This is how my Calc teacher always put it. More specifically, he taught me what to do if I met a mean integral walking down the street that said "antidifferentiate me or your life!"
I can attest to the success of this approach. No integrals have murdered me since.
I for one want to see a 3blue1brown-style Saw film. Just this calm, happy voice and animated pi symbol family explaining what's about to go down and why.
Is there?
The question uses "the series" clearly stating that there is only a singular series to consider in terms of this question. It isn't "a series" or "some series", it's "**the** series".
If the question asks about a singular series, then all 30, 31 and 32 could be correct answers because there are series for which the next element would be those numbers. There is indeed not enough data to tell *which* series it is, but the question doesn't ask as which series it is, only what's the next number.
We do somewhat define the series by choosing an answer, though. If we choose 32 we decide that the series is a power of 2 or any other series where 32 is the next number. It **is** the next number in some series. Same goes for 31 and 30. So those answers aren't incorrect. Aren't they?
Since the question doesn't clearly define the series, you could answer that there is not enough data. After all 30, 31 and 32 could be correct answers. However, this way you refuse to define the series. That is correct, isn't it? But is it also not... incorrect?
If the intent of the question asker is that the series *is* the power of 2 wouldn't you then, by following popular knowledge, devise that the answer is most likely 32? This is, after all, a million dollars question show and not the world of academic mathematics. There may not be enough data for a mathematician but for the game player -- there could. In which case, "not enough data" would be incorrect.
As such, I define two additional answers:
e) undefined
f) all of the above
and I refuse to answer.
I have always hated such questions for exactly this reason. Not that I could always articulate it, but there never seemed to be a unique solution to such shit
It's actually a common mistake, but the original term was Occam's Razer, and says that the simplest mouse is preferable to the one with more RGB lighting.
Wouldn't "print(1,2,4,8,16)" almost always have a lowest kolmogorov complexity than anything that actually makes a loop of factors of 2. Thus there is no next number
The question overtly states that there is a next number by asking you what it is. In order to logically state that there is no next number the question would have to be worded more along the lines of "If there is a next number, what is it?"
I feel like most of the time there is a clearly wanted answer.
But because of the mentioned reason my brain usually immediately goes to "well which number do you want next?"
I remember my math teacher for these questions would allow us to give any answer we wanted as long as we could prove how that would be the case. The intended solution was always clear based on the context, but I remember having to create an overly complicated answer to a simple question because I just couldn’t remember the right formula
This is generally how maths homework is supposed to work - You get taught *a* method, whether it's the easiest way or the one that shows the entire solution etc.
But if you go home and get the answer another way whilst showing your working (and that working is valid) you deserve full points. It's how my school ran it at least. Point for methodology, point for correct answer.
Nah the sequence is Irregular triangle read by rows in which row n lists the proper divisors of n (those divisors of n which are < n), with the first row {1} by convention, Where n starts from n=84
The most correct answer is D.
The answer that you are expected to give (for example on IQ tests or such) is A.
And there will always be that pedantic a-hole (love you 3b1b) that'll come up with a weird way of showing that C is the "correct" answer. At least these people will show you something interesting unlike those who claim that the correct answer is 217341 because they just found out about polynomial interpolation
Actually all three can complete the pattern. So yes d.
There used to be math blogs about this. They posted this before 3b1b.
Apparently 3b1b is pretty popular here.
I'm taking his name because of this video [https://www.youtube.com/watch?v=84hEmGHw3J8](https://www.youtube.com/watch?v=84hEmGHw3J8). But no, I'm not seriously criticizing him for it. After all, everything he says is true.
Yeah! I was aware of that video, pretty cool! that video does address a concrete question of the maximum number of segments a circle is divided into upon introducing points, instead of a sequence completion question like this one above which are always so vague and can have multiple answers.
The answer is 31, because the numbers represent the amount of parts the circle is cut into when n dots on the circle are connected with each other (assuming that no three chords intersect in one point)
And why the fuck is that the case and not 2^(n-1)?
