Q: What number comes next in the following series: 2, 4, 6, 9, 11, 15, 20, 40, 51*, 55*, 60 and 90?See, I thought I had the answer to this, but if so, there are a couple numbers missing.
*Update: The consensus seems to be that Henry Hook and Will Shortz overlooked a couple terms in the sequence and it should be 2, 4, 6, 9, 11, 15, 20, 40, 51, 55, 60 and 90. Hopefully everyone is able to solve it now with the corrected wording. If anyone has direct access to Will's email, perhaps they could ask for a similar correction to the puzzle on the NPR website.
Will Shortz has confirmed (see his comment) that he extended Henry Hook's original series (2, 4, 6, 9, 11, 15, 20) and in the process overlooked the numbers above. The NPR website has been updated as well. Thanks to everyone that helped clear this up.
Edit: My hint was "See, I..." which sounds like CI which is 101 in Roman numerals
A: 101 is next in the sequence. When represented as Roman numerals, each number in the series requires exactly two letters (II, IV, VI, IX, XI, XV, XX, XL, LI, LV, LX, XC, CI...)
Here's my standard reminder... don't post the answer or any hints that could lead directly to the answer (e.g. via Google or Bing) before the deadline of Thursday at 3pm ET. If you know the answer, click the link and submit it to NPR, but don't give it away here.
ReplyDeleteYou may provide indirect hints to the answer to show you know it, but make sure they don't give the answer away. You can openly discuss your hints and the answer after the Thursday deadline. Thank you.
I am coming to that same conclusion. I want to hear how Will describes this puzzle tomorrow (Sunday).
ReplyDeleteAnyone thinking the answer is supposed to be 195526?
ReplyDeleteNot me. My tentative answer is much shorter.
ReplyDeleteVery clever, Blaine. Yes, I, too believe the answer is supposed to be “195526,” and I shall say no more about it.
ReplyDeleteI have a great answer _if_ you throw in 51 and 55, making the series:
ReplyDelete2, 4, 6, 9, 11, 15, 20, 40, 51, 55, 60 and 90
This pattern (with the numbers I added) is so nice, I wonder if the listener who sent in the puzzle made a mistake in leaving them out, or if website transcription is wrong, or if I am just completely off base?
@Rob, I wasn't going to state the numbers explicitly, but I'm wondering the same thing. I'm trying to justify their exclusions, but I think the most likely answer is the puzzle submitter (Henry Hook) and Will must have overlooked those two numbers.
ReplyDeleteRob: I think giving away those two numbers is a bit too revealing. Still, it's possible the transcript is incorrect and they were included in the on-air puzzle, but if so it’s fairly susceptible to a specific Internet search. We'll have to wait and see.
ReplyDeleteRelatively new listener here, and I'm quickly losing interest in these puzzles. This week's puzzle and last week's puzzle, at least, seem very poorly posed.
ReplyDelete@Ruler, let's wait and see if this was a mistake in the transcription on the website. There have been times when Will stated the puzzle correctly on the air, but the version on the NPR website was mistyped.
ReplyDeleteOn the other hand, since Will is the Crossword Puzzle Editor of The New York Times, I usually expect him to be on top of catching mistakes like this. I'm not going to fault him too badly though if this was a mistake, since I want to encourage NPR to present more number/math puzzles. Two in a row is probably a record. :)
Here's a really lame inductive solution that avoids the whole “two numbers missing” issue.
ReplyDeleteDefine a series A = {a_1, a_2, … , a_n, …} with six base cases a_1 := 2, a_2 := 4, a_3 := 6, a_4 := 9, a_5 := 11, and a_6 := 15, and then define the rest of the series thusly: For any n in the naturals (n > 6), a_n := 10*a_(n — 6).
So in this case the answer would be a_11 = 10*a_5 = 10*11 = 110, but I dearly hope this is not the intended series.
Planned Chaos,
ReplyDeleteThis was the first pattern I saw, but I agree with your editorial comment.
