I'm not sure how to clue this... but I'm going to say 865 or 2619.Q: This week's challenge is s a numerical challenge for a change. Take the digits 2, 3, 4, and 5. Arrange them in some way using standard arithmetic operations to make 2,025. Can you do it?
Edit: One possible order to the digits is 3452. The prime factorization of 3452 is 2² x 863. Adding the unique prime factors gives 865.
Another possible order is 5234. Its prime factorization is 2 x 2617. Adding the prime factors gives 2619.
A: If you just take the prime factorization of 2025, you have the answer.I'm sorry to everyone for the times I had to use my moderator powers.
3⁴ x 5² = 2025, or 5² x 3⁴ = 2025.
Note: You could also just use 25 in place of 5²
(3⁴ x 25 or 25 x 3⁴).
One comment I hated to delete was the one about the sum of the cubes of the first 9 integers. (1³ + 2³ + 3³ + ... + 8³ + 9³ = 2025). It also included the related fact that the sum of the first 9 integers squared gets the same result (1 + 2 + 3 + ... + 8 + 9)² = 2025.
This is actually true for the first 'n' integers that the sum of the cubes is the square of the sum. (1³ + 2³ + 3³ + ... + n³) = (1 + 2 + 3 + ... + n)².
Here's a visual proof for the first 5 integers.
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ReplyDeleteI guess so. But it's such an obvious approach.
DeleteThis comment has been removed by a blog administrator.
ReplyDeleteARGH! That's the only clue I was able to come up with, and now you've fricken taken it.
DeleteSolved, but I think I've haven't strictly followed the criteria.
ReplyDeleteThis comment has been removed by a blog administrator.
DeleteI can get to 2025 easily using the 2 4 and 5....what do you do with the 3 ? Is the comma a clue?
DeleteThis comment has been removed by a blog administrator.
ReplyDelete"Over 1000" correct entries this week. (How many significant digits in that number, I wonder?)
ReplyDeleteEveryone, please read the guidelines below. "You may provide indirect hints to the answer to show you know it, but make sure they don't assist with solving."
ReplyDeleteSorry, Blaine. I will try to make it up to you.
DeleteHard to clue. Say the answer in words. If you rearrange the last letters of the words the way _I_ say them, you get two words for a boon a florist might give.
ReplyDeleteHas anyone else noticed how useless ChatGPT is on this?
I remembered your comment from last week and went from there.
DeleteI tried both ChatGPT and Gemini and they both gave wildly incorrect answers with basic incorrect addition. Perhaps these programs are actually smarter than that and trying to lower humans' expectations so they can more easily take over the world.
DeleteIt took Chat GPT a long time for me. Had to give some hints.
DeleteOh, wow.
ReplyDeleteOkay, I think Blaine is right to be very strict. Even a small hint can go a long way in this one. (Although I've liked the clues I've seen! Didn't see Jan's before it disappeared.)
I like the puzzle. The solution is quite elegant. I do wish Will (or the NPR Puzzle web page) had been a bit more explicit about which arithmetic operations are 'standard'.
Agree about "standard" operations. Also, it wasn't immediately clear to me if the numbers could be used more than once.
DeleteOr not used.
DeleteI have an answer that works. As I can see by the number of comment removals, providing a clue will be more difficult.
ReplyDeleteI would also appreciate if NPR/Will had provided what is permitted within "standard" mathematical operations. Multivariable calculus and trigonometric functions are standard in some fields of work.
DeleteI see a lot of comments that have been beaten by the stick of the blog administrator. Careful what you say, folks!
DeleteTrying again….
ReplyDeleteThere are several possible solutions, but only one, which, admittedly, can be expressed in different ways, meets all of Joe’s criteria.
The year-in-review puzzle used to be a lot harder when Will just gave the names of the people who had their moments in the sun. I like the easier version. Speaking of review, that's a good strategy for Blainesvillians looking to solve Lego's nice mathematical puzzle.