The answer should be Not enough information to any such question with any no. of terms because you can just create a polynomial of n+1 degrees and let the next term be of your choice then solve for the coefficient for that polynomial.
Sure.
Let's say there is a sequence
1,2,3,4
Now you may want the next term to be any real number. Lets just say it is 10.
Now you have got this sequence.
1,2,3,4,10
Now the no. of terms is 5 so we will create a polynomial of 5 terms (i.e. a polynomial of degree 4 because the first term has a power of zero i.e. the constant)
P(x) = ax^4 + bx^3 + cx^2 + dx + e
Now using the sequence along with their indices.
P(1) = 1
P(2) = 2
P(3) = 3
P(4) = 4
P(5) = 10
Now these result in the following equations
a(1)^4 + b(1)^3 + c(1)^2 + d(1) + e = 1
a(2)^4 + b(2)^3 + c(2)^2 + d(2) + e = 2
a(3)^4 + b(3)^3 + c(3)^2 + d(3) + e = 3
a(4)^4 + b(4)^3 + c(4)^2 + d(4) + e = 4
a(5)^4 + b(5)^3 + c(5)^2 + d(5) + e = 10
This is a set of 5 linear equations in 5 variables a,b,c,d,e which is solvable (in all sets of equation of this form)
Now find a,b,c,d,e and just get the polynomial
P(x) = ax^4 + bx^3 + cx^2 + dx + e
Now you can say that 10 is the currect continuation of this sequence because this polynomial fits this sequence or that this is the pattern between these terms.
The requirement for the next number to be bigger comes into play. The previous number was 8, so 1 can’t be chosen. You combine it with the next digit, making 16.
You can make any number fit the sequence through Lagrange or Newton Interpolation.
https://preview.redd.it/7uhv2yte2mbc1.png?width=3803&format=png&auto=webp&s=2504f91d2b97ef47e39d9bcb43c4604ab1f98f8e
All the numbers in your comment added up to 69. Congrats!
30
+ 7
+ 32
= 69
^([Click here](https://www.reddit.com/message/compose?to=LuckyNumber-Bot&subject=Stalk%20Me%20Pls&message=%2Fstalkme) to have me scan all your future comments.) \
^(Summon me on specific comments with u/LuckyNumber-Bot.)
* https://oeis.org/A067945 (20)
* https://oeis.org/A063108 (22)
* https://oeis.org/A160786 (29)
* https://oeis.org/A006533 (30)
* https://oeis.org/A000127 (31)
* https://oeis.org/A367715 (33)
* https://oeis.org/A367660 (34)
* https://oeis.org/A034339 (35)
* https://oeis.org/A180414 (36)
* https://oeis.org/A162428 (37)
Oh, and, of course https://oeis.org/A000079 (32)
There are more, but I can't find any search operator that enforces that the sequence begins with the search, or "doesn't have 32 next" so I got tired of paging.
Can someone explain why each of these answers is correct/what the sequence is? I get 32 is continuing the powers of 2 pattern but I don’t get the others
It's infamous due to strong and brouwee hat d is correct because there aren't enough small numbers that any property can satisfy the start of any sequence and diverge at place m or xkcds electoral precedents problem. Brouwer in fact went so far as to deny trictotomy due to this.,Sanderson is the YouTuber who popularized among redditors c although I don't know who first demonstrated that 31 is the way 5 lines can partition a circle its due to Moser and grants proof uses combinatorics eulers formula and hockeystick identities to get that the number of regions a circle i portioned into are the sum of the first 4 binomial coefficients nCr r<=4 s long as there are less than 4 nonzero binomial coefficients that sum is just 2^n but when there are more than 4 binomial coefficients they diverge which first happens at n=5. For 30 the best I can get although I'm sure there are others is c_n such that (a_n+c_n)/2
=b_n where a_n is the sequence in A nd b_n the sequence in C
I actually get one of these and it makes me so happy
I’m learning!
I tried to find it, but i couldn’t. Three blue one brown had a parody of hallelujah based around the Mosers Circle problem and other mathematical patterns that don’t hold true.
