I'm a little annoyed that the example doesn't follow the order of operations and instead must be performed left to right. It would have to be (1 + 23) ÷ 4 x 5 x 67 - 8 + 9 to work correctly in most calculators.Q: This week's challenge is a numerical one. Take the nine digits -- 1, 2, 3, 4, 5, 6, 7, 8, 9. You can group some of them and add arithmetic operations to get 2011 like this: 1 + 23 ÷ 4 x 5 x 67 - 8 + 9. If you do these operations in order from left to right, you get 2011. Well, 2011 was 15 years ago. Can you group some of the digits and add arithmetic symbols in a different way to make 2026? The digits from 1 to 9 need to stay in that order. Will knows of two different solutions, but you need to find only one of them.
I have one expression that works either way, three expressions that work left to right and one that only works using the standard order of operations. I have a feeling that Ed Pegg Jr. provided the two that work using the standard order of operations.
My only hint is 390,625.
I can't imagine how to clue something like this.
ReplyDeleteNor can I... so I guess we'll just post answers on Thursday?
DeleteIf the numbers were reversed:
Delete9+8*7+654*3-2+1 = 2026 | PEMDAS
9*8-7+654*3-2+1 = 2026 | PEMDAS
9*8*7+6-5*4+3+2+1 = 2026 | Left-to-Right
98+76-5*4*3-2*1 = 2026 | Left-to-Right
98+76-5*4*3-2/1 = 2026 | Left-to-Right
To hell with math puzzles. Talk with you all next week. I'm not going to spend any more time on this one! No clues, just the truth!
ReplyDeleteMaybe you're just standing up for PEMDAS and refusing to ignore it?
DeleteSam Cooke- Wonderful world " Don't know much about trigonometry"
DeletePlease excuse my dear pseudonymic Clark
DeleteI posted the same annoyance at the end of last week's thread, Blaine.
ReplyDeleteAlso I was going to give one of the clues/remarks you gave as my clue, but I was afraid it was TMI!
I'll post my answer (which I'm almost sure is one of Blaine's) on Thursday.
I like math puzzles and wish Will would give more of them, but as I said at the end of the last thread, this type of math puzzle is like an anagram puzzle. It's not terrible to muse over it for a while, but ultimately it's pretty boring and not very creative. EPjr, I expect more.
Just 236 correct answers last week
ReplyDeleteAnother year that I'm happy to be among the 235. Names in the News scares me every time. (Maybe because I avoid the news more and more...)
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ReplyDeleteMath has rules in the order of mathematical operations… the example flouts those rules..no hint here .. just frustration..
ReplyDeleteEd Pegg Jr.’s 2011 example works using “Reverse Polish Notation” (RPN) found on HP scientific and mathematical calculators. He should at least have warned us.
ReplyDeleteAnd if you reverse RPN? 😉
DeleteI don't think the left-to-right or RPN stipulation were Ed's doing. I think Will introduced it in his example, and misunderstood Ed's two PEMDAS solutions. As a result Will's changed the puzzle. Fortunately, his revised puzzle has 4 solutions so it can still be solved.
DeleteHard to clue. In my solution, the largest number is associated with a southern state.
ReplyDeleteI don't know if I'll bother to try to solve this one or not. But as far as the on-air puzzle is concerned, I didn't know about the Japanese person and I forgot you-know-who's birth name. But I could have talked on and on about the nameless raccoon, whose story cracks me up!
ReplyDelete(I'm being deliberately vague about the two answers I got wrong to be spoiler free in case anyone listens after reading this.)
I7
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DeleteThough I didn’t see it at the time, I can see now that my remarks would have been better left unsaid. I apologize to Blain and all here.
DeleteMake that Blaine :)
DeleteI'm surprised by the deletions. Without giving anything away, I'm allowed to post that I got the answer from my big brother, but not that I got the answer from Big Brother?
DeleteHappy MVI + DX * C/L
ReplyDeleteI did it! And it works according to the order of operations! It's all x, + and -. The largest numbers are only two digits
ReplyDeleteMy solution uses those three operations too. Maybe the other one uses division, but I don't know as I haven't found it yet.
DeleteSame here.
