s cool and interesting. It completely breaks down with 16 into…something else.

[BigPear]

Oof. This Friday the 13th puzzle was a streak-breaker for me—last miss was the Chip Bok/Charles Schulz debacle of 9/9/22. My main takeaway: what’s the only thing harder than a meta with numbers in parentheses? A meta without numbers in parentheses. Cheers to everyone who solved— and remember, we all count.

[Colin]

Too much excellent World Cup Rugby for me to get this. Kinda got more than halfway there, like all the losing sides in the quarter-finals, but missed No. 1 as a perfect square and didn’t twig the metanism at all. A few rabbit holes including counting in perfect square order around the outside of the ‘perfect square’ that is the grid (ignoring blanks), and then row by row, column by column, etc. but the letters I got looked like a collapsed scrum. After not very long, amd because Page 1 took hours to fill up, I gave up running into immovable Fijians!
Hoping England make it to the Final, but that’s optimism for you!

[Bird Lives]

Oh right, a "digit" is not the same as a "number." I got the solution on Friday, but I didn't realize the significance of the title till Sunday night when I was trying to nudge someone towards the answer.

[MatthewB]

I'm annoyed at myself...I figured that the eleven letters included the 1...so I tried first the square root followed by the square. Clever but not clever enough!

[Flying_Burrito]

Too much excellent World Cup Rugby for me to get this. Kinda got more than halfway there, like all the losing sides in the quarter-finals, but missed No. 1 as a perfect square and didn’t twig the metanism at all. A few rabbit holes including counting in perfect square order around the outside of the ‘perfect square’ that is the grid (ignoring blanks), and then row by row, column by column, etc. but the letters I got looked like a collapsed scrum. After not very long, amd because Page 1 took hours to fill up, I gave up running into immovable Fijians!
Hoping England make it to the Final, but that’s optimism for you!

It will be quite the game vs Bocks (and that first half vs France proved the point that rugby is one the best sports). To me it was anybody but France, so mission accomplished.
Back to the meta. I have seen a very similar meta by one of our board members several years ago (who managed to outwit the great PB). Stuck for a while as I thought the perfect square was made by a 3×3 bigger square where the alphabet # total to a perfect square #. Then stepped back and ... eureka. I still think it was a great meta

[HunterX]

One of the rabbit holes that trapped me for awhile was the almost-FOUR's and one almost-NINE in 2x2 squares: Starting in square #41, there's FOUE, then in #27 you can get FOUI though in an odd order. The middle of POUT is part of a 2x2 that is also FOUI, while #17 is MOUR. There's a "nine" version just below #51 with NITE.

Also starting with #27 and going upwards to the right is another tantalizing FOUR. But the only other one is a zig-zag starting at #41. So that fizzled out quickly.

Since those were limited to mostly using only "perfect square," I figured (pun intended) that path had limited potential.

[femullen]

It's sometimes hard to believe that The Smarter Half is my own flesh n blood. We solved the grid, and I said, "Aha! Perfect squares!"

As I began enumerating them, TSH asked, "What are perfect squares?"

"Stodgy old folks and Boy Scouts," I replied, assuming she was joking.

"Eh?" quoth she. "No, really."

I paused between 16 and 25 to look upon her in astonishment. Was it possible that she'd lived in Quebec so long that her English had decayed to this degree, or did she really not remember what perfect squares were? Could amnesia reach such heights in one so young?

Stifling the urge to blurt, "Quelle farceuse!" I instead quickly explained both the algebra and geometry of perfect squares, adding that, while we were looking for 11 letters, there were only seven perfect squares in the grid.

"But there are 11 digits," observed TSH, which is why she still holds that title. Thinking that we were perhaps onto something, I hailed Isaac to freshen my glass. Before he was able to tip the bottle, though, TSH said, "I got it."

Then she made me find it myself. The brat.

[EVJ]

My problem was due to a complete failure of imagination.

[EVJ]

It's sometimes hard to believe that The Smarter Half is my own flesh n blood. We solved the grid, and I said, "Aha! Perfect squares!"

As I began enumerating them, TSH asked, "What are perfect squares?"

"Stodgy old folks and Boy Scouts," I replied, assuming she was joking.

"Eh?" quoth she. "No, really."

I paused between 16 and 25 to look upon her in astonishment. Was it possible that she'd lived in Quebec so long that her English had decayed to this degree, or did she really not remember what perfect squares were? Could amnesia reach such heights in one so young?