I apologize if I was giving too much away by posting the numbers I _thought_ ought to be in the sequence. I figured I wasn't giving the answer away, just the puzzle as it (maybe) ought to be!
ReplyDeleteThere have been these difficulties before. I remember a listener asked us to find the name of an actor which had each of the vowels one time in it, and it was not Toby Maguire but Tobey Maguire.
Then, oh, fifteen years ago, Will asked us to anagram a bunch of letters, a certain number of Ns, Os, Ss and Es, and he himself didn't give the proper number of one of the letters; some of us got "No Nonsense" anyway.
I am warming up the radio...
Nope! The transcript is just as Will said it. Maybe we are all wrong!
ReplyDelete2 good clues during the on air segment.
ReplyDeleteI too just listened to the radio version of the puzzle. First, I'm completely surprised that Will (or the puzzle solver) didn't explain at all where/how the 25 triangles were found for last week's puzzle.
ReplyDeleteAnd yes, the puzzle transcription matches with what Will said on-air. Unless anyone has a solution that works without adding the two additional numbers, I'm going to have to conclude that both Mr. Hook and Mr. Shortz overlooked them in the sequence. I'm going to add them as a footnote above.
I thought this puzzle would dog me for a while, but I spotted the answer pretty quickly.
ReplyDeleteI agree the more elegant set has to include 51 and 55 - and for once I get Blaine's clue !
ReplyDeleteHowever, on air, Will said this was easy - and he usually speaks with a puzzlers tongue...
(only 120 entries last week - congrats to all that solved !!)
Blaine –
ReplyDeletePer your request, I just sent your update to Will and suggested he might want to look into it.
Chuck
From some of the verbal clues, I can guess a possible answer, although I have no idea why it might be correct! I have great admiration for those of you who were able to find the pattern in a relatively short sequence of numbers with two of the numbers missing! Perhaps this in itself might be some sort of clue about the pattern.
ReplyDeleteAs with PC & Lorenzo, I at first came up with 110, but did not accept it as being correct.
ReplyDeleteI finally got it. Everyone is right about the missing numbers. What a screw up! Would you believe I solved it without using my calculator?
ReplyDeleteJan:
ReplyDeleteGood clue again as usual.
Apparently, some puzzle makers and some puzzle solvers don't see eye to eye.
ReplyDeleteOn further reflection I believe there is another number missing as well. I also believe the true answer is slightly smaller in value than the one intended. Anyone agree with me on this?
ReplyDeleteAgain, this puzzle may turn out to be a lot more pedestrian than some (e.g., PC) seem to think. Jan, if I get your hint correctly, then it is so easy as to be exceptional for WS. (Even the auto-complete fumction seemed to pick it up as I was typing.)
ReplyDeleteFor Will's original sequence I could find something that all the numbers had in common if only the eleven were a ten or a twelve instead. So I was obsessed with circles, clocks and compasses all day, but none of those helped.
ReplyDeleteUntil suddenly one of them did, but not at all in the way I had first thought.
An interesting puzzle! It had me going, at least.
Last week, I thought the statement of the puzzle was needlessly ambiguous. This week, I think the puzzle statement and the answer may be ambiguous. It depends on how one wants to structure the sequence.
ReplyDeleteCertainly Blaine’s update is the more complete and therefore produces a more elegant solution. But I believe one could fashion a rule such that Mr. Hook’s version works, too. However, they produce different answers...
Chuck
Another note:
ReplyDeleteRegarding my last post here, there are actually 4 numbers missing in order to reach what I am sure is their intended solution. The fourth of these numbers is what the solution should be. I am surprised no one else here has noticed this yet. HINT: I don't think you will find it where you have been looking either. I can't say more until Thursday or it will give it all away.
sdb, after your previous post, I suspect we both have the same (correct)answer but are only 90% of the way through fully understanding the solution. In particular, I have not yet found a good reason to rule out my answer minus 2. Agree?
ReplyDelete@ Lorenzo,
ReplyDeleteAs to ruling out your answer minus two, Wikipedia informs us that according to an additional set of rules recently imposed, I can only be removed from vixens.