ReplyDeleteNeed clarification. Use each of the four digits once, or mutiple times ?
ReplyDeleteAll four digits, used exactly once.
DeleteTo be fair the question does not instruct that they be used only once each, but I do believe that was implied for the intended answer. But someone is fond of pointing out information that wasn't in the text!
DeleteIf you could use them more than once there would be hundreds of correct permutations.
A useful and important fact for the solution of this puzzle is almost elementary, and first stated amicably.
ReplyDeleteSolved.
ReplyDeleteThis comment has been removed by a blog administrator.
ReplyDeleteThat's probably TMI
DeleteThis comment has been removed by a blog administrator.
DeleteThanks, JAWS. I didn't think it was tmi either!
DeleteWW's comment pointed me to the answer
DeleteHart-less.
DeleteYes, deer.
DeleteI re-read/saw the puzzle exactly as Will said it, on the npr site. He said ALL digits needed to be used— but he did NOT say they could be used only once. If that’s what was intended, I respectfully suggest that should have been made clearer, stressed more strongly. I agree that there might be some confusion.
ReplyDeleteAnd HNY to all!
Thank you, Diz.
DeleteAll four digits need to be used, but each but once.
LegoWhoGivesTheThumbsUpToFourDigits:1.)IndexFinger2.)Middle(Or"Avian"AsILikeToCallIt)Finger3.)RingFinger4.)PinkyFingerButWhoIsOpposedToThatFifthDigitKnownAsTheOpposableThumb(WhichIsIronicForSomeOneWhoBeganThisSillySignOffByGivingYouAllTheThumbsUp!
Oh, so my answer with 404 "+" signs was no good. Darn. All that wasted typing. :)
ReplyDeleteI’m reminded of one of my favorite songs from 1964-65.
ReplyDeleteAnd Hershey’s…
Congrats once again, lego!
Not a favorite, but I was thinking more like 1986.
DeleteHuh, I was thinking 1975 and 1989! But I wouldn't fight about it.
DeleteHip to be Square. Somewhat of my life’s motto.
DeleteHey, I’m an English professor trying to solve a math problem. The definition of pathos😁😁!
ReplyDeleteSo was I.
DeleteIn my case, solving it was probably dumb luck, although a little logos didn't hurt.
I wonder how Dr. Awkward is doing....
Now you know how I feel as a former math professor trying to solve language problems each week!
DeleteI had to call on my more mathematically-inclined sister!
DeleteI’m an English professor, trying to solve a math puzzle: the definition of pathos!!
ReplyDeleteSorry about duplication of comment—I sent just once, but it appeared again. Mea culpa.
ReplyDeleteI could name a certain game show, but I fear that would get deleted, too.
ReplyDeleteThis is a difficult puzzle to clue. I have but a small contribution to make: the digits do not appear in numerical order.
ReplyDeleteAnd I forgot to say, Congratulations, Lego. You've added to your already high batting average with Will :)
ReplyDeleteHm. Now modify your solution to use the digits 1, 2, 3, 4, and 5 each exactly once.
ReplyDeleteI was just about to say that it might have been a tad more elegant to state the puzzle as, "Take the digits 1 through 5 . . . ."
DeleteYes, though afaik there might be non-trivial new solutions using the "1" ...
DeleteThis comment has been removed by the author.
ReplyDeleteI saw a picture of a phonograph with the caption, "If you were born in 33, you were 45 in 78."
DeleteNow that's a puzzle idea, jan!
DeleteTry: If you were born in 33, you were __ in '__.
or: If you were born in __, you were 45 in '__.
or If you were born in __, you were __ in '78.
Fill in the blanks with two missing numbers that are associated with the third.
