Again, Will has given us a "number" puzzle that doesn't expect any math knowledge.Q: Spell out the numbers from 13 to 20 -- THIRTEEN, FOURTEEN, FIFTEEN, SIXTEEN, SEVENTEEN, EIGHTEEN, NINETEEN, TWENTY. Select one letter from each word, in order, to name another number. No anagramming is necessary. What number is it?
A: INFINITY
For NPR puzzle posts, don't post the answer or any hints that could lead to the answer before the deadline (usually Thursday at 3pm ET). If you know the answer, submit it to NPR, but don't give it away here.
You may provide indirect hints to the answer to show you know it, but make sure they don't assist with solving. You can openly discuss your hints and the answer after the deadline. Thank you.
Wow! This must break the record for Blaine's ability to foresee the puzzle! It's 9pm Saturday on the East Coast.
ReplyDeleteIs this your puzzle, Blaine?
ReplyDeleteNope.
DeleteThis comment has been removed by the author.
DeleteGot the answer. Trying to find a clue.
ReplyDeleteYou could Google the answer, but you won't get far.
ReplyDeleteI like it. I tried 2 different approaches first, and then got it right away.
ReplyDeleteSo, okay Blaine, last week you credited moi for providing you with how you obtained the puzz so quickly. Now it is your turn to do the same for me. LOL
It was posted really early and I subscribe to the RSS feed. I was actually late to noticing it in my feed.
DeleteYou beat me too it. I now see how you got it. I believe this may be the first time it has been posted so early.
DeleteSo now will get my sorry ass outta bed tomorrow?
DeleteThis is the current CarTalk Puzzler:
ReplyDelete"Take the name of a current make of car say, a Dodge, Buick, Ford, or Hyundai.
Now add one letter, scramble all the letters around, and come up with another current make of car.
That's it. Pretty simple, right?
So, you've got one car make, you add one letter, mix everything up, and voilà! you've got another car make.
What two car makes are they?"
The intended answer is not difficult, but I am wondering if anyone else here got the alternate answer? I have driven the second car answer, and it is a piece of excrement.
I found the answer in the sound of the wind in the branches.
ReplyDeleteDidn't you say you were never going to get the answer? Or was that someone else?
DeletePublishing the Sunday Puzzle this early is toying with us.
ReplyDeleteNice.
DeleteThis puzzle's days are numbered.
ReplyDeleteConceptually, the puzzle is flawed. I'll explain Thursday.
ReplyDeleteElegant.
DeleteI agree with Nodd. Thursday should be interesting.
DeleteI concur
DeleteI'm with you, Nodd. --Margaret G.
DeleteI concur as well, Nodd. Will's marked misunderstanding of some math concepts is brazenly showing here.
DeleteDitto.
DeleteI feel incredibly lazy.
ReplyDeletesail cement
DeleteThe middle of the number is European.
ReplyDeleteWhen I looked at my NPR puzzle page, at 7:25 A.M., it said fifteen hours ago. That means it was posted between 4 and 4:30 Saturday. That's a little fckd.
ReplyDeleteThe answer can be found in aerobatics.
ReplyDeleteI have an answer.
ReplyDeleteMy answer works for at least one other clue. It hit me like a ray of sunshine on a foggy morning.
DeleteI'm with Nodd on this one. But I will think of a clue anyway and be back later.
ReplyDeleteI own a Hyundai Ioniq. But this week I'm traveling, and I rented a Nissan.
ReplyDeleteNot a Tesla?
DeleteAs the morning marches on, I feel number and number. No novocaine needed.
ReplyDeleteIt took me longer to solve this than it should have. An anagrammer helped.
ReplyDeleteAt least we don't have to rotate any digits, like Will's number puzzles often require.
ReplyDeleteAnother long driving day in front of us. I thought I’d never solve it in time, but once I thought outside the common categories, it didn’t take as long as I feared it would.
ReplyDeleteSolve it in time!? The puzzle was posted 15 hours before it aired!
ReplyDeleteSorry 16 hours.
DeleteThis comment has been removed by a blog administrator.
ReplyDeleteI'm feeling better picturing the answer with a red hat.