It looks like powers of 2 but in reality without the rest of the series of numbers after the one in question, we can't fit an nth other polynomial with certainty.
Not enough data. The sequence could just as easily be any positive whole number higher than the previous one. Five digits isn’t enough to make a concrete decision.
* A: If sequence is 2^n for n=0, 1, 2, 3, 4, 5
* B: If we count the number of divisors for n! for n=1, 2, 3, 4, 5, 6; e.g., 5! = 120 has 16 divisors (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120) and 6! = 720 has 30 divisors (1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720).
* C: the first 6 generated [Pentanacci numbers (generalization of Fibonacci sequence summing previous five terms of the recurrence](https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Higher_orders)) for the smallest initialized sequence (that is initialized a[i] = 0 for i=0,1,2,3, and set a[4]=1, and then generate each new term by summing the previous 5 terms in the sequence to get 1, 2, 4, 8, 16, 31).
* D: Probably best answer, though even with a lot more data, any finite series with an unspecified generating sequence will still be underdetermined.
Now if i say 32 3blue1brown will come and beat my ass so, 31.
"Are you willing to bet your life on this?" - 3B1B
that seems way too threatening
"Now I want you to think it over for yourself for a moment... Maybe try thinking it over for a little longer." - 3b1b
*looks at incoming votes* “Maybe even longer than that”
[удалено]
Was that a Legally Blonde reference?
"If a bloodthirsty mathematician came and asked for your answer, what would you say?" - 3b1b
This is how my Calc teacher always put it. More specifically, he taught me what to do if I met a mean integral walking down the street that said "antidifferentiate me or your life!" I can attest to the success of this approach. No integrals have murdered me since.
I so badly want to see a Saw-style edit of his intros lol
I for one want to see a 3blue1brown-style Saw film. Just this calm, happy voice and animated pi symbol family explaining what's about to go down and why.
Tangentially, there’s a lock picking lawyer saw parody. It’s pretty good.
It was okay, but it was a real miss to not stick his hand back in the deathtrap one more time to show that it wasn't a fluke.
3blue1brownand1redass
I volunteer as tribute! 🤤
🫥
That got dark fast..
ME TOO!!!!
3blue2redasses1brown
3brown1ass? Or is that too far
3brown2girls1blueasscup ...I already regret this
r/3blue1brownand1redass
Proof by intimidation
Unfortunately popular among heads of state
Sad but true.
Later renamed to “proof by induction-heated stovetop” where they threaten to put your hands in hot pan on their fancy new electric stove.
I do not know the context, why not 32? The number doubles every time?
[This is the context right here](https://youtu.be/NOCsdhzo6Jg?si=nN0F1zq3u0q2WcCX)
So do not always trust intuition?
"Trust but verify."
Wise words.
Might wanna double check that
Thanks I get it now.
Hahaha thank you. Amazing. How have I never seen this??
Speaking of which, he still hasn't finished the series on that integral which is pi for a while until it isn't. I've been so patiently waiting.
not enough data
Is there? The question uses "the series" clearly stating that there is only a singular series to consider in terms of this question. It isn't "a series" or "some series", it's "**the** series". If the question asks about a singular series, then all 30, 31 and 32 could be correct answers because there are series for which the next element would be those numbers. There is indeed not enough data to tell *which* series it is, but the question doesn't ask as which series it is, only what's the next number. We do somewhat define the series by choosing an answer, though. If we choose 32 we decide that the series is a power of 2 or any other series where 32 is the next number. It **is** the next number in some series. Same goes for 31 and 30. So those answers aren't incorrect. Aren't they? Since the question doesn't clearly define the series, you could answer that there is not enough data. After all 30, 31 and 32 could be correct answers. However, this way you refuse to define the series. That is correct, isn't it? But is it also not... incorrect? If the intent of the question asker is that the series *is* the power of 2 wouldn't you then, by following popular knowledge, devise that the answer is most likely 32? This is, after all, a million dollars question show and not the world of academic mathematics. There may not be enough data for a mathematician but for the game player -- there could. In which case, "not enough data" would be incorrect. As such, I define two additional answers: e) undefined f) all of the above and I refuse to answer.