LegoWhoSuggestsThatjanDeleteHisPostThenI'llDeleteMineAndThenjanWillSendThePuzzleToWillWhoWillHappilyUseItOnNationalPublicRadioAndInTheMeantimejanAndIShallDeleteOurPostsButNotBeforeScoresOfBlainesvilliansHaveReadThePuzzleAndWillSubmitTheirCorrectAnswersAndPlay"ThePuzzle"OnAirWithWillAndAyesha!
For the sake of clarity: Are only +,-,*,and / allowed and can the numbers be combined? Can you use 54 as a number for example?
ReplyDeleteThis comment has been removed by a blog administrator.
DeleteIt doesn't say. If you are getting stuck, keep questioning your assumptions.
DeleteThis comment has been removed by a blog administrator.
DeleteSeems like this puzzle is more about "can I guess the rules" vs. am I good at math.
DeleteRG The puzzle is a a fair one, no tricks involved. The operations are all usual arithmetic/algebra ones.
DeleteI'm not a math enthusiast, but I came up with a couple variations that work
ReplyDeleteThis comment has been removed by a blog administrator.
ReplyDelete3^4*5^2 is the prime factorization of 2025.
DeleteAnd Blaine noticed that too.
DeleteAs did I. My clue was:
"A useful and important fact for the solution of this puzzle is almost elementary, and first stated amicably."
Euclid, in his *Elements*, almost stated and proved the Fundamental Theorem of Arithmetic, aka the Prime Factorization Theorem.
But an actual proof didn't come until Kamāl al-Dīn al-Fārisī published his number theory book, *Tadhkira al-ahbab fi bayan al-tahabb* ("Memorandum for friends on the proof of amicability").
Since we are talking about dates, and attaching significance to the order of numbers, I have to bring up the opening chapter of "The Confessions of Zeno" by the "real" Italo Svevo (although his name was actually Aron Schmitz) in which he discusses his attempts to give up smoking:
ReplyDeleteThat disease brought me the second of my afflictions: the effort of freeing myself from the first one. . . . On the frontispiece of a dictionary I find this beautiful written and somewhat ornate inscription:
«Today, February 2, 1886, I changed from the study of law to the study of chemistry. Last cigarette!!».
That was an important last cigarette. I remember all the hopes that accompanied it. I was fed up with the legal canons that seemed so far removed from life and ran to science, which dealt with life, although reduced to a test tube. That last cigarette signified my desire for a life of activity (and manual work) and for serene, sober and hard thought.
I later returned to the law in order to escape the chain of the combinations of carbon which I could never comprehend. . . . That was an error which was also celebrated with a last cigarette which I memorialized by recording the date in another book. . . .
Once, when I changed rooms as a student, I had to pay for the recovering of the walls of the room because I had covered them with dates. I probably had to leave that room because it had become the cemetery of my good intentions; I did not believe that it would be possible to form any new plans to replace those that had gone before them. . . .
The dates on the walls of my room were inscribed in various colors and also in oils. The resolution, repeated each time with even more naive faith, expressed itself in the force of the color that had to outshine the one that had gone before. Certain dates appealed to me because of the harmony of the numbers. I remember one date in the last century memory of which seemed to seal the coffin into which I wanted to put my vice: "The ninth day of the ninth month of 1899." The new century brought me particularly musical dates: "The first day of the first month of 1901." Even today it seems to me that if that date could return, I would know how to begin a new life.
But there is no shortage of dates in the calendar and with a little imagination it was always possible to find some that had a certain balance. I remember, because it seemed to me contained a supreme categorical imperative, the following: "The third day of the sixth month of 1912, 24th hour." Each figure doubled the preceding one. . . .
Many of the dates that I recorded in books or on the backs of pictures stand out for their asymmetry. As an example, the third day of the second month of 1905 at six o'clock! It has a recognizable rhythm because every single figure denies the previous one. Many events, indeed all, from the death of Pius IX to the birth of my son, seemed to me worth celebrating with the usual iron resolution. Everyone in my family marvels at my ability to remember anniversaries, both happy and sad, and think I am such a good person for it!