ReplyDeleteThis comment has been removed by a blog administrator.
ReplyDeleteI am reminded of the American Songbook standard, St. James Infirmary.
ReplyDeleteThis comment has been removed by a blog administrator.
ReplyDeleteUh, this is a bit of a NONEVENT. For newcomers, here is my vote for the greatest Sunday puzzle of all time: Sort all Roman numerals into alphabetical order ... What is the last one? (!)
ReplyDeleteAssuming we’re not looking at a trivial act of alphabetizing, the last, “one,” like the first, “one,” will be an, “I”.
DeleteI vaguely remember that puzzle. But I had to work it out again -- I couldn't remember the answer.
DeleteCool, I it!
Just to give some evidence that I have the answer: the numeral is a palindrome.
I meant:
DeleteCool, I LIKE it!
To be clear, by "Roman numerals" I meant not individual letters, but whole numbers, e.g. MMXXVI for 2026. The question is: Which Roman number would be last in an alphabetical sort? (Yes there's only a finite number of them!)
DeleteIf I'm correct, there's a connection to the American Kennel Club.
DeleteThat's interesting, Rudolfo -- I guess I'd always assumed you could just stack up more and more 'M's. But in any case... it doesn't matter! The answer to the question is the same in the variant of Roman numerals in which you can just list longer and longer strings of 'M's to get bigger and bigger numbers, in secula seculorum.
DeleteHow'd you happen to know that,Blaine?
DeleteRe Crito MMMMMM's: Works for me, but there is a Roman numeral syntax that that violates. E.g. apparently 990 is CMXC and not XM. I don't know whether such rules are ancient or modern.
DeleteOnce again, this Blog proves to be the most informative site on the Internet! It was only by combining Blaine's comment with what I figured to be the answer that I learned something absolutely fascinating about the American Kennel Club.
DeleteI'm going to let the cat out of the bag here so you don't have to.
DeleteOuch, WW! What happened to Thursday?
DeleteLancek, I figured since it's not the official puzzle we could discuss today. We need something interesting to ponder now, yes?
Delete. During these dog days of summer, we need some stimulation and spark!
I could not care less about dogs. What concerns me is horses and their negativity. Are they all neigh sayers?
DeleteI would hate to be saddled with having to answer that question.
DeleteYes, but don't Dally-Man; remember you are supposed to meet Lariat the bunkhouse.
DeleteWhat's your mane point?
DeleteKeep them doggies rollin'.
DeleteAnd try to make your saddle soar.
Deletee
ReplyDeleteThe number e has infinitely many digits.
DeleteIn our alphabet, the first letter is 'a' and the last letter is 'z'.
ReplyDeleteI was a little lethargic early this AM but once I had my breakfast I was able to score a 100% on this puzzle. I also noticed an interesting property associated with this number.
ReplyDeleteThis one is impossible to pin down. SO slippery.
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteThe answer (assuming, of course, that I have the right one) is counterintuitive. (Perhaps this is what Nodd was thinking of above, too.)
ReplyDeleteI'm thinking of the movie "Side Ways"
ReplyDeleteI have an answer, but I really don't like it. I am hoping I'm wrong, but reading a lot of the comments is making me fear I'm not.
ReplyDeleteYeah, I think we have the same answer.
Deletebed bath & table
ReplyDeletebed bath & (to infinity and) beyond!
DeleteI believe I've chased down the intended answer, but don't like the puzzle.
ReplyDeleteI think my understanding of this puzzle has progressed downward.
ReplyDeleteListing
ReplyDeleteI have an answer if we limit ourselves to 13-18, but not the puzzle as stated.
ReplyDeleteThis puzzle would be a nonevent, if I could reinvent the Roentgen ray.
ReplyDeleteOhhhh, I get it! And now I get Rudolfo's earlier joke too!
DeleteI was racking my brains, but the answer was in the palm of my hand.
ReplyDeleteHere is a sneak peek of a riff of Will Shortz's NPR Puzzle Challenge that I intend to run on this Thursday's Puzzleria!:
ReplyDeleteSpell out the numbers from 94 to 100:
ninety-four, ninety-five, ninety-six, ninety-seven, ninety-eight, ninety-nine, one hundred. Select one letter from each word, in order, to spell a word for another number. No anagramming is necessary. What number is it?