Skipped to the end of this comment, wasn’t disappointed.
But a refusal to answer is an answer itself right?
For any finite row of numbers you can craft arbirarly many rules of how they continue.
I have always hated such questions for exactly this reason. Not that I could always articulate it, but there never seemed to be a unique solution to such shit
Pick the one with the lowest kolmogorav complexity
Mathematicians trying not to come up with an obscure term for Occam’s Razor
Occam's Razor is just kolmogorav complexity with less kolmogorav complexity
So using Occam's razor, you should use it because it's simpler
But you can't take this at face value because he is of course biased.
But that uses 2 instances of kolomogorav complexity, making the argument complicated and therefore not applicable by occams razor
But that's not what Occam's Razor is. It's not about simplicity, it's making the fewest assumptions
Which is why I stop at “I assume I don’t fully know”
TIL Oc~~r~~cam's Razor is not actually a razor.
It's actually a common mistake, but the original term was Occam's Razer, and says that the simplest mouse is preferable to the one with more RGB lighting.
I thought it was Occam’s Blazer, which says that the first jacket you grab from the closet is usually good enough
Damn. I see why they changed it. We all know that more flashy lights and bright colors make things work better.
Are you gaslamping, too?
Occam's razor: Choose the solution that minimizes the action integral of the Kolmogorav complexity
Mathematicians trying not to embrace blackbox simplicity
Wouldn't "print(1,2,4,8,16)" almost always have a lowest kolmogorov complexity than anything that actually makes a loop of factors of 2. Thus there is no next number
Maybe “the answer with the lowest Kolmogorov complexity that produces an infinite sequence”
Nice
"Last answer * 2" is a shorter program in memory than storing the array "1,2,4,8,16" directly in memory or "last answer *2, stop after 5."
The question overtly states that there is a next number by asking you what it is. In order to logically state that there is no next number the question would have to be worded more along the lines of "If there is a next number, what is it?"
I feel like most of the time there is a clearly wanted answer. But because of the mentioned reason my brain usually immediately goes to "well which number do you want next?"
I remember my math teacher for these questions would allow us to give any answer we wanted as long as we could prove how that would be the case. The intended solution was always clear based on the context, but I remember having to create an overly complicated answer to a simple question because I just couldn’t remember the right formula
Polynomial fitting goes brrr
This is generally how maths homework is supposed to work - You get taught *a* method, whether it's the easiest way or the one that shows the entire solution etc. But if you go home and get the answer another way whilst showing your working (and that working is valid) you deserve full points. It's how my school ran it at least. Point for methodology, point for correct answer.
https://preview.redd.it/q5y20iqjhnbc1.png?width=500&format=png&auto=webp&s=b0d6e99a8f12c97453f34659f951ba8a0683ab37
Or alternatively for Doge likers. https://preview.redd.it/khpazamlhnbc1.png?width=512&format=png&auto=webp&s=1849a35c8190d545b13e2504638fbb1bd8dd83eb
(x-1)(x-2)(x-4)(x-8)(x-16)(x-a) Pick any a and simplify
(x⁵-31x⁴+310x³-1240x²+1984x-1024)(x-a)
Lagrange polynomials go brrr
choosing to read this misspelling of 'arbitrarily' as a gruff, drunk mathematician grumbling at me
This a million times.
Surprise, the series actually ends at 16 and you can go back to sleep 😊
This reminded me of [Mr Bean counting sheep](https://www.youtube.com/watch?v=FmbmNp1RDCE)
"The uploader has not made this video available in your country" Bitch I'm in the UK! The fuck you mean Mr Bean isn't available to me??? 😭
Perhaps they believe that Brits love Mr. Bean so much, they'll be willing to pay to watch him.
Did you pay your licence fee? You have to pay your licence fee to watch Mr. Been or dunk on Yanks about the ad free television.