Lorenzo:
ReplyDeleteYou may be right, but I am having some trouble being sure I understand your post as you mean it. You may be on the same wave length as I, but I cannot tell for sure. I wish I could be more open here, but it would be too revealing. Too bad some of us cannot email each other.
PC:
ReplyDeleteInteresting. I will have to look further into this.
I just finished doing a little Wikipedia checking and assuming their information is correct then I will have to retract my recent statements asserting there being more than 2 numbers missing from the problem. Same for the answer. Therefor I will go along with the puzzle as Blaine has presented it above. I will make further comment on this matter Thursday.
ReplyDeleteFunny, but I recall seeing this number sequence at a train station!
ReplyDeleteRoRo -> This should be an easy puzzle for you!
ReplyDeleteHenry Hook was free to add his own rule to the normal rules used to generate the sequence.
ReplyDeleteIt seems to me that the correct answer is likely to be given for the wrong reason.
Extra restraints governing the transition from one number to the next take care of apparent problems.
Will Shortz here.
ReplyDeleteA huge, huge apology for messing up the challenge puzzle this week. Henry Hook submitted it to me, correctly, with just the first seven numbers. I liked the puzzle but thought it needed more numbers to be fair, so I extended the series. In my haste -- perhaps because I was jet-lagged from flying back from Hungary the day before, or perhaps just out of carelessness -- I overlooked 51 and 55 in the series.
Very sorry!
Blaine has posted the correct series.
Straight from the horse's mouth :)
ReplyDeleteChuck
OK, but what about 45?? Why isn't that in the series?
ReplyDeleteNever mind. Co-workers helped me see the error with 45.
ReplyDeleteI now see that I too missed 45.
ReplyDeleteTherefore the correct series should now be:
ReplyDelete2, 4, 6, 9, 11, 15, 20, 40, 45, 51, 55, 60, 90.
Nope, 45 is not in the series.
ReplyDeleteIt is amusing that the NPR website with the puzzle now includes 51 and 55, but there is no mention that the puzzle has been corrected.
ReplyDeleteThe NPR website has posted a correction:
ReplyDeleteCorrection Nov. 14, 2011
Some numbers were left out of the number series for next week's challenge, both on the air and in a previous version of the Web text. The correct sequence should be 2, 4, 6, 9, 11, 15, 20, 40, 51, 55, 60 and 90.
I wonder if Will actually tries to solve the submitted puzzles himself or not ?
I just read Will's response & APOLOGY posted on the Crosswordman blog - check it out !!!
ReplyDeleteI have long wondered about that question too.
ReplyDeleteDaveJ:
ReplyDeleteHe also posted it on here.
Katherine:
ReplyDeleteTake a look at 95 too.
You'd think it would be 95, but since that is after 90, that would have been the answer, but it's not. It turns out that Excel has a function that helps with this. Check it out.
ReplyDeleteKatherine:
ReplyDeleteI agree. I just finished some research on all this and will post on Thursday with references. One thing I learned is that 45 and 95 do not work. This has all been an interesting learning experience for me.
Dave J:
ReplyDeleteHas anyone else been listening long enough to recall the week Will post a puzzler that was impossible to answer? If I recall correctly, the only "winner" that week was the person who "proved" the impossibility.
-- Orangebus
Blaine's hint posted Saturday night is missing
ReplyDeletea prefix. The answer to the puzzle reminds me of a 1960's cigarette ad.
EKW:
ReplyDeleteWould that be Winston?
SDB: No, it is not Winston.
ReplyDeleteBuilding off EKW's hint, a musical clue to this week's puzzle might be "La Bamba".
ReplyDeleteI hope I'm on the right track, these puzzles sure make me feel punch-drunk like Rocky Balboa. For a musical clue would Frank Sinatra work? or possibly Andrea Bocelli?
ReplyDelete@Katherine & SDB,
ReplyDelete45 is not part of the series nor is 49. Search Wikipedia for a relevant article; the first external link is helpful.