Now spell out the numbers from 90 to 84:
ninety, eighty-nine, eighty-eight, eighty-seven, eighty-six, eighty-five, eighty-four. Select one letter from each word, in order, to spell the same number as the one in the paragraph above. Again, no anagramming is necessary. What number is it?
The answer is the same for each part of this two-part puzzle.
Lego
Please, do not post any answers here, at least for a while. You are welcome to provide hints that suggest that you have solved it, however...
DeleteLegoWhoAsAlwaysGivesThanksToBlaineForProvidingUsWithThisWonderfulForum!
Nice one, Lego! There's a logical issue with the wording, but I don't know another way that's better.
DeleteUm, uh ... but what if the answer is NEITHER ?!
DeleteI must admit, Rudolfo my friend, that NEITHER is, alas, a perfectly legitimate answer!
DeleteLegoWhoHasAlwaysBeenABeneficiaryOfAndShallAlwaysRemainInAweOfRudolfo'sPuzzlingProwess
And thanks also to Lancek, whose posted comments are always thoughtful, helpful and wise.
DeleteLego...
Most mathematicians would have a problem with the intended answer.
ReplyDeleteMost fifth graders would have a problem with the intended answer.
DeleteGoodbye, Dolly.
ReplyDelete:(
She seemed eternal.
💔
DeleteShocked and saddened at Dolly's passing. She gave so much to so many, especially children.
DeleteAnd we will always love her.
DeleteI think it is more than a little interesting that Dolly Parton was one of twelve children to her parents, yet she had none herself. She certainly had plenty of opportunity having been married to the same man all her adult life. Why is this interesting fact being mostly overlooked with her flip reply?
DeleteSDB, I hear what you're saying, but she was diagnosed with endometriosis and had a partial hysterectomy in her 30s, which affected her ability to have children. She poured her maternal energy into helping millions of children worldwide.
DeleteI was not making any kind of judgement at all, but only saying I found it interesting and worthy of exploration. Also, I am not one who believes women are required to procreate.
DeleteShe was very candid for years - since the 1980s. Having children was not a priority and she was pretty happy not having children:
Delete“I haven’t missed [having kids] like I thought I might. [...] When you’re a young couple, you think you’re going to have kids, but it just wasn’t one of those burning things for me.”
"“I haven’t missed [having kids] like I thought I might.”
She "also said bringing kids into today’s society wouldn’t sit right with her with 'everything that’s going on.'"
https://pagesix.com/2023/12/22/entertainment/why-dolly-parton-says-she-hasnt-missed-having-children-with-husband-carl-dean/
I think some here are misunderstanding my post about why she did not have children. I am wondering how her having 11 siblings in a poor family may have influenced her desire, or lack thereof, to procreate. Also, why did she choose to be born into that particular family.
DeleteWhy not worry about Carl Dean's fertility, her husband of 60 years?
DeleteWhat does fertility have to do with it?
DeleteWe should all be concerned whether Carl Dean carried on his family genetics and whether his family and upbringing played a part.
DeleteWell I'm not!
DeleteThen why worry about hers?
DeleteCan't you understand my post simply was expressing an interest in her being one of 12 siblings, and how that may have influenced her?
DeleteI am merely pointing out that you (and many others) exclusively focus on women's fertility and not men's. This is not unique to Parton.
DeleteWhat an odd discussion going on here. Might we please just let Dolly rest and let it go? Thank you.
DeleteAgain, you are not understanding my post, but making a false accusation. I would have posted the same had she been a male. It has nothing to do with men, women or procreation per se. It is about 14 people living in a one bedroom house with little money. It must have major influencing on how someone is affected.
Delete1. Apparently not to (some of) the other 13 siblings, as she has numerous nieces and nephews.
Delete2. Family sizes across society have shrunk dramatically with the advent of birth control, women's legal liberation, social norms changing, among other societal changes. The percentage of people being childfree is at its highest. This is a well-documented phenomenon across developed societies by sociologists, economists, and anthropologists.
