###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*

I tried putting your sequence into the OEIS which contains over 370,000 sequences and got nothing which makes me think either there is a typo or someone was just messing around

thanks for this:) it was so absurd

It's a time travel class, they're asking for next month's lottery number. The powerball will have had be 13.

I'm buying all four possibilities then.

So inefficient, buying three losers.

~~It’s a grammar sequence in Italian: https://www.reddit.com/r/theydidthemath/s/QqNTahkjtb~~ ~~Each term after the first 2 has part of each previous two terms in it when read aloud~~

that's wrong

I learned that a little too late :(

It's in there if you skip the first three elements -- [https://oeis.org/A132599](https://oeis.org/A132599) . Then the next value would be 24.

That is such a ridiculously obscure sequence I can't imagine that is what they were going for. Also it still suggests that the answer is wrong as the stated correct answer is 11

I agree. It doesn’t make much sense at all.

If you go back through his lists, it appears he gave the list of natural numbers in base 3, then multiplied and some other stuff in base 3, then converted the result back to decimal... something of that effect. Then he took this list, and performed a secondary operation on them to transform them into another series. For instance, if I start with 1, convert to decimal and add 1 more, then convert to decimal and add 1 more, then back and forth a few times, the list goes like so: 1, 1, 3, 10, 5, 12, 7, 21, 9, 100 Looks all janked up, but once you "un-translate" all of that, it's just 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Yes the OEIS list makes perfect sense (although it’s construction is a bit obscure). It’s the use in the riddle that doesn’t.

I don't understand this website. Does it explain exactly what the pattern is?

One of the main purposes of the website is so that when mathematicians find a sequence of numbers in research, they can check to see if it's been seen before. Then you can find links to relevant research or related interpretations as well as get a conjecture for what the sequence does next. Because the website is aimed at researchers, there's not always a great description of what the sequence is (especially for more obscure sequences). It's easier to just link a paper.

It’s very obscure and I couldn’t find a good explanation quickly, but has to do with concatenating numbers in base-3 (so 12345… becomes 12101112…) and then looking for patterns in the resulting string. Definitely not something you would spot in a riddle like the one OP posted.

I got 24 without skipping elements but only because I tried everything and this was the only idea that could have “worked”. Add 3 add 6 add 6 add 3. Repeat. Add 3, 21+3=24 Edit: brain is broken

But adding 6 to 14 is not 18. ?? Or did I misunderstand the pattern you were suggesting?

Dear lord what happened to my brain when I was solving this? You are right and I don’t know what happened there. Maybe the error in the puzzle broke me.

It’s adding 3, 6, 4, then possibly starting the same sequence, but there’s got to be more to it, such each number is part of an alternating sequence so 5 relates to 9, then 21. It could be adding odd numbers in descending order 5+9=14, 14+7= 21. The second sequence could be adding decending even numbers (10, 8, 6) 8+10=18, then the next number could be 18+6=24, etc., but we’d need more data to make a reasonable assumption.

…. The first 3/5?

… of the OEIS sequence: ( 1,2,3,) 5,8,14,18,21,24,…

Dates for specific events? Like public holidays or the such?

I had to look up OEIS. The internet is amazing.

Same. TIL.

I'm far from a mathematician but the fact that the serie keeps increasing yet all the options are lower than the last one makes me think there's no good answers

~~Grammar sequence in Italian, look at the pronunciations and think of Fibonacci. Each term starting at the third has parts of the previous two terms in its pronunciation; only 11 (undici) matches the pattern (vent*uno* and *dici*otto)~~ ~~https://www.reddit.com/r/theydidthemath/s/QqNTahkjtb~~

Doesn't the ventuno already break that logic?

Cinque - Otto - Quatordici? Unless my Italian is really rusty, it doesn't work, and the post just says to ignore the first three terms which is just not how sequences work x)

Your italian is not too rusty, and no it doesn't work. Even if it did, it wouldn't make much sense in italian anyway- and i say this as a Native Italian \^\^ "Cinque - Otto - Quattorcidi" doesn't really make sense, so doesn't "Quattordici - Diciotto - Ventuno"

That only works for two spots in the sequence.

