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@Hand Solo Well, it is related to numbers and their written representation, and this is Numberphile, not Mathphile after all. So it's on the borderline of "belongs here". It's an [for me] entertaining variety on the "usual" content that's on this channel.
Major flaw at 4:00 while it was obvious for me that the roman numeric system was used. Thanks to six being very obvious, you literally said with the next image that only the numbers matter not the word. I found it funny but still... you should have noticed that while editing...
Him: Don’t get distracted into looking for something that’s too complicated Also him: * looking to be confused at his own solution * there’s an invisible zero.
+Patrick Salhany My guess on the first sequence was that I took the last digit in the previous term and then the whole term before that, and put them together - like for example 4 and 8 make 48, 8 and 48 make 88, and 48 and 88 make 488. That actually did give me the answer 888 for the next term, but that was obviously very different from the method in the video.
Me too 😅. Also, I thought his ”eban numbers” -sequence was missing something: 1000, 1002, 1004, 1006, 1030, 1032,…; and then I got the catch. What is it? I’ll let you work it out.
1, 2, 48, 46, 37, 2000, 48, 48, 48, 27, 19, ... what's next and why? Answer: 18 because that was the list of the numbers I randomly came up with when I wrote this comment, and 18 is the next one I'm thinking about.
If there are are not other language versions of eban already on it, you could submit them to the OEIS? I don't know if they'll be approved, but you'd think they must be a chance?
In Dutch we have: 5,8,12,20,50,80,5000000000,8000000000,12000000000,20000000000,50000000000,80000000000,5000000000000000,... I don't have enough knowledge to know whether this goes on forever :p
From now on I’m using my own font where none of the numbers has any holes. Always leaving a hole in the loop. See? I found the loophole in the first sequence.
@@Tytoalba777 So that's a loophole inside their loophole... But then there is no loophole to find a loophole inside of. Is this a loophole inside your loophole inside their loophole?
I’ve watched this like 10 times and I keep coming back and watching it again. Same with all of his videos. I love this guy so much. Please keep doing more with him.
Me too. Obviously those puzzles aren't about the numbers themselves. Instead they're about different representations of numbers. THOSE ARE TWO DIFFERENT THINGS! oh so angry.
EMIRPS is actually correct. It's "PRIME" backwards then put in plural. It's more accurate because you can then say "an EMIRP" to speak of an element of the "EMIRPS sequence"...
Many people are really taking this too seriously. Numberpile isn't a channel for rigorous mathematics, it's a channel for having fun with math and numbers. Of course people are interested in unexpected and mysterious patterns but not every video has to be about that and this one clearly isn't trying to. Numberphile also shouldn't be your go to source for learning about mathematics. I think Neil has a very nice style and the sequences were cute.
Which is fine, but like the last video on moon numbers it doesn't make it even remotely clear this is the purpose. it started by saying 'these numbers might be taught in school" and then goes on to say "well we just made stuff up, it has no practical purpose whatsoever in your daily life" And this video aren't (to me) interesting rules. It's extremely narrow usage of numbers. erimps were somewhat interesting, eban numbers also, but even eban suffers in that it is language dependant, and that kind of shows the weakness of these things to me. It becomes so situational that pretty quickly this numbers tend to shoot up like crazy, and become so far and wide apart as to be meaningless. Notice how Tadashi often showed toys or other interesting tricks or ideas, but they were are math related where the maths behind it is interesting. Not just "we took this arbitrary rule"
@@blazerer2424 These sequences might be arbitrary but studying them is not pointless. You don't need to study an object because you expect an interesting outcome, you can study them mathematically just bexause you want to see the patterns that emerge! And evem though these sequences are highly specific to the representation of numbers they are (can be) nontheless well defined and non trivial. Try finding a formula for the sequence "number of 'e's in n", you will have to figure out the rules how we combine our words to make new number words, maybe draw a graph laying out the grammar of this process, don't underestimate the maths you can do with specific objects.