Blaine:
ReplyDeleteYou are right and I posted this above a bit earlier today after I did some further research.
Musical Clue - Franki Valli
ReplyDeleteThese puzzles are going to put me in the hospital.
ReplyDeleteThey're going to have to replenish some fluids
Ralph Loizzo:
ReplyDeleteThe liquor store can replenish fluids too, and cheaper.
Skydiveboy: my wife already went. After I figured out the puzzle I gave her the task of figuring it out.
ReplyDeleteNeedless to say, she is livid!
Will Shortz destroys another marriage.
ReplyDeleteIf you can think like Suzie Orman, the numbers may come easier.
ReplyDeleteOK, I got it now. Revised musical clue: B-52's
ReplyDeleteWill could have hung tough with his original series by privately adding a rule that governs the selection of terms from the now official series. But he honestly went with his intentions.
ReplyDeleteThe rule: from the now official series, form a second series by removing entries that have "digits" of lesser value than those which appear in preceeding term. Messy, but probably at odds with Will's on-air comment, "not too difficult".
A more interesting session - warts and all.
Another musical clue: Metallica.
ReplyDeleteHi Tom W. Your shout out pulled me right out of the box I was stuck in and I am now running from spotted dogs as well. Nor do I tend to gravitate toward Biblical revenge but in this case?
ReplyDeleteHow many King Henry's were there?
ReplyDeletef5575a18-7651-11e0-8f0a-000bcdcb471e:
ReplyDeleteI take at you have a Hankering to know.
This reminds me of a guttural joke from the movie The Deer Hunter, when all the steelworkers are in the showers and locker room at the beginning. Does any body else get it?
ReplyDeleteRoRo -> I'm glad you got it! I'm sure there are others still working on the puzzle, so I will say no more for now. It's always a wonderful feeling to solve the puzzle and see how the clues relate to the answer. On the other hand, sometimes trying to solve the puzzle can keep you thinking day and night!
ReplyDeleteReminds me of those entry level classes that college freshmen have to take.
ReplyDeleteIt seems legions of puzzle fans would understand the pattern?
ReplyDeleteThe Pope should know the answer.
ReplyDeleteLee J:
ReplyDeleteYour post makes me wonder if your full name is, Lee Johns.
Since many new hints are still coming in, let me share the ones I posted on Sunday on "the other blog":
ReplyDelete"I too have an obvious answer with two additional numbers between 40 and 60. But, maybe because I am French (my usual excuse 8^), I think that the mix-up is normal, with Christmas on my mind and all."
Catrina the cat invites her friends over for a delicious spaghetti lunch every Wednesday.
ReplyDeleteskydiveboy:
ReplyDeleteInteresting you mentioned that! My last name starts with a very similar sound. I might not have picked up on your clever homophone except I once had someone actually think my first name was Legion!
Lee J.:
ReplyDeleteThanks, suddenly it all clix.
Nice one Lee J. Great clue.
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteJim-->I remember the joke! A bit off-color but I remember it. I hadn't noticed your post until now. Man I need a new pair of eyes.
ReplyDeleteI've been trying to think what Will Shortz might call a course on puzzles if he were to teach it.
ReplyDeleteWell, SDB, if it's a brief class, it might be called a Shortz course. Or, if it's about crosswords, it might be a crisscross course.
ReplyDeleteCurtis:
ReplyDeleteTomorrow I will disclose the name I am think of.
Don't base too much off this, but any introductory course in computer science will tell you the answer is 5. Besides, I told you that you knew the answer already. Everyone knows it.
ReplyDeleteI'm a day late but the new puzzle is up at Midweek Puzzle Break.
ReplyDeleteClick, click, click...
Clues & explanations:
ReplyDelete"I've been trying to think what Will Shortz might call a course on puzzles if he were to teach it."
He might call it Puzzles 101.
"Thanks, suddenly it all clix."
C, L, I, X are Roman Numerals involved with this puzzle.