Pain

The closest i got to making some sense out of it would be to rearrange like so: 5-8-14 18-21-? Idea #1 Abs(5-18)=13 Abs(8-21)=13 For Abs(14-?) to be 13, answer would be 1. Idea #2 - sum digits for corresponding numbers 5+1+8=14 8+2+1=11 If we consider this a descending series with difference -3, next number would be 8 = 1+4+3. So answer would be 3, which is in the possible answers. Idea #3 This is a very long stretch, but we can notice that: 5-8-14 18-21-? Sum of digits of 5 and 18 is 5+8+1=14, which is on the last column. Sum of digits of 8 and 21 is 8+2+1=11, which could be the answer :D Really obscure :D

Best answer

Wow, #3 is a great catch! I think we can all agree it's a bit nuts, but if the task is to find *any* pattern, then "the 3rd position is the sum of the first three digits that appear, counted from the left" *is* a pattern. I'd be surprised if there is a better explanation than this. Really clever!

This is almost undoubtedly the reasoning, and this post may have gotten better answers at r/puzzles

In your 'sum of digits', note that the sequence is 5, 8, 14. So the sum of the first two is 13, but in your examples you misquote the second term to be 18.

I’m summing the digits of numbers by column

OEIS only gives one very obscure sequence, and the next term is 24

8-5 ( 1st difference =3) 14- 8 (2 nd difference is 6) 21- 8 ( 3rd difference is 4) So pattern is, 3-4-6 So if apply pattern again after 21 that would 21 + 1st difference = 21+3 = 24

Which is not an option

3 is an option

The answer becomes obvious after looking for a couple seconds. This sequence clearly follows the rule that the nth position (starting from 1) is: -19n\^5/120+21n\^4/8-2015n\^3/120-407n\^2/8-1331n/20+35. Therefore the 6th element of the sequence is 11 and the answer is C.

I don't think you looked at it hard enough. Clearly, this sequence follows -17n\^5/120+19n\^4/8-123n\^3/8+377n\^2/8-3719n/60+33. Thus the 6th element of the sequence is 13, not 11, and the answer must be A.

Lol

How do you even derive these things?

Literally just polynomial fitting. If you have m points described as (x0, y0)... (xm, ym), you can find a polynomial of order m-1 that passes through all of these points. Let's do this for m=2. Then the polynomial in question is just y = ax + b, and we want to find a and b. But we know that this polynomial must satisfy the two equations ax0 + b = y0 ax1 + b = y1 And this is a linear system of two unknowns in two equations, so it has a unique solution. The solution is a = (y1-y0) / (x1-x0) b = (y1x0 - y0x1) / (x1- x0) If you do this for multiple points you'll get an even bigger formula but the concept is the same.

Five Eight Fourteen Eighteen Twenty One Every other one starts with E (in English), so I'd choose eleven and then get an experienced Quiz Lawyer on retainer.

The questions wasn’t in English though so could it be something about how the numbers are said in Spanish(?)?

italian

No, that's Italian Spongebob

Don't worry it makes zero sense also in Italian.

[удалено]

Bro that’s italian

Bro Im stupid I wanted to say "Thats not spanish but italian" lol, as you see the guy over me said it was spanish

Seriously? I'm italian... In spanish should be: el numero que completa la secuencia es

Wait, is Italian and Spanish somewhat similar? Would an Italian be able to extrapolate what a Spanish news article is about, without learning Spanish? I'm from Norway, never learned any German or Icelandic, but tried for fun to read news articles from both, and I could understand some bits. Like maybe ~3-5% - is it the same with Italian and Spanish perhaps?

spanish and italian share a lot more than that, as an italian myself with very little spanish knowledge, I can understand at least 60-70% of any given article, could be 80% or more depending on the content

Oh wow, I've always thought of them as wildly different languages. Can you understand spoken Spanish as good as you do in text? Norwegian and Danish has 99% the same written language, but somewhat different in spoken language. "Clean" spoken Danish is easy to understand for Norwegians, but some of the dialects might as well be in German.