@@blazerer2424 Since you mentioned the moon video I also want to comment on that. Algebra is all about studying how different algebraic operations behave and what structures emerge, so I wouldnt underestimate it. Maybe you come up with a funny operation and end up showing that you can express it with algebraic objects that you already know (groups, rings, morphisms, actions), wouldnt that be cool.
Wait I got this : so if I translate the english words for those numbers into korean, then back , then into French then back and then wrote them on a wall, an armadillo would point at them in this specific order. I get it now
For some reason if you do that, 2 literally just disappears?? one two three four five six => 일이 삼 사 오 육 => Un trois quatre cinq six => One three four five six ???? Where did 2 escape 2?
Watching Neil Sloane videos makes me feel like I'm hunched over the Fountain of Truth wild-eyed, drinking deep its Waters in fervent Gulps with bright and beautiful Madness shimmering in my Eyes, seeing the World not as It Is or as It Should Be, but as It Could Never Be.
I loved this one: 61, 21, 82, 43, 3, 64 Because I got it right thinking of something completely different. I added 6+1=7; 2+1=3 and 8+2=10. So, since the next numbers are 43 and 3, both, when added, sum up to 7 and 3, I thought it was a recurring thing for the algarisms to sum in a loop 7, 3 and 10, 7, 3 and 10. So, the next one had to have a second algarism that was one value higher than the last (because it starts as x1, y1, z2, a3, b3... I supposed the c would be 4), it had to be c4 and c+4 had to be 10, therefore, 64.
My Dad used to do that because the original computer keyboards had the zero like that to distinguish it from a capital O. It meant when I lived at number 20 one item of my post got sent to number 21 because the slash looked like a correction, which confused the postman. [It looks more like a phi than a theta!]
I noticed immediately that he was careful to write the first "4". I didn't think much of it, but noticed that it may be important. I guess it was, to close the hole.
When I was in primary school, I had always thought about that is it legit for a maths test to ask us what is the next term of a provided sequence? Isn't that you can somehow make a formula for any number to fit in the next term?
There's an inherent problem with "continue the sequence" puzzles: it's always possible to find a mathematical justification (indeed, any number of such justifications) for *any* continuation of the sequence. That's demonstrably the case (had thos theorem taught to my in my Calculus 101 class back in the day). PS: I found the intended continuation for the second sequence without guessing the comma shift thingy. One more drawback of those puzzles is that you only get the output, without the reason for it.
True 🎯. That’s, why my mathematician Friend hates these sequences, and doesn’t consider them mathematics. Including every sequence. Like: ”1, 2, 3,…”, and: ”0, 0, 0,…”.
Actually, i know there exist a certain theorem that ANY number can be the next number..... (take for example, in a simple series like 1, 2, 3, 4, 5, 6....... and logically, we know the next must be 7, but indeed, according to this theorm, it could be 7, 8, 9, or indeed, any number. Unfortunately, i cannot remember what the name of this theorem is...... Can someone help?
I actually came up with a different rule for that one and it works: 2:00 (0), 61, 21, 82, 43, 3, 64, 24, 85, 46, 6 (+61-40+61-39-40)(+61-40+61-39-40)...
@@ubertoaster99 No he said it does count, IDIV sis not count in the video. Though it is complicated with Roman numbers, there are several set of rules, some allow for IIII being four, some allow to subtract ones from big numbers...
@@TheLetterT511 no, on the standard rules for Roman number, the subtraction works only between 2 letters close in magnitude, so when the second one is 5 or 10 times the first. So: IV = 4, IX =9, XL= 40, XC = 90, CD =400, CM =900 But ID, or XM doesn't make sense
Guys Im not sure if you have already figured thos out or seen it somewhere but I came out with this one myself. Number in sequence,n if you were to sum up is equivalent to the square of last number in the sequence and then minus all the numbers before it. e.g - 1+2+3 = 3^2-2-1, 1+2+3+4 = 4^2-3-2-1 and so on. Why. Look, number in sequence, n represented by dots and the likes,if you were to arrange in order will form a triangle. So if you square the number, it means you add x dots to form a square. The x dots are the numbers beforw the last number. Since the x dots are not really there, therefore the x dots should be substracted. So the square is no more, exactly what we are trying to find - the triangle. If you are unable to understand this, feel free to ask.