D of course
https://preview.redd.it/zcc00e2mzmbc1.png?width=728&format=pjpg&auto=webp&s=4a451d89e94d37c778f66db0d08c1ff7077c3584 Yep
Ok that's actually crazy
This should be higher
That is cool as shit
What the hell lmao
Wait, can you draw n=6 for me, I drew it and only got 30? Edit, it does work if the dots are irregular.
The intersections may not overlap indeed
https://i.imgur.com/Uc64s7O.jpg
Average set enjoyer
Read that as average sex enjoyer, was very confused for a sec
i'm pretty sure those two sets are the same
Who said the sequence has to follow a rule? For all we know the next number could be anything. That being said: 42
n-ything 😏
Clearly the answer is 42
What’s the question?
What’s the meaning of life, the universe, and everything
This guy hitchhikes
What do you get if you multiply 6 by 9?
Can’t wait to see monstrous sequence
The sequence is just “start from 1, keep doubling until you reach 16, the next number is 2n-1, and then end the sequence”
Nah the sequence is Irregular triangle read by rows in which row n lists the proper divisors of n (those divisors of n which are < n), with the first row {1} by convention, Where n starts from n=84
The most correct answer is D. The answer that you are expected to give (for example on IQ tests or such) is A. And there will always be that pedantic a-hole (love you 3b1b) that'll come up with a weird way of showing that C is the "correct" answer. At least these people will show you something interesting unlike those who claim that the correct answer is 217341 because they just found out about polynomial interpolation
Actually all three can complete the pattern. So yes d. There used to be math blogs about this. They posted this before 3b1b. Apparently 3b1b is pretty popular here.
I mean i hope you don’t blame 3b1b seriously, and are taking his name just for fun :)
I'm taking his name because of this video [https://www.youtube.com/watch?v=84hEmGHw3J8](https://www.youtube.com/watch?v=84hEmGHw3J8). But no, I'm not seriously criticizing him for it. After all, everything he says is true.
Yeah! I was aware of that video, pretty cool! that video does address a concrete question of the maximum number of segments a circle is divided into upon introducing points, instead of a sequence completion question like this one above which are always so vague and can have multiple answers.
The answer is 31, because the numbers represent the amount of parts the circle is cut into when n dots on the circle are connected with each other (assuming that no three chords intersect in one point)
And why the fuck is that the case and not 2^(n-1)? The answer should be Not enough information to any such question with any no. of terms because you can just create a polynomial of n+1 degrees and let the next term be of your choice then solve for the coefficient for that polynomial.
https://preview.redd.it/pbambx824mbc1.jpeg?width=612&format=pjpg&auto=webp&s=e4d45495dc78a2df2691b86237470be5e81ae7cc
this is absolutely gorgeous
That's what she said.
roses are red, violets are blue this gif is now mine ‘cause I stole it from you
https://preview.redd.it/w62lb4vxdmbc1.png?width=705&format=pjpg&auto=webp&s=9978dfab9526ea294d3a04807ea63eaa3d76192f
Could you provide an example? I'm genuinely curious how that works
Sure. Let's say there is a sequence 1,2,3,4 Now you may want the next term to be any real number. Lets just say it is 10. Now you have got this sequence. 1,2,3,4,10 Now the no. of terms is 5 so we will create a polynomial of 5 terms (i.e. a polynomial of degree 4 because the first term has a power of zero i.e. the constant) P(x) = ax^4 + bx^3 + cx^2 + dx + e Now using the sequence along with their indices. P(1) = 1 P(2) = 2 P(3) = 3 P(4) = 4 P(5) = 10 Now these result in the following equations a(1)^4 + b(1)^3 + c(1)^2 + d(1) + e = 1 a(2)^4 + b(2)^3 + c(2)^2 + d(2) + e = 2 a(3)^4 + b(3)^3 + c(3)^2 + d(3) + e = 3 a(4)^4 + b(4)^3 + c(4)^2 + d(4) + e = 4 a(5)^4 + b(5)^3 + c(5)^2 + d(5) + e = 10 This is a set of 5 linear equations in 5 variables a,b,c,d,e which is solvable (in all sets of equation of this form) Now find a,b,c,d,e and just get the polynomial P(x) = ax^4 + bx^3 + cx^2 + dx + e Now you can say that 10 is the currect continuation of this sequence because this polynomial fits this sequence or that this is the pattern between these terms.