(Thanks for indulging me with this ultima citazione.)
I found submitting the answer could be as challenging as the puzzle itself.
ReplyDeleteI have an answer where all numbers are used once. A math purest, though, would argue that a second 2 is needed.
ReplyDeleteNo, I think not (speaking as a math purest).
DeleteAny spelling purIsts thinking what I'm thinking?
DeleteSheesh, darn autocorrect!
DeleteI do believe I've solved it! And this conversation confirms my answer. I think one has to be a real nerd to get it.
DeleteMaybe nerd isn't quite the right word. But I think iykyk.
DeleteI was thinking (3^(sqrt 4) x 5)^2 and my thinking was “why does 4 get a special operation to turn into a 2?”
DeleteThis comment has been removed by a blog administrator.
ReplyDeleteGood puzzle, Lego. A welcome respite from lists and anagrams.
ReplyDeleteHappy new year to my fellow bloggers….. The operation(s) I used for my answer conjure(s) up a place that would make this a rather apt puzzle.
ReplyDeleteOut of curiosity, can you use parenthesis in the solution?
ReplyDeleteOr do you have to come up with a solution that follows PEMDAS?
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DeleteAnything you see in a math equation is fair game.
DeleteWhat's the record for greatest quantity of post deletions in one thread?
ReplyDeleteSurely this week is in the running for most deletions.
DeleteI think Blaine needs to delete some posts in last week's blog, from before the new puzzle was posted!
DeleteYes, and more here today. Let's smash that deletion record!
DeleteThis comment has been removed by the author.
DeleteGood question. Does anyone know?
DeleteThis week, there are 15 deletions thus far.
Make that 20 deletions thus far.
DeleteReminds me of that Disney movie: One Hundred and One Deletions.
DeleteWell spotted, SDB.
DeleteCrito, I am laughing now because I was anticipating using that exact response if someone corrected my above spelling. So congratulations to beating me to it.
DeleteYears ago a coworker told me how unhappy her son was with his school photos because they made him look unnaturally pale. "They make me look like an Albanian!" he complained.
DeleteTo which I responded, "At least he doesn't look like a Dalmatian."
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ReplyDeleteBlaine?
ReplyDeleteWe just accepted a new horse for boarding, and one of the resident horses lunged for the newcomer. I think I heard my wife mutter, “Darn equines.”
ReplyDeleteGadsby
ReplyDeleteI certainly don't mean to slight Mr. Young, but I don't do math puzzles. I'm sure there is a clever way to get the answer, but I'm not about to get involved. If this were Puzzleria!, I would definitely ask for hints in my first post on the blog. But since the blog administrator is on the loose this week, I fear I couldn't do this one if I wanted to. To paraphrase Samuel Goldwyn, puzzlers, include me out.
ReplyDeletepjbIsSureJosephHasANiceNumericalPuzzle,ButNoCanDoThisTime(Sorry!)
I have it...
ReplyDeleteThis comment has been removed by a blog administrator.
ReplyDeleteI love it!
DeleteI just solved it, too, it being the kind of fun I like to have with math.
DeleteVery nice, Mister E!
DeleteLegoogolPlexiGlassyEyedGiveItAnA+
I'm glad I got to enjoy Mister E's post before it was removed!
DeleteI think the number of correct answers will be lower than most people expect.
ReplyDeleteThis comment has been removed by a blog administrator.
ReplyDeleteI hope Blaine doesn't delete me. I'm going back to the universal clue -- e
ReplyDeleteAlways glad to see the universal clue! It's pretty much undeletable, since the connection can be made in so many unpredictable ways. Kinda like using Bob Dylan as a musical clue.
DeleteMovie Reference: Do The Right Thing
ReplyDeleteI know very, very little about math, but I believe I finally figured it out by trial and error.