For the second one I had the correct answer with a different method. 61,21,82,43,3... The sum of the numbers make : 7,3,10,7,3... Then the sum of the last one is 10. Considering that the 4 on the fourth term is 2 below 6 and 3 is 2 above 1, I use the same method : 8 → 6 and 2 → 4 That way you find 64 !
I did something similar, seeing the sum of the numbers. I also got 64 another way. I saw that the first digit of each number was always a different even (6,2,8,4,0) and assumed the pattern repeated from there, so the first number is 6. Then I saw that the second number was increasing regularly (1,1,2,3,3), so 4 must be the next second number. Hence, 64.
Subtract 40. If *resulting* number could be subtracted by 40 add on 1. If the number *you subtract currently* can't be subtracted by 40 add on 1 infront of it. 21 - 40 would 82 It freaking works out even further in the series. Idk when it breaks or if it breaks but every number shown works lol.
I'm not certain but I don't think is a valid Roman numeral either, even though it looks like it ought to be 499. I think that according to the rules only C can subtract from D, only X can subtract from C, etc. 499 is CDXCIX.
I get similar patterns which are completely unrelated. The 2, 4, 6 thing makes a bit of sense as only numbers below six, you get to 66 and break (obviously because numbers after it have 'e', but it looks like there is a mathematical definition).
61, 21, 82, 43, 3 - I guessed this one right because I thought the pattern was that if you add each of the digits of each number (6+1, 2+1, 8+2, 4+3, 3), you get 7, 3, 10, 7, 3... so I figured the next number's digits must add up to 10; next, I looked at the two that add up to 7 (61 and 43) and 3 in the pattern (21 and 03) and saw that the first digit just transferred a 2 to the second digit (6 -> 4, 1 -> 3 and 2 -> 0, 1 -> 3) and determined that the next number must be 64 (8-> 6, 2 -> 4).
I had a similar process, recognizing that the sum of the digits was a pattern, but I ended up seeing that the first digit had a pattern of subtracting four each time, starting over at ten when zero was reached (6-4=2, 2-4=8, et cetera) from that, I figured the last digit had to have a 6 in the tens place, and the sum had to be 10, making the ones a 4. Therefore, 64.
Yeah, that one was sorta obvious because the camera zoomed in on the IX in "six" ... and the fact he was writing out the words meant it had to be something to do with the letters ...
It's like Neil Sloane is the lone wizard who is custodian of all types of magical numbers, be they powerfully useful, or trivially entertaining. But he enjoys them all and will pass them on to any visitor that cares to seek him out.
The first sequence could be defined without using holes, if you take away 1 you get. 0+4=4, 4+4=8, 8+4*10=48, 48+4*10=88, 88+4*100=488, 488+4*100=888 and so on. If n is generic element of the sequence then n=(n-1)+4*(10^i), with i=0,1,2,.... The power can be defined i'll think about
5 ปีที่แล้ว
Yeah, I had a similar solution. but I need given n1=1,n2=4,n3=8. then the rest comes with following algorithm: n[i] (with i>=4) = n[i-2]*10+last digit from n[i-1]. n4 = 10*4 + 8. n5=10*8+8. n6=10*48 + 8. and so on. well, the n1=1 isn't used here...
The solution I had was that it was simply ascending binary numbers (4 being binary 0 and 8 being binary 1) the 1 at the beginning throws that off though.