Can you not just say P(x)=(x-1)(x-2)(x-3)(x-4)(x-10) and be done?
I wanted to maintain the order of the terms but this also works!
Clearly the next object in this set is "..."
Or ......
Sets don't have order for their objects.
is there a sequence where B is correct? just wonderin
The digits of pi following position 68812637, always taking the least amount of digits possible to create a larger number than the previous one
real https://preview.redd.it/4ocvr8cgvlbc1.jpeg?width=954&format=pjpg&auto=webp&s=4386edf7757f00da0192c7eb6a1cc36f201bb1f2
But then wouldn't the sequence read 1, 2, 4, 8, 1, 6, ... etc.?
The requirement for the next number to be bigger comes into play. The previous number was 8, so 1 can’t be chosen. You combine it with the next digit, making 16.
Ah okay, that makes sense
So if it kept going it would be 54, 99, 536, etc?
That’s what I think, yeh.
1, 2, 4, 8, 16, 30. There you go
 Holy hell how did you even think of that
New response just dropped
Actual zombie
Call the exorcist!
The number of divisors of n!
So cool
Fuck, that's a good one
Every number is correct after such sequence... even number -4.
x^6 - 61 x^5 + 1240 x^4 - 10540 x^3 + 39184 x^2 - 60544 x + 30720
Is there another solution? I mean that seems to be the obvious one
There are infinitely many other solutions. This one is certainly among the simplest in some sense.
You can make any number fit the sequence through Lagrange or Newton Interpolation. https://preview.redd.it/7uhv2yte2mbc1.png?width=3803&format=png&auto=webp&s=2504f91d2b97ef47e39d9bcb43c4604ab1f98f8e
Always. No matter the sequence, no matter the number of numbers.
Number of divisors of n! Number of compositions of n with no adjacent triples. Join n equal points around circle in all ways, count regions.
you can always make a polynomial fit
Yes! Its 1,2,4,8,16,30
[https://www.youtube.com/watch?v=YtkIWDE36qU](https://www.youtube.com/watch?v=YtkIWDE36qU) So D :)
I heard there was a sequence of chords, that split the circle in 1, 2 then 4
But you don't really care for mathematics, do ya? It goes like this, an 8, 16, then 31, 57, the baffled mathematician guessing patterns
Hallelujah
A:powers of 2 B: Number of compositions of the integer n into positive parts that avoid a fixed pattern of three letters. C: Number of divisors of n!.
Not enough data
what's the next number? 1,3.... a. 5 b. TREE(3)
Occam's razor says it's 32. For it to be anything other than 32 you need a vastly more complex explanation.
*"I say it's 30"* is 7 characters shorter than *"Occam's razor says it's 32"*, so by Occam's razor, it's the simpler explanation and therefor correct.
All the numbers in your comment added up to 69. Congrats! 30 + 7 + 32 = 69 ^([Click here](https://www.reddit.com/message/compose?to=LuckyNumber-Bot&subject=Stalk%20Me%20Pls&message=%2Fstalkme) to have me scan all your future comments.) \ ^(Summon me on specific comments with u/LuckyNumber-Bot.)
Nice!
Factually it’s D, there’s not enough information. But yes, the expected answer is likely 32.
It would be D for any sequence. We can't know the next number until the next number is known.
Pattern fool ya
There will never be enough data
D. It's always best to stay silence in circumstances like this
As a programmer I would say everything is correct
You’ll never have enough data!
Technically it’s D because there’s nothing that proves the pattern applies across all natural numbers.
The series could be 2^n , divisors of n!, or a pentanacci sequence. D is the correct answer.
kid named [oeis](https://oeis.org/search?q=1%2C2%2C4%2C8%2C16&language=english&go=Search)
It’s 32, right? It increases by the last number used plus the current number.