She did not have "13 siblings" as you say, but only a paltry eleven.
DeleteDog nose typo and an irrelevant discrepancy as the point is made.
DeleteSplainit, dog nose? Happy National Dog Day from my pup to yours!
DeleteYou may consider your misstatement irrelevant, but I do not. Just as I insist you are misrepresenting my original post. I would back this up by informing you I am now nearing the end of a new non-fiction book, The Zorg, A Tale of Greed and Murder That Inspired the Abolition of Slavery. I previously believed I had a fairly good understanding of what it might be like being a slave prisoner on a sailing ship intending to deliver its cargo to Jamaica. I was woefully under informed. I thought sardines were tightly packed, but now I know the details of what it meant to be a slave on board one of these ships and I realize, had I been one and survived the crossing, I would not have wanted to even come close to a gravy boat the rest of my life. I can also state I see little difference between that situation and being crammed into that tiny one bedroom house with 13 others. Sorry you are unable to separate my curiosity from your obsession with procreation, which I have no interest in.
DeleteYour windmills have tilted.
DeleteIs COINVEST a 2 syllable word or a 3 syllable word?
ReplyDeleteIf a United States Marine Officer observed an episode of extreme disregard for regulations that caused the deaths of marines and was subsequently covered up, could it be said he was shaken to his Corps?
ReplyDeleteFive days a week, I provide a segment called “Ted’s Track” on a dj friend’s classic oldies show. I've almost never changed the song selection after I’ve submitted the week’s tracks to him along with each day’s background music info, but yesterday for only the second time in 12 years I changed the pick at the last minute to Dolly’s tribute to Porter Wagoner, “I Will Always Love You.”
ReplyDeleteR. I. P. Dolly Parton. You will be sorely missed.
R.I.P. Tim Curry, also 80.
ReplyDeleteI was a fan.
DeleteObviously his most... memorable... performance is "Sweet Transvestite from Transylvania," but I remember a friend playing his Fearless album for me in college. I do the rock, myself...
I never saw the movie in a theater, but frequently saw long lines of costumed patrons waiting in line for the midnight showings. This reinforced my not wanting to see the film because I knew it would be noisy and I would not be able to appreciate what I was watching. Later, when it came out on DVD I watched it and found, much to my amazement, that I thoroughly enjoyed it and have watched it several times since, but always at home rather than in a theater.
DeleteI will miss Shelley too. It's difficult to believe that "Ride the Wild Surf" is 62 years old. But, on a lighter note isn't it a shame that the mnemonic for the Great Lakes will now have to be changed?
DeleteLiterally a shame! Nice one, CnD.
DeleteINFINITY
ReplyDelete. . .which, as any 5th grader will tell you, is a concept, not a number.
I do hope I am not obganiating you with this repetition of a basic, basic, basic concept.
INFINITY
ReplyDeleteBuzz Lightyear’s catchphrase is, “…to infinity and beyond…” While a more direct reference to “Toy Story,” was probably TMI, slipping in a comment that early posting of this week’s challenge was, “…toying with us…”, passed muster.
A wag suggested starting a pool on the number of correct submittals this week, but couldn’t come up with an appropriate name…
And, as Nodd elegantly pointed out, infinity is a concept, not a number.
Infinity
ReplyDeleteINFINITY
ReplyDeleteYes, I’m in agreement. Infinity is not a “number.”
Hint: “I was racking my brains, but the answer was in the palm of my hand.”
—> --> -->
“To see a Heaven in a Grain of Sand
And a Heaven in a Wild Flower,
Hold Infinity in the palm of your hand
And Eternity in an hour.”
—William Blake, “Auguries of Innocence”
Dr. Awkward?
Most excellent!!
DeleteThanks, Dr. A. I really thought you would get there first.
DeleteBlake-wise, perhaps I need more Experience.
DeleteI think of myself as Innocently Experienced or Experientially Innocent.
DeleteI wrote, “The answer can be found in aerobatics.” A Lazy Eight is performed by a plane’s gradual climbing, banking, and turning to trace an imaginary figure eight on its side. And Lazy Eight is a nickname for the infinity symbol that looks like an eight on its side.