Well in math therms it's a bit more complex, but if you want anche algorithm to use on a calculator you set i to be:if n is the index of the generic sequence element as i meant before, then the generic sequence number S(n)=S(n-1) + 4*10^(i) where (i=n-1 if n is odd number) otherwise (i=log((S(n-1) - S(n-2))/4) if n is even) with base 10 but probably doesn't work for first elements. I'd need some more time to work the first elements
I used a different approach to determine the next numbers in the first sequence by using a substitution system. The first digit of each number is replace based on the following rules to determine the next number: 1 -> 4 4 -> 8 8 -> 48 Which results in the sequence 1, 4, 8, 48, 88, 488, 888, 4888 etc
@ 0:22, I found the same number by using this method: take the second integer of a term and combine it with the whole previous number (starting from the fourth term which is 48, doesn't work with 1, 4 and 8). Ex: So 48, take the second integer 8 and combine with the previous number 8 = 88, 88, take the second integer 8 and combine it with the previous number 48 = 488 488, take the second integer 8 and combine it with the previous number 88 = 888 888, take the second integer 8 and combine it with the previous number 488 = 4888 4888, take the second integer 8 and combine it with the previous number 888 = 8888 etc... give me the Nobel prize.
@@bastiens5219 I did the same and I also got the 64 right without realising the comma stuff. I just thought the rule was -40 if the result was positive, else +61. I don't know exactly why but it works for the next numbers as well.
The second one 61, 21, 82, 43, 3 has an other relatively simple rule: Add 60 to the previous one, take the rest of the division with 100 , if the sum of both digits is more than 6, add 1. So it continues with .... 64,24,85,46,.... which is also correct with the comma shift one.
I remember reading a Martin Gardener article in Sci Am many years back about "What number comes next". He said the correct answer is always 19. He said you can always find a justification for any following number if you try hard enough. It was a great article. (I wish I could find it again! (Sad Face)).
How is changing the sequence by moving commas and then adding random zeros *not complicated*? It goes against the very conventions that make a sequence a sequence.
Here the mathematical approach. 61 - 40 = 21 If the resulting number could be subtracted by 40 again, add on 1. If you go below 0 just keep on going (you know as if you take over 1) so 21 - 40 is 82 (20 - 40 wpuld be 10 then 00 then 90 then 80. I think you know what I mean.)
The graphic at 1:06 is correct, it says the number that divides the plane into n regions. 1 divides into 1 region, 4 divides into 2 regions, 8 divides into 3 regions. Am i missing something, I dont understand the need for the correction in the description.
The invisible zero one was complete nonsense. Why would numbers be having one invisible zero? Why didn't 61 have 061? Oh, it has to be only two digits? Well what happens when sequence gets above 100? The problem of sequences is also that there are always multiple solutions anyway. My solution is at least consistent, unlike his: 61, 21, 82, 43, 3, 46, 7, 53, 13, 66, 27,... Edit: the sequence start cycling once it reaches 55, it has a 36 number cycle. I just HAD to check. We know that is infinite number of sequences that could be a consistent continuation of the first 5 numbers. And yet he picks one that is inconsistent and says others are wrong. :)
Subtract 40. If *resulting* number could be subtracted by 40 add on 1. If the number *you subtract currently* can't be subtracted by 40 add on 1 infront of it. 21 - 40 would 82 X)
Damn I did get that it would be 64, but mainly because I assumed that first digit would follow pattern 6,2,8,4,0 and last digit seemed to be increasing, but having third 3 in a row would be weird for the sequence...
Yeah I did a similar thing, I got it by adding the previous number to the first number 61. it should've been 05 not 03, but adding 61 to 03 got me 64, which turned out to be right for all the wrong reasons =P
Funny to see how angry people get at this video. I found it frustrating too, when the rules were a bit "creative" but what's the point of getting angry at it? It's just different.