ReplyDeletehttps://www.youtube.com/watch?v=TMdxow3-k04&t=8s
ReplyDeletehttps://www.iexitapp.com/New%20York/I-81/Exit%2025/27395
DeleteThis reminds me of an old hymn.
ReplyDeleteOf all the weeks in a year only one includes a day whose name is also a command.
ReplyDeleteThis comment has been removed by a blog administrator.
DeleteThis comment has been removed by a blog administrator.
Delete... and the birthday of a friend, she is very proud of its uniqueness!
DeleteThis comment has been removed by a blog administrator.
DeleteI don't like to lead, so I'll March 2nd.
DeleteThis comment has been removed by a blog administrator.
DeleteI do believe I heard that joke on "Laugh-In"!
DeleteIf so, it was... over a half century ago.
I think you’re right. As I said, an old joke.
DeleteI believe Robinson Crusoe could say it 4 or 5 times a year….
DeleteThe deleted dates in this thread remind me of May 35th.
DeleteIsn't that the day each year we all wonder what happened to May 32, 33 & 34?
DeleteIt means something else in China.
DeleteCome Thursday at 3pm EST, hopefully someone much smarter than me will explain all the deletions in this conversation. I'm really confused.
Deletejan, oh so good.
DeleteI'm so glad I could offer a clue which was not redacted. 52 weeks in a year (5 squared) times command day, March 4th, (3 to the 4th power) equals 2025.
DeleteMy solution procedure was a backward deconstruction, but I couldn't find the crucial first step until I saw a now deleted comment.
ReplyDeleteThis comment has been removed by a blog administrator.
ReplyDeleteMusical Clue: Clair de Lune
ReplyDeleteThis comment has been removed by a blog administrator.
ReplyDeleteAmericans are math phobic. Maybe a third of that, tops.
DeleteWith how many comments have been deleted, folks need to do a better job keeping the answer a secret.
ReplyDeleteAn elegant puzzle. Can be done with 3 numbers also.
ReplyDeleteRIP Peter Yarrow. I remember watching Peter, Paul, and Mary flub the lyrics to "Blowin' In The Wind" on the steps of the US Capitol, in the Spring of 1971, probably because they were as stoned as the rest of us there were.
ReplyDeleteOnly Paul now.
Deletejan, do you remember what they sang instead? Oh wait, no, of course you don't.
DeleteThey just mixed up the order of the verses.
Delete"The Amplifier," the Times'Tuesday and Friday music column (by Jon Pareles, this installment) is dedicated to the 1965 Newport Folk Festival, where Dylan scandalously went electric. The 15 tracks listed in the column (with links) include Peter, Paul, and Mary's "If I Had My Way" (Peter Yarrow, lead) and a rendition by ensemble, including Peter, Paul, and Mary, of “Come and Go with Me to That Land.”
DeleteThis comment has been removed by a blog administrator.
ReplyDeleteNaughty, naughty…
ReplyDeleteThere's no clue in there!
DeleteDoes anyone else see an omen in 2025?
ReplyDeleteDidn't Mae West say "Oh men!"?
DeleteI am so excited about our future now our newly elected leader is making plans to declare war on Denmark to put and end to their naked aggression. Why have none of our previous presidents had the courage to resolve this ongoing problem? Now I am thinking perhaps he should also consider an invasion of Monaco. After all, they must have lots of cash, and isn't that a critical resource we need to take over the world? Scotland may be taken soon after our glorious spoils are won. I hear Scotland has golf courses, and we could sure use more of those. Let's show our support and get those flags flying!
ReplyDeleteI haven't heard anything about a war over Greenland. I thought Trump was talking about buying it. with Denmark making pro forma protestations that it's not for sale. In fact, I'd bet the Danes would be thrilled to make some money while having us take the island off their hands. It's a drag on the Danish economy, with half the Greenland government revenues coming from grants from Denmark. My impression from the few episodes of Borgen that I watched is that Danes consider Greenland to be a cultural and socio-economic backwater.