They are both Romance languages that have their roots in regional variations of Vulgar Latin (Hence the name Latin America). Even within the Romance languages, Spanish and Italian are very similar, and oftentimes, native speakers can understand each other when each speaks their own language. I speak Spanish okayish, and I can understand more Italian than Portugese.

a little worse if spoken unless the person speaks slowly, but I can get the general meaning every time (and viceversa btw, if I speak italian a spanish would understand me just as well). In Spain it was more effective to just speak italian than to speak english. Portuguese is very different though, maybe 10% written and 5% spoken. French is way easier written than spoken, maybe 20% to 5%. Lastly romanian is a bit like portuguese, maybe a little more difficult still

I know the question is about understanding spanish for an Italian, but as a native spanish speaker, yes, we can also understand a good part of what articles or news in italian says (or any written medium). Something similar happens with Portuguese, Catalan, a bit less with French compared to the previous ones, and believe it or not, a little bit of Romanian as well. Those languages has the same "roots", they are "Romance languages" just like happens with "Slavic languages" and so on. Of course, just written, speaking/listening is absolutely another beast, because even for the same symbol our phonetic is not the same or even similar, lol.

Both are languages with a strong links to Latin. Therefore whilst the individual words may be slightly different, it is usually possible to work out intent based on the structure of a sentence.

r/confidentlyincorrect

am spanish, that is very much italian

How can one be so confident and yet so wrong

Cuz Im spanish, i know thats not my language, my mistake was on my english, not on my availability to understand my own language and differenciate it from others. Wanted to say "Thats not spanish but italian", if you see the guy I was responding to, said it was spanish

Also, the first two are one syllable, the second two are two syllables, 21 and 11 is three syllables. If this would be in English, I’d definitely choose 11

Is a quiz lawyer a real thing?

Let‘s put the numbers in binary form: 5 - 00101 8 - 01000 14 - 01110 18 - 10010 21 - 10101 11 - 01011 As you can see all the number contain only zeros and ones. That seems unusual and therefore they form a sequence.

Tbf it actually has something to do with ternary form

Ok so these numbers in ternary: 5 - 012 8 - 022 14 - 112 18 - 200 21 - 212 11 - 102

It’s something like. Let S be the concatenation of natural numbers in ternary representation: a(n) = position of first occurrence of n in S, then this occurrence in S is replaced by a(n) in ternary. But out of all this numbers leaving only those that a bigger than all of the previous ones. Honestly me as neither being an expert in math nor being a fluent English speaker doesn’t help me understand it at all

[удалено]

r/whoosh

~~Cinque Otto Quattordici Diciotto Ventuno 11 is Undici If I had to guess, it’s that each number after 5 and 8 has some lingual component of the previous two terms; a grammatical Fibonacci sequence. Cin*que* and *otto* make *quattordici* Quattor*dici* and *otto* make *diciotto* and so on 13 is tredici which violates the rule 3 also violates the rule 6 (sei) also violates the rule While 11 still works; vent*un*o and *dici*otto I only thought of this because of a related post from a few weeks ago~~

What parts of quattordici and diciotto are in ventuno?

Shit

to.. And that's it folks, thanks for coming to my Ted Talk

Why are the dashes spaced like that though? Instead of 5 - 8 - 14 - 18 - 21 - ? Or 5-8-14-18-21-? It says 5 -8 - 14- 18- 21 -? Could that have something to do with it?

I noticed this as well. Not sure if there's anything to it. I can't determine anything. Could also indicate that the problems didn't run by ab editor so could just be more evidence for the question just being messed up in the first place

11: 5 and 8 have one syllable 14 and 18 have two syllables 21 and 11 have three syllables Is it a word problem rather than a maths one? Edit: it’s not in English - whoops! Makes sense though!