ReplyDeleteThe reason I felt better picturing the answer “in a red hat” is that cardinal numbers are used to count elements of a set, and it is useful to assign cardinal numbers to infinite sets. The set of all counting numbers is “countably” infinite, and its cardinality is what most people mean by the “number” infinity. Infinity is not a real number, but it does live in the strange and mysterious world of transfinite numbers. (The first mystery is that countable infinity is not as big as it gets.)
ReplyDeleteINFINITY
ReplyDelete> You could Google the answer, but you won't get far.
I wanted to be cute and say you could Googol the answer, but I didn't think that would pass muster.
> I own a Hyundai Ioniq. But this week I'm traveling, and I rented a Nissan.
Like "Ioniq", "Infiniti" changes the last letter of a real word. (But I rented a Sentra.)
> At least we don't have to rotate any digits, like Will's number puzzles often require.
If you rotate an 8, of course....
Infinity
ReplyDeleteFollow on. Did anyone else remember the opening scene of the TV show Ben Casey, with Dr. Zorba (Sam Jaffe) intoning, “Man, Woman, Birth, Death, Infinity,” as he drew the symbols on a blackboard?
ReplyDeleteINFINITY
ReplyDeleteI wrote that the answer is counterintuitive because intuitionist mathematics does not generally accept infinity as a number but merely as a potential attribute. (Of course, non-intuitionist mathematics doesn't accept infinity as a single number for a totally different reason, namely that there are an infinite number of infinities, as Georg Cantor proved, perhaps what Mike Ecsedy was referring to when he said that most mathematicians would have a problem with the intended answer.)
I gave two clues. One was
ReplyDelete"In our alphabet, the first letter is 'a' and the last letter is 'z'."
But in the Hebrew alphabet the first letter is aleph, and in the Greek alphabet the last letter is omega, and those (א, ω) are used to denote infinities.
My second was responding to ZenoCosini, asking "Didn't you say you were never going to get the answer?" Zeno's paradoxes of space and time involve taking infinitely many steps, which Zeno thought meant they could never be completed.
My post:
ReplyDelete- “I was a little lethargic early this AM but once I had my breakfast….” - this referred to “lazy” and “ate=eight” as in “lazy eight”, the symbol for infinity.
- “I was able to score a 100% on this puzzle.” - refers to one hundredth, or centesimal, which is an anagram of “lemniscate”, a term for the infinity symbol.
- “I also noticed an interesting property associated with this number” - the word infinity has eight letters, consistent with the horizontal symbol for infinity.
Our brilliantly creative friend Tortifude takes center stage on this week's edition of Puzzleria!
ReplyDeleteHere ever-popular "Tortie's Slow but Sure Puzzles" this week, titled "Stellar Tortoiseshell Dwellers," features a quintet of puzzling excellence titled
~ “Femi-name-ity!”;
~ “Flighty” actress?;
~ “An Alternating Alphabetical Order”;
~ “That adder holds an herb in his piehole!”; and
~ “Storks come home to roost?”
We plan to upload Puzzleria! very soon this very afternoon (or as soon as we can!)
Also on our menus this week are:
* a Schpuzzle of the Week titled "Frightful Tigerfish! Freightful Chevron Ships!"
* a Flambée Hors d’Oeuvre titled “Pilot-lit litanies,”
* a “Gold-Plated Pastries Slice” titled “Spatulalia Bacchanalia!”
* a Stunning Dessert titled “Surname’s the Same,” and
* eight Riffs of Will' Shortz's NPR Puzzle Challenge, titled "Confounded by boundlessness?"
So, Slowly but Surely, Mosey on over to "our little cyberworld puzzle-shop" and enjoy generous helpings of mind-joggling fun!
Lego
Wow, really good reasons have already been posted for why 'infinity' is not the name of a number!
ReplyDeleteI agree, a good way to start to make 'number' precise is to say all cardinalities are numbers (and "the rest is the work of man"), but there are rather a lot of different infinite cardinalities. (Love the red hat clue!)
