meta 0:10

hello and welcome to episode #615 of

**matt gaffney’s weekly crossword contest**, a guest puzzle from

**peter gordon**called “Transcendental Meditation”. the instructions for this week 2 puzzle are:

**What is the answer to the question in this puzzle? (Hint: Z = 26)**

okay, well, the question in the puzzle, split across six across answers, is: THE LETTERS WHOSE / POSITIONS ARE / PERFECT / SQUARES / CAN SPELL WHAT / MARCH OBSERVANCE? the answer was pretty strongly suggested by just the timing of the puzzle, let alone the title, but let’s work through it. the perfect squares less than 26 are 1, 4, 9, 16, and 25, corresponding to the letters A, D, I, P, and Y if we associate letters with their number positions as per the hint. those can be arranged to spell **PI DAY**, or march 14, which was this past saturday. i can definitely remember being a math nerd as a kid and this “holiday” not really being A Thing, but at some point in the past decade or two, it has become A Thing.

in case you’re wondering about the title: in math, transcendental numbers are a subset of irrational numbers. an irrational number can’t be written as a fraction with integer numerator and denominator. a transcendental number is one that can’t even be written as the solution to any polynomial equation with rational coefficients. for example, the square root of 2 is irrational, but it’s not transcendental, because it’s a solution to x^2 – 2 = 0. pi is the most famous example of a transcendental number; e is another. there are, of course, infinitely many more, but they generally don’t have special names or symbols, and without names, it’s hard to even talk about them, because they can’t be neatly written in decimal or fraction form.

so this was a tidy little puzzle based on a curious mathematical observation. it would have been even cooler if the positions of the appropriate letters were somehow “circular numbers” instead of squares, as that would have been more appropriate to pi, but what can you do? math is math, even if it doesn’t always lend itself to the perfect wordplay.

as somebody with an interest in mathematics, i was mildly tickled by the puzzle. how about you?

Thanks, Peter and joon. 563 right answers this week.

Nice, tight puzzle, as always from Peter G. He never disappoints.

It felt more like a week 1. But last week’s week 1 felt more like a week 2, with its extra step. So it averages out.

I thought this was an interesting idea for a meta. The solution has nothing to do with the crossword itself, so the only thing that makes it a meta-puzzle is that the

expectationthat it will be a meta-puzzle serves as a red herring (I’m sure I wasn’t the only one to try using the numbers in the grid as the positional indices at first). It’s kind of a meta-meta.The idea is neat, and I think potentially very effective—but the “Z = 26” hint rather spoils the effect, in my opinion. To my mind, this would have been more interesting as a Week 3 or 4, without the hint. I wonder how many would have solved it under those circumstances.

I stared at the damn thing forever until I noticed the hint. Don’t know if I would have gotten it otherwise. But, then, since I have nothing but time on my hands to stare at a grid right now, it may have occurred to me.

ditto. I saw the prompt friday morning when i opened the email, but didn’t get around to solving until friday night, at which point i remembered the prompt, but not that there was a hint attached. Tried all sorts of things before i decided to look at the prompt again and make sure i wasn’t missing anything.

Interesting. Due to the instruction that Z=26, I never considered the ambiguity that “positions” could refer to the numbered boxes in the grid (which is what usually happens). MEATPTLS. ST PAT ELM? Palm Sunday’s in a few weeks; does no one do a PALM TEST beforehand?

I stared at MEATPTLS for far too long in my (failed) solve attempt.

so this was a tidy little puzzle based on a curious mathematical observationIf the starting point of this puzzle was, “I wonder what the numerical positions of the letters of PI DAY are—hey they’re all squares!” it was a curious mathematical observation, but my guess would be that the starting point was, “How about a meta-puzzle that works by exploiting the solver’s knowledge that it’s a meta-puzzle?”

Step 2: “Perhaps we can do this by directing him to the letters corresponding to certain numerical positions. The true interpretation of this will be their alphabetical positions, but the expectation that this is a meta-puzzle will lead the solver to the letters occupying the corresponding numbered positions in the grid, a red herring.”

Step 3: “Square numbers are a convenient set of numbers to use for this purpose. They can be denoted concisely, and there are 5 of them in the alphabet and about 8 in a typical crossword: enough to spell something reasonable, while not being too large to anagram in one’s head.”

Step 4: “What can we spell with the letters whose position in the alphabet is a square number? ADIPY… Hmm, well there’s PI DAY. All right. Let that be the solution.”

Step 5: Matt receives the puzzle, decides that, as it references a date, it would be a nice touch to run the puzzle on or about that date, so saves it for the week of PI DAY instead of running it during Guest Constructor Month. Since the closest Friday to PI DAY is a Week 2, he adds a hint to bring the difficulty level down.

That’s how I believe this went down.

That’s completely ridiculous. The seed of the puzzle would be noticing either that the letters in PI DAY are the square number letters, or that the square number letters anagram to PI DAY. Then the puzzle is made and saved for an appropriate weekend. It’s only a meta insomuch as the puzzle literally asks a question.

jefe is correct

Matt says you’re correct, so that’s that, but I can’t see why my idea was “completely ridiculous”. Seems to me like a perfectly logical way to construct a puzzle, and doesn’t require any coincidences (which is why I guessed it was constructed that way).

Agreed that it’s not a ridiculous idea. It’s easy to think, say, “I wonder what the prime-digit numbers are? Can they spell anything?” and if they can, to make a puzzle out of it.

(they can’t: B C E G K M Q S W)

“completely ridiculous” feels too strong for me but I think your “no coincidences” also feels strong. Step 1 to Step 2 feels like a pretty large coincidence in my mind. I mean, there are infinitely many ways to create a puzzle using the ‘exploit a meta-solver’s knowledge that it’s a meta’ strategy, so jefe’s thought process just seems much more likely from a practical standpoint (ie it’s much more directly relatable to this specific puzzle).

I spent way too much time trying to map the positions in the grid to squares. I tried both the set of 225 positions, as well as just the white squares.

After a couple days and seeing the correct answers pile up, I got my head out of the grid and solved it.

Not sure if I used the hint at all …

Nice timely puzzle!

Is it possible that there is no overlap of Matt Gaffney solvers and followers of Will Shortz’s weekly puzzle on NPR? This puzzle is essentially the same one posed last week.

To paraphrase, that puzzle was,”The letters of PI DAY have what interesting mathematical property?”

I laughed when I heard the puzzle on the radio because I had just finished the WSJ crossword. I wish I had heard the radio segment first.

Coincidence. Peter found the idea months ago, as I assume the NPR listener from Minnesota did. Neither Peter nor I knew about it until solvers began to mention on Friday.

2020 Pi Day Rant w /coronavirus: https://www.youtube.com/watch?v=Y4Lc5-6L1pE

Interesting (to some) Letter-Math Words: https://digitalcommons.butler.edu/cgi/viewcontent.cgi?article=4319&context=wordways

> it would have been even cooler if the positions of the appropriate letters were somehow “circular numbers” instead of squares, as that would have been more appropriate to pi

There is of course the famous Basel problem connecting the square numbers to pi:

1/1 + 1/4 + 1/9 + 1/16 + 1/25 + … = π²/6

also, everybody knows that (despite their circular appearance) pie are square

How exactly is this a meta?