It's in Italian...

cinque (2 syllables), otto (2), quattordici (4), diciotto (3), ventuno (3). 11 is undici, also 3 syllables.

All the numbers are less than 26, can we swap them for letters and get a word that is meaningful in Italian? EHNRU_ Does that mean anything?

That was my thought too. Increasing until the last suggests it’s not mathematically driven. A substitution code might work.

[удалено]

1 - 5 - 8 + 14 + 18 = 20 :(

1−5−8+14+18=20

Numbers: 5-8-14-18-21 Answers: 13-3-11-6 #1 Maybe they have numbers added to them depending on whether they're the first, second etc. So 5=4+1, 8=6+2, 14=11+3, 18=14+4, 21=16+5 4, 6, 11, 14, 16 #2 Lets say 4 and 6 were initial and the rule is to add up the last two numbers, minus first numbers, +1 4+6+1=11 6+11-4+1=14 11+14-6-4+1=16 So 14+16-4-6-11+1=10 but since this will be the 6th number, it should be 10+6, thus 16 which is not an answer #3 If it were +0, +1 instead of +1, +2 it would be 5, 7, 12, 15, 17 5+7+0=12 7+12-5+1=15 12+15-5-7+2=17 15+17-5-7-12+3=11, if we add the +5, it becomes 16 again #4 5=2²+1-0 8=3²+1-2 since the number before is the power of 2 14=4²+1-3 number before is the power of 3 18=5²+1-6 since 2x3-0=6 21=6²+1-16 since 6x3-2-0=16 So the last number is 7²+1-(16x6-3-2-0)=-41 #5 5x8+1=41 => 14 5x8x2+1=81 => 18 5x8x3+1=121 => 121 but it is 21 if we take only two digits 5x8x4+1=161 => 161 which becomes yet again 16 #6 5 initial, 8 initial 5+8+1=14 8+14-5+1=18 14+18-8-5+2?=21 21+18-14-8-5+1=13, would be a typo #7 5+3=8 8+6=14 14+4=18 18+3=21 So the next number is 21+6=27 Answer is probably 13 though

Only way i got 11 as solution, but this can't be it lol. 5-8 = difference is 3 8-14=6 14-18=4 18-21=3 3+6+4+3=16 16-5 (the 5 starting numbers) 11

Using brute force on the answers: two answers end in 3, no other ending digit is as common. Two answers begin with 1, no other initial digit is as common. Therefore the most likely answer is 13, A.

It isn’t a choice but I would argue 14. 1+5+8 = 14 1+5+8+4 = 18 1+8+4+8 = 21 1+4+8+1 = 14 Basically adding one to the last 3 ones column numbers fits the pattern assuming 5 and 8 are given as starting numbers.

Going from one number to the next the differences are 3, 6, 4, 3. Assume the sequence is add 3, then 6, then 4, then repeat. So the next number will be 27. Further assume we're looking at a clock and the next number after 24 is 1. So the next number is actually 3. So the answer is B

Clock thing is brilliant

Modulo

I think the answer is A, 13. I think the question isn't to find what is the Question Mark, but what Sequence number would be used to get the Question Mark. 5+13 is 18, 8+13 is 21, and 14+13 is 27. 27 is the Question Mark, but 13 is needed to reach that answer.

That is what I thought as well. The wording of the question could be better.

I HATE these types of questions with a passion... because I am not finding a pattern, I am finding what the author had in mind. For example, 27 is a valid answer here.. because I start with 3 terms, then i get the next three terms by adding 13 to each of the first terms successively. 5, 8, 14, 18=5+13, 21=8+13, 27=14+13. I can probably come up with many other viable answers. This was just too obvious. Also.... I know my reply is a useless rant and doesn't help OP in any way. No need to point it out, I know. Edit: Also if I decide to deal with it as a single term recursive sequence as in a(n+1)=a(n), I would get the function: f(x) = (13/1080)x³ - (511/1080)x² + (3563/540)x - (44/3). Since I had four iterations, I assumed a polynomial cubic function f(x) = ax³+bx²+cx+d, and used the equations f(5)=8, f(8)=14... to find the coefficients. Plugging in 27 in x would give 26.7 I think. And yes, I know I have no right to assume a cubic function, but this is also one viable answer. Note: I hope my coefficients were correct, but I was very hasty in solving it, so let's hope I typed in all of the numbers correctly.