INFINITY. I wrote that the puzzle is conceptually flawed. It says the answer is “another number.” In most of math, infinity is not a number, although there are branches of advanced math where infinity acts like a number, as in set theory where infinite sets can have different sizes.
ReplyDeleteI disagree. Infinity is commonly accepted as a number in many areas of math. It is not a real number, or a rational number, but it can still be considered a number. As someone noted, it can be a transfinite number.
DeleteThat was Lancek (with the great 'red hat' comment), but as others have noted there are many transfinite numbers. (And by 'many', I do mean many!) There are the infinite cardinals: א1, א2, א3.... (And maybe a whole bunch in between those!) And there are the transfinite ordinals, starting with ω, ω+1, ω+2...
DeleteI doubt any mathematics in the past 150 years has taken 'infinity' to be the name of any particular number.
Whoa. I tried to put subscripts on my alephs, but it looks like that html tag is not available. But... I'm getting autocorrected to put my numerals before my alephs! I'll just leave them there even though that's not how it's done in set theory!
There are different ordinal and cardinal infinities, but it is still often the case that the number infinity is used. The size of a set might be infinity. A limit of integration might be infinity. A volume might be infinity.
DeleteAlso, all the computers designed in the last 50 years have treated plus and minus infinity as numbers.
Correction, Crito: By construction, there are no cardinal numbers between the alephs. Aleph_1, for example, is by definition the second infinite cardinal. What standard set theory does not tell us is whether the cardinality of the continuum (c), or of the set of infinite binary strings, is aleph_1. There may be many cardinals between aleph_0 and c, but not between aleph_0 and aleph_1. Cantor's famous continuum problem was to determine whether c = aleph_1. Gödel and Cohen proved that standard set theory (ZFC) does not decide the question.
DeleteSorry, I just want to try something...
Delete{\displaystyle \nexists S\colon \aleph _{0}<|S|<2^{\aleph _{0}}}.
Darn. There's no way to put it in here so it looks pretty.
DeleteAnyway, what I was going for was: The continuum hypothesis says there isn't cardinality between ALEPH_0 and 2^ALEPH_0.
But I see your point, and stand corrected, about the adjacency of ALEPH_0 and ALEPH_1.
Jumping in a little late to the aleph party but wondered if you have read "The Aleph," a short story by Jorge Luis Borges, published in 1945? The concept he describes has always stuck with me since learning about it as a junior in high school. "The Aleph" details a point in space that contains all other points, allowing one to see everything in the universe simultaneously. It's found on a certain step of a staircase. The story explores themes of infinity and perception, making it a significant work in Borges' literary career.
DeleteI never have! I'll definitely look.
DeleteDo you happen to know "The Analytical Language of John Wilkins"?
I think it would have been more fitting if he had renamed it Lake Leave It To Beaver.
ReplyDeleteRenaming it Lake Obnoxious would have been approriate, and would preserve the HOMES acronym we learned in school.
DeleteOther candidates, which I hope our Neighbors and friends to the north adopt:
DeleteLake Epstein
Lake Narcissist
Lake Bonespur
Lake Spite
Lake We’re Ignoring You (preferably in Cree)
Hey Nodd - with Lake America, the acronym can be reordered to become SHAME.
DeleteLake Neighborly
DeleteLake Tariff-ick
Someone is suggesting renaming a leaky, algae filled, DC landmark, with peeling paint, Lake Trump.
DeleteThat might be just a bit too brazen even for Trump, but why not rename the reflecting pool Lake Ontario? After all that name is now up for grabs.
DeleteIf you restrict the letters to be from the numbers 13-18, you can spell “trente” which is an actual number in French.
ReplyDeleteWas really hoping for an answer in the roofie/novovcaine/codeine genre.
Last Sunday I said, “I am reminded of the American Songbook standard, St. James Infirmary.” Infinity, Infirmary…it was as close as I could come without going over the line.
ReplyDeleteWhen in Rome: According to someone there's a syntax for legal Roman numbers, such that e.g. 40 must be XL and not XXXX. By that law, the last Roman number in an alphabetical sort is: XXXVIII = 38 . Strikes me as odd ...!