DeleteI just finish an early dinner while listening to NPR as I was cooking and he said today he would invade to take it if he has to.
DeleteTrump probably thinks that Greenlanders are the blond Northern-European types he admires, rather than the darker multi-ethnic and Inuit type he avoids.
DeleteI am getting ready to sharpen my bone spurs.
Deletejan, did you intuit that Inuit post?
DeleteYeah, he definitely said he is "not ruling out military force."
DeleteHarry Truman offered Denmark $100M (in gold) for Greenland. I think that was not in the right ballpark. I read somewhere that the WSJ estimated the price of Greenland at about $6 trillion -- I didn't read it in the WSJ, but the estimate was attributed to them.
Let's combine two threads...
DeleteYou might want to read what Joyce Vance has to say re: Trump's war threats:
Deletehttps://joycevance.substack.com/p/whiplash?utm_campaign=email-half-post&r=40v6sn&utm_source=substack&utm_medium=email
This comment has been removed by a blog administrator.
DeleteSorry Blaine.
DeleteI may sound like I have a sore throat, but I'll ask anyway: the permitted operations in this week's puzzle include what? [Just to be clear, don't answer that; it's (I hope) a sufficiently obscure reference to my solution.]
ReplyDeleteWow, parentheses inside brackets. That reminds me of those letters to 60 Minutes.
DeleteMy hint relates to temperature.
ReplyDelete(3^4) (5^2) = 81 x 25 = 2025
ReplyDelete"Another fun fact about 2025?
45 x 45 = 2025" was pointing quietly to the POWER of numbers.
"Hart-less" points to Stefanie POWERS, the actress who played Jennifer Hart on Hart to Hart.
How many deletions did we end up with this week?
(3^4) deletions this week
Delete(3^4)(5^2) → (81)(25) = 2025</b)
ReplyDelete(5 ^ 2) x (3 ^ 4) or (3 ^ 4) x (5 ^ 2) = 2025
ReplyDeleteLast Sunday I said, “This is a difficult puzzle to clue. I have but a small contribution to make: the digits do not appear in numerical order.” And as you can see from the answers above, with the multiplication terms in either order, the digits are not in numerical order.
Concerning this kind of puzzle, I wonder what percentage of listeners know what exponentiation is, much less how to express it. Although many computer languages use the upward pointing caret as their standard exponentiation symbol, I believe the usual way of denoting an exponent is by using a superscript. Unfortunately, the NPR messaging system doesn’t know about superscripts – it changes them into normal digits so if you print an equation out, it gives you a funny-looking and wrong answer.
Anyway, congrats to Lego for a timely, non-alphabetical puzzle!
I’ve been preoccupied with the LA fires. My brother lives in an assisted care facility in Torrance and my nephew lives in San Pedro. Both are less than an hour south of the area.
Chuck, I don't know if you will even see this comment, but I know what you mean. My (older) son lives only about six miles east of Santa Monica, so I believe that is even closer than you are describing or your brother and nephew.
DeleteWell I hope all your family and all of mine remain safe. These huge fires destroy everything in their path.
DeleteYes indeed, Chuck. I hope likewise....so far so phew!
Delete(3^4) (25) = 81 x 25 = 2,025
ReplyDeleteHint: “I’m reminded of one of my favorite songs from 1964-65.
And Hershey’s…”
—> Candy and the Kisses’ “The 81”
Hint: “We just accepted a new horse for boarding, and one of the resident horses lunged for the newcomer. I think I heard my wife mutter, ‘Darn equines.’” (The first sentence was true; the second was not, though she did mutter something else.)
—> “Darn equines” is an anagram of “nine squared."
And, after the fact, I understood why Blaine removed my “old joke.”
Sorry, Blaine.
Overall this week, I counted 22 removals by Blaine. Does anyone know whether or not that's a record?
In any case, congrats again, lego!