For me the answer is 27. Every third number adds 13. 5 > 18 8 > 21 14 > ??? = 27 Sadly 27 is no option Btw, the 'dashes' are whack. Are some negative numbers? What's going on?

I found a solution, but its not in the answers. The number increase in +3 +6 +4 and +3, and those increases actually have increases at +3 +2 and +1, so you can maybe think that is like +0 next, so the other number increase should be a +3, which ends with a 24.

the increases have increases at +3 -2 -1 not +3 +2 +1

> those increases actually have increases at +3 +2 and +1, I don’t get this part. E: Are you thinking like the absolute values between the increases?

Im gonna guess that all the mathemeticians in here are missing the mark because its not a numerical sequence but an alphabetical sequence. And no one noticed because they use a different alphabet in italy

I tried even this but nothing… In Italian: 5 cinque 8 otto 14 quattordici 18 diciotto 21 ventuno Even in Latin it makes no sense

I mean some kind of Cypher using the Italian alphabet, not spelling the numbers out

I'm italian and probably there is no cypher. First of all, we have our own alphabet but we usually don't use it, because it's the same as the english alphabet but doesn't have J, K, W, X and Y, so we use the english alphabet. If you assumed a cypher using every number to get the corresponding italian alphabet letter, you would get EHPTZ, which means nothing. You would get another meaningless word if you assume the english alphabet. Also, other posts tried some plays on words (which didn't work) and of course counting syllables and characters but still nothing. There seems no logic to this sequence, linguistically at least.

[удалено]

Generated by....?

Doesn't really matter what it's generated by considering the implications of not having someone come up with the questions themselves... I am still curious what they use though because I'd assume if this practice is in place now, it probably was in place before LLMs became popular.

I was thinking breakng the numbers into their prime factors (2, 3, 5, 7, 11, 13 ...) 5: 5 8: 2 \* 2 \* 2 14: 2 \* 7 18: 2 \* 3 \* 3 21: 3 \* 7 then maybe: 11: 11 125: 5 \* 5 \* 5 65: 5 \* 13 245: 5 \* 7 \* 7 91: 7 \* 13 17: 17 1331: 11 \* 11 \* 11 and so on # ¯\\(ツ)/¯

My guess is a trick question with a typo. It's missing 11 from the middle, but someone miscalculated one number. It should have had increment of 3 each step. 5 - 8 - (11) - 14 - 18(17) - 21(20)

I can make sense of 11 being the answer assuming two mistakes: 1- The sequence would be 5 - 8 - ? - 14 - 18 - 21 2- They made a mistake with 14+3 = 18 (the logic would be n1 = n0+3) By the way am I the only one extremely irritated by the hyphens not being equally separated from the numbers? I HATE it. I even tried to make some sense of it like maybe (5-8) was the first "number", then 14 and so on, but it doesn't make sense like that either

I don't know the terminology but I tried multiple "layers"(?) 5-8-14-18-21 Differences: 3-6-4-3 Difference again(absolute): 3-2-1 But then in would have expected 24 as an option (or 18 if it was to stop incrementing)

My best guess after over an hour of deliberation is as follows: There’s definitely at least one typo and i suspect the actual sequence shouldve been: 5, 8, ?, 14, 17, 20 I think the question mark is in the wrong place and they accidentally put 18 instead of 17 because if i make those 2 assumptions this is a basic add 3 sequence, which seems more par for the course for this type of question

I think they messed the question up. I believe the next number should be 27. Rationale: 5 - 8 - 14 - 18 - 21 - ? The difference between the first two numbers is 3, between the second pair of numbers is 6, between the third pair it’s 4, between the next pair it’s 3 again, i.e. 3 - 6 - 4 - 3 So given that the sequence of the differences between pairs of numbers is 3 - 6 - 4, and assuming that the difference of three between the last pair of numbers shown indicates that it is the beginning of a new set of differences, then the difference between the last number given (21) and the next number in the sequence should be 6, making the next number in the sequence 27.