ReplyDeleteAnd, in case anyone missed it, the connection to the American Kennel Club cited by Blaine is truly amazing. Word Woman posted a link, but it was a text link and thus easy to miss.
DeleteI came up with ten x nine =90
ReplyDeleteI love it! Will should surely accept that as a clever alternate.
DeleteI agree, it's about as correct of an answer as INFINITY
DeleteI'm glad Crito explained his comment--it was all Greek to me. I was referring to "L'Infinito," a poem by the nineteenth century author Giacomo Leopardi, in which he describes how the sound of the wind through the branches, by contrast with the silence in which he had been contemplating the landscape before him, reminded him of all the dead seasons that he could not see or hear, concluding with the lines
ReplyDeleteSo my mind sinks in this immensity:
and foundering is sweet in such a sea.
The whole poem is worth a read; Wikipedia furnishes several alternative translations.
I had also submitted ten x nine, to represent 90. I didn’t really like it, but it also seemed to fit some of the clues. I commented that it hit me like a ray of sunshine, because an array size can be described using AxB. Tesla has a model X, which is why I asked Jan, “Not a Tesla?”
ReplyDeleteINFINITY
ReplyDeleteI wrote I believe I've chased down the intended answer, but don't like the puzzle because the young actress Chase Infinity has made a name for herself this year.
I wrote that I don't like the puzzle because I don't like the puzzle. Because Infinity is not a number.
So I sent in Infinity, then lodged a formal complaint with the Boss. But what do I know, I just work here.
Infinity is a number. If it is not a number, what is it?
DeleteWhat is infinity? Well, the answer is different in ordinary usage than in mathematics. In plain English, it's something like "a quantity more than any number". But in mathematics, people discovered that there are different levels of moreness, so the word "infinity" is rarely used because you need to be specific about which level.
DeleteNot so different. Webster's defines infinity as "an indefinitely great number or amount" and "the limit of the value of a function or variable when it tends to become numerically larger than any preassigned finite number". In other words, infinity is a number that is greater than any finite number.
ReplyDeleteRight, but "indefinitely great number" isn't a number. It's indefinite. Numbers are definite.
DeleteIf someone asks you how many Will Shortz puzzles you have solved, and you say, "A whole lot," or "a great number", your answer isn't a number.
As for "a number that is greater than any finite number..." There are a lot of those, that's the point that some of us were making above. There's ω, that's the first transfinite ordinal. There's ω+1; unsurprisingly it's the second transfinite ordinal. There's ω+2, ω+3... you get the idea. And there's 2ω, and 2ω+17, and 17ω+86...
There are a lot of ordinals. A whole lot.
Dictionaries and mathematicians say infinity is a number. That is good enough.
DeleteThese puzzles have some flexibility in use of definitions. If some people consider infinity a number, that is good enough to justify a puzzle.
Numbers can be quantified. How can you quantify infinity?
DeleteHow can 0 be quantified? How can -1 be quantified? There are whole math books on how to deal with infinity.
DeleteToday’s Puzzle…
ReplyDeleteWhat’s the difference between Mitch McConnell and Schrödinger’s Cat?
You can look to see if the cat is dead or alive!
Jeff
I like it so very much!
DeleteINFINITY
ReplyDeleteYes, there has been some debate over whether or not infinity is actually a "number" by definition. I'm just glad it actually came to me later in the day Sunday. I did notice somebody else here found NONEVENT in those numbers, too. First word I thought of, actually.
pjbSawThereAreAlsoSimilarPuzzlesOnThisWeek'sPuzzleria!(MostLikelyHeWon'tFindThoseNumbers,Though)
Adding my two (finite) cents worth..
ReplyDeleteThe reason why infinity isn’t considered a number is that a number has a specific value. 50, is different from 60, 70, e or Pi, each having a unique value. Infinity has no specific value.
Also, infinity doesn’t obey the normal rules of arithmetic. When you add two numbers together, you get a new number; when you add 1 to infinity, the result is infinity..
Nor can one discover the square root of infinity. And how about trying to divide infinity by 3? The more I try, the number I become.