DeleteI've solved it, but it strikes me as a disappointing puzzle. And another disappointment: While Will did mention "lots of answers" to last week’s puzzle, I’m especially sorry he did not specifically mention the "esse" solution, which thoroughly satisfied the puzzle’s criteria.
ReplyDeleteDr.K-
DeleteI came across "esse" myself while perusing a seven letter word list, looking for four letter words in two syllables, but as I explained on thursday, did not believe it qualified as being valid, but now realize it is. When I still thought it was valid I thought about emailing Will Shortz to advise him. I have done so in the past, and he has thanked me for so doing. I suspect he may not have been informed of your "esse" answer. Keep in mind it has only been 39 years now that NPR has been running their weekly puzzle bit, and they most likely have not had time to work out all the kinks yet.
Thanks, sdb. I appreciate it. I don't think anyone has ever figured out exactly what takes place between submission and selection. It's probably something we'll never know.
DeleteI’m great with anagrams, but can’t deal with the math puzzles. Not that I’m bad at math, just that I don’t find those kinds of puzzles interesting. So I’ll give this week a bye.
ReplyDeleteI have a solution. It was ho hum getting there.
ReplyDeleteAnyone know why Polish Notation (and the later Reverse Polish Notation (RPN)) is named after his nationality rather than the logician/philosopher Jan (nod to our jan!) Łukasiewicz?
Easier to spell!
DeleteGaah. Learning to spell someone's name? It's not that hard. Almost like puzzlers saying they don't do math puzzles.
DeleteI've had parents tell me they "don't do math" so they can't help their kids with math. I'd say "Well, I don't do reading." and smile a sardonic smile.
Ł u k a s i e w i c z
Ł u k a s i e w i c z
Ł u k a s i e w i c z
1, 2, 3, 4, 5, 6, 7, 8, 9
Smiling away. . .
Hey are you leading a cheer??
DeleteGotta be the least interesting football team in history.
As opposed to the Sicilian Defense, popularized by Gioachino Greco (né Cusentino�)--who was not Greek, despite the nickname he was given, nor Sicilian (he was from Calabria, hence his other nickname "Il Calabrese").
DeleteWhat does all this prove? That I haven't got a clue about this week's puzzle--which I mean idiomatically, not literally.
Pietro Carrera first, though. 1617. He was Sicilian.
DeleteIn "Katabasis", R F Kuang claims that all Magick grad students are into chess. I don't usually read fantasy, but I'm enjoying this one. A little Harry Potter Goes To Grad School, and a lot Harry Potter Goes To Hell. Here's a line I liked: The protagonists, Alice (like the girl who went down a rabbit hole) and Peter (like the rabbit), newly arrived in Hell (via a spell, not dead), are getting a tour of a huge academic library in the First Circle (Pride). Their guide disses the various Shades they pass: "Now, that one keeps saying he went to school in Boston and expecting everyone to know what he means. Every few years the other Shades gang up on him and brick him up behind the stacks."
DeleteI stand corrected. Let me atone by sharing my mother's second favorite joke:
DeleteA recently deceased soul is being led to his place in Hell by a demon. As they walk down a long hallway he asks the demon who is behind a door they have just passed. "Oh, that's Jews who mixed meat and dairy." "And that room?" "Muslims who drank alcohol." "What about that room?" "Catholics who ate meat on Friday." "And who's in that room?" "Episcopalians who used their salad fork for their entree." [https://www.youtube.com/watch?v=g-4-gLlF0uw]
I have a solution that works whether you use PEMDAS or do the operations in order.
ReplyDeleteMe too.
DeleteAnd so does Blaine.
Moi aussi.
DeleteMe too. But I am not particularly interested in finding the other one.
DeleteSame here.
DeleteYessiree, Bob!!!
Deletenot my cup of tea, but enjoy, y'all!
ReplyDeleteI do not enjoy winter; cold weather makes me numb. Brrr!
ReplyDeleteI was on the road all day. Got home a few hours ago, and after eating, and putting some stuff away, I figured out a solution in about 15 minutes. My solution follows PEMDAS, and has two prime numbers in it.
ReplyDeleteSame here.
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