My answer was 3^4 * 5^2
ReplyDeleteMy two clues:
-- e, the "universal clue," which relates in this case to "exponents," the key operation
-- Claire de Lune, my "musical clue." Claire de Lune was penned by Claude Debussy. Claude's initials are (kinda) C DEB
And C DEB codes to 3452
Which hints at my answer -- 3^4 * 5^2
3^4 x 5^2 =2,025
ReplyDelete(3^4)*(5^2)=2025
ReplyDeleteI wanted to post a hint pointing to the very old joke about a young boy seeing a motorcycle cop wearing jodhpurs and asks, "What manner of men are these who wear their balls in parentheses?" However, I thought it would be TMI and join the flock who got removed by the Grim Deleter this week.
3^4 x 5^2
ReplyDelete> Is factorization TMI? [Deleted]
I guess so. But it's such an obvious approach.
>> Solved, but I think I've haven't strictly followed the criteria.
> Yes. The operation you are questioning is considered arithmetic. [Deleted]
Really? All I said was that one of the operators (I didn't mention exponentiation) involved might incorrectly be thought not to be arithmetic.
> Sorry, Blaine. I will try to make it up to you.
Max Factor is a brand of makeup.
> I could name a certain game show, but I fear that would get deleted, too.
Does the blog administrator Fear "Factor"?
>> Out of curiosity, can you use parenthesis in the solution? Or do you have to come up with a solution that follows PEMDAS?
> One of those letters is TMI... [Deleted]
So, simply referring to the letter E (for exponentiation) (among five other letters) is going over the line?
> Gadsby
A 1939 novel by Ernest Vincent Wright, written without the letter E. Solved that problem!
> I think Blaine needs to delete some posts in last week's blog, from before the new puzzle was posted!
Last week's blog included two mentions that 45 squared is 2025, which got deleted this week when Word Woman posted it.
Given the number of comments that were deleted, I am somewhat surprised that the PEMDAS comment to which you were replying was not deleted.
DeleteMe too
DeleteEconfusions returns this week to Puzzleria! Our friend Ecoarchitect (designer of elegant structures as well as elegantly structured conundrums) has created nine crafty word puzzles for us that he has dubbed “Ooh Baby, Baby, it’s a Wild Word…”
ReplyDeleteWe will upload Puzzleria! sometime very soon, this very afternoon!
Also on our menus this week are:
~ a Schpuzzle of the Week titled "News from around the globe!"
~ an Artistic Trio Hors d’Oeuvre titled "Pictures at an Exhibition,"
~ a Literary Slice titled "Objectionable adjective,"
~ a Verbal Evaluation Dessert titled Alphanumeric Synonymity, and
~ 11 riffs of this week's NPR Puzzle Challenge titled "Reviewer: Huff & Otto."
We invite you to join us in a bit of refreshing "Nuclear Ecoconfusion!"
LegoWhoThanksAllWhoCommentedOnMyNPRMathPuzzleAndWhoPraisesTheEverStalwartBlaineForHisBlogAdministrativeDiligence!
I wrote, “Say the answer in words. If you rearrange the last letters of the words the way _I_ say them, you get two words for a boon a florist might give.” That’s “Twenty-five times three to the power of four,” with last letters rearranged to FREE ROSE.
ReplyDelete3^4*5^2=2025
ReplyDeleteI was never good at math, but I thought I had cleverly solved it: 52-3-4 squared. (If you say "squared" aloud, you don't need the extra 2.) Well needless to say, I feel pretty stupid now that I know the solution. When I said you have to be nerd to solve it, I was thinking you have to be a square.
ReplyDeleteAs Dr. K used implicitly, 5^2 is 25 ... a non-trivial fact, so his can formally be considered a different solution: (3^4)*25 = 2025
ReplyDeleteStrictly speaking, the answer can be written using no mathematical symbols at all, using the usual raised numbers for the exponents and concatenation for the product. I was going to point that out, but it would surely have been deleted. Kudos to Rob for anticipating the puzzle last week with his mention of Nicomachus's Theorem (nicely documented by Blaine above).