DeleteWhen you say infinity does not obey the usual rules of arithmetic, you are conceding that it is a number. -1 is a number, but it has no real square root.
DeleteIf the puzzle had said the answer was something that is considered a number in some but not all areas of math, that would have been accurate.
DeleteInfinity is considered a number in all areas of math.
DeleteAnd Trump is considered a successful businessman.
DeleteOkay, you are trolling.
Delete"No, infinity is not considered a number in all areas of mathematics. As there is a consensus among users on Mathematics Stack Exchange, infinity changes its role depending on the branch of math you are using. It acts as a standard number in some advanced systems, but only as a conceptual idea in others." https://www.google.com/search?q=is+infinity+considered+a+number+in+all+areas+of+math&rlz=1CABBMB_enUS1011&oq=is+infinity+considered+a+number+in+all+areas+of+math&gs_lcrp=EgZjaHJvbWUyBggAEEUYOTIHCAEQIRiPAjIHCAIQIRiPAtIBCTM0NTYyajBqN6gCALACAA&sourceid=chrome&ie=UTF-8
DeleteIf I had given a clue here, it would have been, "Reminds me of when my nan was visiting", since NAN is used in computer science to mean 'not a number'.
DeleteI can't resist commenting late on the debate. In my experience, *no* area of mathematics treats 'infinity' simpliciter as a number. When we write that some integral = infinity, we are always told that this is syncategorematic shorthand for 'the integral diverges, is not defined, and in particular, successive approximations become ever larger'. If successive approximations become ever smaller (negative), we write that the integral = -infinity, but again, officially, this is shorthand for just a certain way of being not well defined. It is not by mathematicians regarded as a number. As someone astutely observed, what one often means by infinity is the first infinite ordinal, omega, or the first infinite cardinal, aleph_0, which are usually identified with each other. The observation that infinity does not obey the normal rules of arithmetic is very relevant here. When he first discovered his "symbols of infinity" that eventually became the ordinal numbers, Cantor refused to call them numbers at all until he had discovered their structure and their peculiar rules of arithmetic. He needed to know that at least they had rules somewhat similar to ordinary numbers, though indeed different. And again, even after renaming his 'anzhalen' to 'ordinal numbers', he would not call his "powers" cardinal numbers until he understood their structure and peculiar arithmetic. But there are systems within which infinite numbers *do* obey the ordinary arithmetic of real numbers. You can find this for example in non-standard analysis and numerosity theory. While Cantor's theory of infinity is still dominant, many different conceptions of infinity are possible and internally consistent. There is even a fringe philosophical view that in fact, there is only one size of infinity, and this is also a coherent if perhaps limiting point of view. Under that conception, I think it would be very reasonable to call infinity a number: It is the number of elements in any infinite collection. So I think mathematicians have been overzealous about insisting that infinity is not a number. After all, there are no precise rules for what does and does not count as a number, and the wide field of different kinds of numbers has been expanded many times. But I also think it is just a sociological fact that the people most educated on infinity, namely, philosophers and mathematicians, almost universally deny that "infinity" is itself a number. So if there is any standard, authoritative answer to the question whether infinity is considered a number, it's not, and it would only be under a fringe view or a somewhat generous interpretation (omega, aleph_0) that "infinity", unqualified, *should* count as a specific number.
Nonetheless, I thought it was a cool puzzle, a nice observation, and when I found the answer, I understood.
DeleteYeah, the problem didn't get in the way of solving the puzzle at all.
DeleteThis week's online challenge comes from Ben Bass, of Chicago. Think of a state capital and say it out loud. Change one vowel sound in it to name something many schoolkids study. What things are these?
ReplyDeleteAnother childish puzzle anyone could solve in a moment.
DeleteThere's a little joke that would make a decent clue, but I think it would be TMI.
ReplyDeleteBut I'll be somebody makes it here. Maybe they can disguise it well enough to avoid TMI.
Really?
ReplyDeleteActually I do have it. It's pretty easy. Waiting for Blaine...
DeleteEasy. You can also get something lots of kids study by changing a non-vowel sound.
ReplyDeleteThis should have read, you can also get something lots of kids study by changing a non-vowel sound in another capital.
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