I would now like to explain some of my confusion re: the correct usage of Roman Numerals, which I do not claim to be particularly knowledgeable about.
Several years ago, I think it was 1998, I happened to come across a little puzzle in a major publication (I don't recall which one) that asked the question: "What are the fewest Roman Numerals that can be used to express the year 1999?" Their answer was: MIM. I thought this was very elegant and have always remembered this puzzle, but now I find it does not conform to the standard usage of Roman Numerals. So for me solving this puzzle has been a bit of a learning experience. I also discovered I am far from being alone in my ignorance on this. I prefer simplicity and think we should change this immediately before it is too late! (Mild panic in voice.)
I was impressed with Will Shortz's apology for leaving out 51 & 55. He did it the right way and did not say, "I did not have sexual relations with that puzzle!" or "I have never abused a puzzle!" Clearly he would not do well in politics, so perhaps we should all write him in as a candidate next year. Puzzle Abuse has been a serious problem in this country for a long time now and an honest mea culpa is a refreshing change.
I wanted to say more, but I have just been informed my aqueduct is leaking again.
It just occurred to me that Noah's Ark would have been an interesting clue.
ReplyDeleteThe '60's cigarette ad was for Chesterfields that
ReplyDeletewere 101 millimeters long. The key phrase in the
ad was "a silly millimeter longer!" Jan's La Bamba
hint referred to the music in that ad.
I saw several clues to spotted dogs, I assume a reference to 101 Dalmations. I was also thinking of referencing service animals which would have been a clue to "seeing eye" dogs. Phonetically that sounds like "C & I" dogs. :)
ReplyDeleteIf anyone is familiar with oeis.org (the Online Encyclopedia of Integer Sequences), this specific sequence is A195526 hence my early comment about thinking the answer was 195526.
ReplyDeleteI didn't pick up on the 101 Damnations (whoops! that should be Dalmatians, maybe). I thought Jan, by saying dogged, was referring to the wolf symbol of Rome. Now I am not so sure.
ReplyDeleteHey, did anyone ask Will why he didn't explain last week's 25 triangles answer in any way? Not that I necessarily expected him to reference my movie or this blog, but not even the on-air player described the location of the triangles. With only 120 correct answers, I'm thinking there must have been lots of regular listeners lost as to how that answer came about.
ReplyDeleteBlaine:
ReplyDeleteMild skepticism here regarding your modesty. I believe we ALL here expected Will would have referenced your blog in order to explain the solution to the millions and millions of listeners who are still wondering how the correct answer was achieved. I hope this mass confusion is not affecting our national productivity.
I wrote:
ReplyDelete"Don't base too [base 2] much off this, but any introductory course in computer science [CS 101] will tell you the answer is 5 [when interpreted as a number in base 2, 101 is 5]. Besides, I told you that you knew the answer already. Everyone knows it. [the italicized text is from Orwell’s 1984, and is a reference to Room 101.]"
PlannedChaos: Impressive!
ReplyDeleteTo ensure a bijection exists between Arabic and Roman numerals, to which I was referencing in this reply to Lorenzo, see the Wikipedia entry (which SDB undoubtedly discovered afterwards).
ReplyDeletePost 101! (Sorry, couldn’t help it.)
ReplyDeleteSo, I guess I was too far out of the box. I came up with 141 because I divided the numbers in groups of 4 (2 columns of two each) and used slanted rows to sum the next numbers to the top right and an alternate of across the bottom and up and down right side to get the next bottom numbers. Seemed to be a working pattern so I went with it.
ReplyDeleteHere are explanations for my clues. Seeing the number sequence in a train station referred to a clock with Roman Numerals (they are very common in Europe). Orman can be rearranged to spell Roman. Metallica's song: Wherever I may Roam. And the reference to Wednesday being spaghetti day (Italian) from Maryann Cocca-Leffler's book. My cat insisted I post the last clue!
ReplyDeleteRoRo -> Sorry you missed my clue. I was trying to get you to think "Roman". But don't despair, because there's a new puzzle on Sunday, and I'm really enjoying these analytical puzzles!