ReplyDeleteOops ~ my sister is an MD, and her name starts with K, so replace "his" with the gender-neutral equivalent.
ReplyDeleteI'd like to see Leo's three number solution.
ReplyDeleteHe may mean 45² = 45^2 = 2025.
DeleteI asked "Does anyone else see an omen in 2025?" DJT became the 45th President in 2017. Does his returning to power mean that we will see 45 squared (whatever that might mean) in 2025?
ReplyDeleteMy clue - “Happy new year to my fellow bloggers….. The operation(s) I used for my answer conjure(s) up a place that would make this a rather apt puzzle” - the new year’s greeting and additional clue were referring to Times Square- which are two of the operations used to solve this puzzle!
ReplyDeleteNice!
DeleteMy post Blaine deleted while on his (to-the-fourth-)power trip:
ReplyDelete"This is the first time I can remember that my answer in the NPR confirmation email was not the answer I submitted."
OBVIOUSLY, I confused the text box on the Submit Your Answer site by including a superscript character and it came back as "3? x 25 = 2025." Sincerest apologies to the multitudes of you led directly to the correct response by the transparency of my clue. My feelings of shame and regret have increased in severity with each passing day exponentially.
Yet oddly, my comment that submitting an answer was more difficult than the puzzle itself was allowed to stand.
DeleteI probably will add nothing new to this forum except confirmation of the correct answer. The thing to break down 2025 is the fact that it's divisible by 3 and 5. Any number is divisible by three if the digits add to 3, as they do in 2025. Naturally, any number ending in 5 is divisible by 5. It came down to 25, 5 to the 2nd power, times 81, 3 to the 4th power. Oh well...
ReplyDeleteThat is, if the numbers add to a number divisible by 3.
DeleteI just went 45 to the 2nd power (squared); round to the nearest multiple 3 4 5 2 and 3 to get 2025. No phone call though.....eeyore.
ReplyDelete5 to the fourth = 625 x 3.24 = 2025
ReplyDelete3^4*5^2 = 2025
ReplyDeleteMy hint: This reminds me of an old hymn.
What came to mind was "There is power, power, wonder-working power"
My hint was "I may sound like I have a sore throat, but I'll ask anyway: the permitted operations in this week's puzzle include what?"
ReplyDeleteThis had two indirect allusions to power: sounding like a sore throat is hoarse, which may make one think of horsepower, and "what" sounds like "watt" (with apologies to those who pronounce initial "w" with a following "h" differently from initial "w" without a following "h").
By the way, that's two completely different horse references in the hints that have appeared here, namely mine and Dr. K''s.
DeleteI had said, "I see a lot of comments that have been beaten by the stick of the blog administrator. " The opposite of the stick is the carrot, which is a homophone of carat, which is the standard symbol in spreadsheets (like Excel) to indicate exponents.
ReplyDeleteI also commented that It thought there would be a lower number than expected correct answers. There were two reasons for this. One was that some submissions would get caught up in the NPR website problem, where superscript text could get messed up.
The second reason was that the puzzle finished with the question, "Can you do it?" I pointed out in my submission that a correct answer should answer that question, so my submission started with, "Yes, I can." I suspect most answers did not include that.
A reminder to all that we're just 3 comments away from the 200 comment limit. You will have to scroll to the bottom and click on "Load more" to see newer comments (even in the middle of the blog).
ReplyDeleteAlternate solution: (5 x 3^2)^√4
ReplyDeleteThis week's challenge comes from listener Greg VanMechelen, of Berkeley, Calif. Think of a well-known international location in nine letters. Take the first five letters and shift each of them 13 places later in the alphabet. The result will be a synonym for the remaining four letters in the place's name. What place is it?
ReplyDeleteCongrats again, ecoarchitect!
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