Stifling the urge to blurt, "Quelle farceuse!" I instead quickly explained both the algebra and geometry of perfect squares, adding that, while we were looking for 11 letters, there were only seven perfect squares in the grid.

"But there are 11 digits," observed TSH, which is why she still holds that title. Thinking that we were perhaps onto something, I hailed Isaac to freshen my glass. Before he was able to tip the bottle, though, TSH said, "I got it."

Then she made me find it myself. The brat.

I love this! Can I give two thumbs up?

[woozy]

So....

COUNT = Going from 0 to 60 meant we needed to count the number squares starting at 0. That way the last number square in the grid would be not, 61 but 60. We still only have 8 perfect squares but CIRCULAR SAW means you go to the start of the grid and keep going. When we get to the end of the grid a second time we have counted to 121 which is perfectly 11 squared. Unfortunately that is 12 perfect squares if we count 0. But .... well, lets not count 0.

....

So did anyone note that this a weird meta in which it is ONLY mechanism. There is no word play, no pattern in grid, no cleverness; just find something to do that comes only from the one nudge listed as a nudge and do it.

I didn't like it at first as digits are arbitrary and mean nothing in themselves. I think NUMEROLOGY would be a more appropriate description than MATHEMATICS.

Somehow it never occurred to me that the "digits" in the title was relevant. I just assumed digits were somehow related to numbers in most people minds and would impress most people as being most equivalent. Realizing that "digits" was actually instructions to apply the offensively arbitrary step of numerologically taking the digits of the perfect squares, I don't dislike the puzzle as much.

[mattythewsjpuzzler]

Great puzzle which I didn't crack. Tried every permutation...but that one! For my money PB is THE most talented puzzle constructor out there because he does SO many format including all the Variety puzzles in the WSJ which are awesome. Love his cluing and his meta's while less frequent -- are always tight and high quality. Congrats to those who solved!

[Richard]

I submitted MATHMATICS as a Hail Mary.

Waiting for the email regarding the mug.

Richard

[VanVeen]

Google led me astray on this one. I did a search of 'perfect squares' and it told me they were 4, 9, 16, 25, etc., totally skipping 1. So I couldn't figure out how to get 11 letters out of 6 words.

I'm not a math guy, is 1 being a perfect square common knowledge? It makes sense that it is, but I think I've read somewhere that 1 is not a prime number, so maybe I assumed it worked that way for perfect squares, too.

Ugh. Math.

[mlvilv]

I caught on to the perfect squares immediately and set about looking at those numbers 1, 4, 9, etc. Then couldn't make sense out of what to do with them since they didn't spell anything. I then tried the whole first letter, 4th letter, 9th letter until I was like wait there's not going to be a 16th or 25th letter so I dropped it. I didn't think to take each digit separately. And as I type this now I realize I should have since I literally just said 'digit' and that was in the title. Not sure if it's worse to be on the right track and not follow it all the way through or to miss it completely. I did have less time to devote to this because we were on an empty nester long weekend trip to Disney which was absurd but fun.

[MikeMillerwsj]

The contest answer is MATHEMATICS. For each answer whose clue number is a perfect square (as suggested by the clue for PERFECT/SQUARES), take each digit of the clue number and find the letter in that position. (For example, for 16-Across, take the first and sixth letters.)Those letters, in clue order, spell the contest answer.

It's always a treat when crossword genius Patrick Berry creates a contest puzzle for us, and this was one for his highlight reel. We are in awe of what it took to create a grid where the numbers--and clue lengths--yielded this solution (e.g. 36 had to be a word where the 3rd letter is T and the 6th is I, and so on). It was an unusually challenging contest, with only 491 answers, about 75% (our typical rate) correct -- so a big hats off to the hardy few who got this one right.

Incorrect answers included METACARPALS (funny pun, 10 submissions), EXPONENTIAL (9), MILLIONAIRE (5), PYTHAGOREAN (4), HEXADECIMAL (2), SYMMETRICAL (2) and a few others.

Congrats to this week's winner: Diane Stegmaier of Denton, Tex.!

[moron]

Ashore thanks to the last call zoom. After the rabbit holes I tripped into, I'm going to need some alcohol that is "High-proof" (60a).

A brief description of some rabbit holes I "visited."
Perfect Squares include 1, 4, 9, 16, 25, 36, 49 right? I looked at the clue attached to each number and initially didn't know what to make of it.
1 - TALC has a ONE on the moh's hardness scale
9 - NIOBE for her hubris, had her NINE children slain
16 - MLK jr day was the 16th of January this year (the 1 from January can be ignored due to being mentioned in the clue as "Jan. Honoree")
25 - ESAU was first mentioned in Genesis 25:25
49 - LOMAN is featured in Death of Salesman released in '49 (I acknowledge how flexible I am to posit such a stretch)
with 4 and 36 unable to be attached to the puzzle by any stretch of the imagination.