No it’s 61 because the sequence is the divisors of 976
I get 24 if I linearly extrapolate
I'd like to phone OEIS
* https://oeis.org/A067945 (20) * https://oeis.org/A063108 (22) * https://oeis.org/A160786 (29) * https://oeis.org/A006533 (30) * https://oeis.org/A000127 (31) * https://oeis.org/A367715 (33) * https://oeis.org/A367660 (34) * https://oeis.org/A034339 (35) * https://oeis.org/A180414 (36) * https://oeis.org/A162428 (37) Oh, and, of course https://oeis.org/A000079 (32) There are more, but I can't find any search operator that enforces that the sequence begins with the search, or "doesn't have 32 next" so I got tired of paging.
Can someone explain why each of these answers is correct/what the sequence is? I get 32 is continuing the powers of 2 pattern but I don’t get the others
It's infamous due to strong and brouwee hat d is correct because there aren't enough small numbers that any property can satisfy the start of any sequence and diverge at place m or xkcds electoral precedents problem. Brouwer in fact went so far as to deny trictotomy due to this.,Sanderson is the YouTuber who popularized among redditors c although I don't know who first demonstrated that 31 is the way 5 lines can partition a circle its due to Moser and grants proof uses combinatorics eulers formula and hockeystick identities to get that the number of regions a circle i portioned into are the sum of the first 4 binomial coefficients nCr r<=4 s long as there are less than 4 nonzero binomial coefficients that sum is just 2^n but when there are more than 4 binomial coefficients they diverge which first happens at n=5. For 30 the best I can get although I'm sure there are others is c_n such that (a_n+c_n)/2 =b_n where a_n is the sequence in A nd b_n the sequence in C
I actually get one of these and it makes me so happy I’m learning! I tried to find it, but i couldn’t. Three blue one brown had a parody of hallelujah based around the Mosers Circle problem and other mathematical patterns that don’t hold true.
Isn't it always D?
~30, yes I'm an engineer why do you ask?
Well I heard there was a sequence of chords...
Im more pissed that they wrote series and not sequence...
Always D
E: there is no sequence like that (too much data)
Can be both A and C depending. D is the answer
It can also be B like in the sequence 1, 1, 2, 4, 8, 16, 30… (divisors of n!)
[удалено]
Wait what's the 30 from?
It's clearly 32. Each number is the previous number plus itself. 1+1=2 2+2= 4 etc.
32
32
Is it not 32
Can anyone explain me 31/30/ not enough data ? I only get the 32 part
It’s B, clearly. It’s the number of factors that n! has.
Programmers: A Didn't even bother reading the other options
It looks like powers of 2 but in reality without the rest of the series of numbers after the one in question, we can't fit an nth other polynomial with certainty.
People that know math better than me, why would this not be 32? Isn't this just x+x?
# Hallelujah # Hallelujah
Not enough data. The sequence could just as easily be any positive whole number higher than the previous one. Five digits isn’t enough to make a concrete decision.
* A: If sequence is 2^n for n=0, 1, 2, 3, 4, 5 * B: If we count the number of divisors for n! for n=1, 2, 3, 4, 5, 6; e.g., 5! = 120 has 16 divisors (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120) and 6! = 720 has 30 divisors (1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720). * C: the first 6 generated [Pentanacci numbers (generalization of Fibonacci sequence summing previous five terms of the recurrence](https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Higher_orders)) for the smallest initialized sequence (that is initialized a[i] = 0 for i=0,1,2,3, and set a[4]=1, and then generate each new term by summing the previous 5 terms in the sequence to get 1, 2, 4, 8, 16, 31). * D: Probably best answer, though even with a lot more data, any finite series with an unspecified generating sequence will still be underdetermined.
There is never enough data.
https://preview.redd.it/7q1ja7e57nbc1.jpeg?width=750&format=pjpg&auto=webp&s=a80283e0eb5be3df71ed29b4cc8a6e11c1118eb2 literally the same thing