ReplyDeleteTom W.:
ReplyDeleteI wouldn’t expect the Sunday puzzle to stay as analytical as they’ve been these last two weeks.
Roman <--> Arabic Numeral Converter (using the modern rules).
ReplyDeleteMy clues:
ReplyDeletePair of eyes - II
Replenish fluids - IV
Rocky Sinatra bocelli all Italian
My wife was LIVID. Not proper roman numerals but all of them are.
Chicago won the Super Bowl in 1986. It was XX
Sometimes I think the answer's relationship to the clues are harder to solve than the actual puzzle.
ReplyDeleteBlaine –
ReplyDeleteHere are some thoughts on your earlier comment regarding the 25-triangle puzzle. I think what we have here is the lack of a feasible timetable and process, not a lack of interest on Will Shortz’s part in providing more complete information about a puzzle’s solution.
Will is a really busy guy – the Sunday puzzle being only one thing – and perhaps a small thing – in his weekly schedule. The show is taped Fridays at noon Eastern. Will works from a script (or at least the outline of a script). If the mountain won't come to Muhammad, Muhammad must go to the mountain :)
In the future if there is a puzzle (like the 25-triangle puzzle) which cries out for a visual aid – drawing, spreadsheet, video, whatever – here’s what I would suggest.
Submit the aid – or a link to the aid – directly to Will, not NPR. Send it no later than Thursday. Earlier in the week would be much better. He’s going to need some time to get your email, check out your submission, see that it’s right, possibly have the NPR IT folks vet it (antivirus, etc.) and get it into his script by Friday noon.
Obviously I can’t speak for Will Shortz or NPR. But under the circumstances above I think Will would be happy to occasionally (remember it’s _his_ show) use an outside visual aid. And I imagine he’d be grateful for your (or anyone’s) assistance in making the segment more meaningful and enjoyable for his audience.
Chuck
Chuck:
ReplyDeleteWill recently referenced this blog without any of that process that is unworkable, i.e. we don't even have Will's email address.
Yeah, I don't have his direct email address, but I've been sending mine for years to NPR. :)
ReplyDeleteLast time, with the hat puzzle, I sent my answer with direct links to the puzzle diagrams along with a mention that they would made public after the deadline.
This time I did a similar thing with the video, sending a private link to the video in my response. However, I noticed that no viewings of the video occurred before I made it public, so that tells me nobody clicked on the link until perhaps it was too late.
If someone feels it might be worthwhile, let Will know that I'd love to have his direct email address and I'd gladly send links to diagrams for future puzzles like this. Have him send me an email to nprfan(at)penguin(dot)e4ward(dot)com and I'll reply with my real address.
Will's email address is not that hard to find with a Google search:
ReplyDeleteshortz@nytimes.com should do it.
Will e-mailed me a few months ago to let me know that NPR was going to use my puzzle as the weekly challenge, so I have his personal e-mail address. I'm sure that he prefers that the general public doesn't have it.
ReplyDeleteI got this week's answer by reading the clues that were sent into the blog. Some of the clues gave the answer away. Thanks to all!
How much you guys wanna bet that the next puzzle will be another math one?
ReplyDeleteI don't have money to bet, but I do have this farm.....
ReplyDeleteum... what?
ReplyDeleteThere seems to be a mistake in the wording of the new puzzle.
ReplyDeleteA mistake in the wording? It is now 10:14pm PST and STILL I can't see next week's puzzle either at http://www.npr.org/series/4473090/sunday-puzzle
ReplyDeleteor at http://www.npr.org/programs/weekend-edition-sunday/
Blaine, there was a time before that NPR had not yet published the upcoming Sunday puzzle at either of those two sites, yet you still were able to post the upcoming puzzle BEFORE either of those sites had it up themselves. Could you perhaps work your magic again? ;-)
Done! And the missing word (I believe) is 'followed'
ReplyDeleteBy the way, it isn't magic. I found it referenced from another link on the NPR site:
ReplyDeleteGames & Humor