What if every one of the perfect square clues was just short of a perfect square in the meaning? Like a one-under-esque situation.
4 LOMAN is 63 years old (one off of 64 years old)
16 MLK jr day will be the 15th of January next (our upcoming holiday in 2024 is closer than the one in 2023) (one under 16)
25 OMEGA is the 24th letter of the greek alphabet (one under 25)
I looked through so many Wikipedia pages for years and numbers that seemed interesting, but a twitchy feeling in my gut was sure this was entirely misplaced effort (it was not enough to stop me).

I also thought of mathematics as a possible answer purely speculatively. Some things to support this:
- "set of values"
- PERFECTSQUARES ofc
- COUNT
- "unit" from FRANC
- ACCUMULATED
- PROOF
- WENTDUTCH (division?)
- FORMULATED (formula....)

The actual solution was so much simpler. Anyway, plot summary for Amsterdam by McEwan was interesting (does not reference significant digits in case you are wondering).

[Abide]

I submitted MATHMATICS as a Hail Mary.

Waiting for the email regarding the mug.

Richard

Dear Richard:

We drew your name for the mug. Since you submitted a ten-letter word, we had to draw again.

Sincerely,

Mike Miller

[BarbaraK]

I had rabbit holes galore on this one. None were all that meaty, so they may not impress a true connoisseur like our Rabbit, but if you'll take quantity over quality...

21D clues COUNT as "Go from 0 to 60, say" There are 61 numbered squares in the grid, so if you renumber them starting at 0, you end at 60 and the perfect squares spell ... ISBOLSL

The two 11 letter entries, ACCUMULATED and CIRCULAR SAW have 6 (yes, 6!!) letters in common, including the trigram ULA. The leftover letters from the first are an actual word, "muted"! From the second, irrsw - maybe not.

Take all the entries with at least 9 letters and take the 1st, 4th, and 9th from each. MLT could point to MLK. WTH - that's more like what I'm feeling:)

The perfect squares are significant, what if they were missing?
1 -> ILLS
4 -> OMAN (ooh, this is looking promising)
9 ->THE (OK, had to use the across instead of the down, a bit inelegant, but it is a word)
16 -> OLD ME
25 -> MEGA (yay, this is working, though I don't recall any of these in the clues or any obvious synonyms)
36 -> uh oh, neither SQUARS nor ATERIES can possibly be anything, even though...
49-> SAMS (though again using the wrong direction entry)

Perfect numbers mean something in math, let me look that up. The first two are 6 & 28. (The third is bigger than 61) 6 TROUBLE + 28 WANE is 11 letters, but not an 11 letter word.

What about making 4x4 squares of letters? The two in the grid don't seem interesting. WANE/WINE/WIFI would be a 4 step word ladder with the addition of WIFE. Couldn't find others though.

Speaking of WINE, that could change to nine; but no others. Also EON is an anagram of ONE, but again no others. (In fact, not likely to spell out numbers because of the X in sixteen and the V in twenty-five. X & V are also the reasons my looking for Roman numerals didn't go far.)

Analyzing with https://boisvert42.github.io/mechapuzzle/ the letters where the number of occurrences is a perfect square are BCEFNQWZ - another not-even-close-to-a-word.

There are 11 clues with 4 words; their grid entries spell LPHWSPEWWSA - don't even need an anagram solver to tell me that can't be anything.

I think that's most of what's intelligible on my paper. Never did figure it out until the Last Call Zoomers showed me the way.

Congrats to all who got it!

[ricky]

I found this same thing, and it's an example of the worst problems with search engine results.

On my own I had to wonder why 1 wouldn't be included in the list of squares and consult a more reliable site.

I recently googled something like "list of countries in Africa." Google itself tells you that there are fewer than 40.

That is very wrong.

Google led me astray on this one. I did a search of 'perfect squares' and it told me they were 4, 9, 16, 25, etc., totally skipping 1. So I couldn't figure out how to get 11 letters out of 6 words.

I'm not a math guy, is 1 being a perfect square common knowledge? It makes sense that it is, but I think I've read somewhere that 1 is not a prime number, so maybe I assumed it worked that way for perfect squares, too.

Ugh. Math.