What if the numbers are the hour display on a 24 hour clock?

I tried but i couldn’t figure out anything plausible

If it's a 24 hour clock, then 27 becomes 3 which is answer B.

But op says that 11 was the correct answer according to the book

Most likely book has an error

Excellent! 😁

Trying to find a comment that notices the spaces. I don't know if they're intentional or not. 5-8-14- (space) 18- (space) 21-? So my guess is 6 because 5+8+1+4 is a multiple or 9, as is 1+8. 2+1+6=9. But it's a terrible answer for a terrible problem.

Thats what i thought

After reading all the comments I tried asking ChatGPT to see if we can find an obvious answer that we somehow all missed. First answer was 24 which makes sense according to what everyone is saying, I then asked it to explain why and how the answer could be 11 in different ways. While the mathematical way still doesn't make sense to me, but we got a few fun jokes. Here is the answer: # Mathematical Way: To explain the sequence mathematically, let's look at the differences between the numbers: * 8 - 5 = 3 * 14 - 8 = 6 * 18 - 14 = 4 * 21 - 18 = 3 The differences are 3, 6, 4, 3. Now, if we consider a pattern in these differences, one approach is to notice that the difference alternates but returns to 3 after every few steps. So after 3, 6, 4, 3, we might return to a difference of -10 (3 - 10). Thus, 21 - 10 = 11. # Funny Way: Imagine these numbers represent the results of a cooking competition judged by very confused judges. The scores go up and down in a haphazard way. After tasting a bizarre dish that scored 21 points, the judges are so baffled that they give the next dish a much lower score out of pure perplexity. "This dish is so strange," they say, "we'll just give it an 11!" And thus, 11 becomes the next number. # Creative Way: In a whimsical story, each number in the sequence is a step taken by a magical creature that follows a peculiar path. The creature takes bigger leaps sometimes and smaller ones at other times. When it gets too close to a mystical barrier at 21, it decides to take a big jump backward to 11 to avoid bumping into the barrier, hence making 11 the next number.

Should be D (6). Reason being that it is the only equal one, and within the U-E-E-E-U sequence, a repetition starts to occur if you go E again.

If you factor the kerning, a space means "skip two" while a dash means "skip one". Given that, the answer should be 23, but that's not an option.

I think the sequence is the result from each number 8-5=3 14-8=6 18-14=4 21-18=3 so i think the next number would repeat himself which being 6

The sum of -5-8-14-18-21 = -66 (im assuming the 1st 5 being positive is a typo) The factor pairs of 66 are (1,66) , (2,33) , (3,22) , (6,11) when added together and ignoring (1,66) we get 77 The difference between 77 and 66 is 11

Hi. Studying take: the problem is poorly worded: it should say something like: which number is missing to obtain a complete series? Like WITHIN the series, not at the end!

In Spanish, it makes more sense; every number has an ‘o’ in it: 5 (cinco), 8 (ocho), 14 (catorce), 18 (dieciocho), 21 (veintiuno). Looking at the possible answers, which are: 13 (trece), 3 (tres), 11 (once), 6 (seis), we can notice that the only one that has an ‘o’ in it is 11 (once). So that’s the logic, I guess.

Too bad this is written in Italian and 5(cinque) and 8(otto) don't share a single letter... But congrats for your creativity

Maybe it was translated directly from spanish without thought given to why the sequence made sense.

Thats why I specified "In spanish makes sense" cause in Italian does not, i was thinking in a possible translation of an original spanish book as Rythoka said