@@oldcowbb No. Old videos feature a lot of popular or funny numbers that happen to have wonky properties or features. Pointless ones often which you could find for just about any random number if you put the time in and get creative with your approach, but rigorously mathematical ones. These are just silly, non mathematical rules one might come up with to blow the minds of some 12 year olds but hardly something you approach an expectant and somewhat mathematically savvy audience with. They will be met with blank stares and and an invitation to see yourself out.
For the second sequence I got the right next term, 64 - but it was an accident: funnily enough if you simply look at the difference in value between each term, 61 -> 21 (minus 40), 21 -> 82 (plus 61), 82 -> 43 (minus 39), 43 -> 3 (minus 40 again)... so if one goes back to the beginning and follows the minus 40 with plus 61... 3+61=64 :) (the next one comes out as 25 instead of 24 though)
I found a more complicated pattern in 61, 21, 82, 43, 3. subtract 4 from the left most digit and loop back if you go below 0, so 2 minus 4 would be 8. around increase the right most digit by one, which would give you 64 for the next in the sequence
I love OEIS for programming. Need to generate a particular sequence of numbers? OEIS probably has an efficient way to calculate the n-th number instead of brute forcing it.
for the 4,8,48... function you could do: f(x)=sum{n=0 to x-1}(4*10^(floor((n+.1)/2))) this works for every value of x except 0 desmos code: f\left(x ight)=\sum_{n=0}^{x-1}4\cdot10^{\operatorname{floor}\left(\frac{n+.1}{2} ight)}
The way I worked out the first one was start with: 1, 4, 8, Go back 2 numbers (4) and take that number and multiply by 10 and add 8 = 4*10+8 = 48 and append this number to the end of the sequence. Now, go back 2 numbers (8) and take that number and multiply by 10 and add 8 = 8*10+8 = 88 and append this number to the end of the sequence. Now, go back 2 numbers (48) and take that number and multiply by 10 and add 8 = 48*10+8 = 488 and append this number to the end of the sequence. Now, go back 2 numbers (48) and take that number and multiply by 10 and add 8 = 88*10+8 = 888 and append this number to the end of the sequence. This makes a lot more sense to me.
The Roman numeral sequence has appeared once on Only Connect, but with the.letters replaced by the digits - F4V, S1X, SE5EN, and they had to figure out the fourth element was E1GHT
61,21,82,43,3 The first digit goes down by 4 each time The second digit hits each even number once and each odd number twice. The next number would be 64. This doesn't work with the "real" answer past the next digit, but it functions enough to work for this term and also requires the invisible zero
misdirection by not giving all the information is just lying. what about all the other missing zeroes before all the other numbers screwing up your "simple" solution . does not make your 'simple answer' simple. there is an easier one than the one you provide.
@@ludvercz Subtract 40. If *resulting* number could be subtracted by 40 add on 1. If the number *you subtract currently* can't be subtracted by 40 add on 1 infront of it. 21 - 40 would 82 It freaking works out xD
Catch two new bits of merch...
A world map poster based on Euler Spiral: teespring.com/shop/euler-spiral-world-map
Belphegor's Prime Decal stickers: store.dftba.com/collections/numberphile/products/belphegors-prime-decal-pack
Do you still sell the brown paper strips from your videos?
D DD DDD DDDD DDDDD...
I prefer to use Roman numerals.
Sometimes - they also get sent to Patreon supporters.
@Hand Solo Well, it is related to numbers and their written representation, and this is Numberphile, not Mathphile after all. So it's on the borderline of "belongs here". It's an [for me] entertaining variety on the "usual" content that's on this channel.
Major flaw at 4:00 while it was obvious for me that the roman numeric system was used. Thanks to six being very obvious, you literally said with the next image that only the numbers matter not the word. I found it funny but still... you should have noticed that while editing...
Him: Don’t get distracted into looking for something that’s too complicated
Also him: * looking to be confused at his own solution * there’s an invisible zero.
😂😂😂😂
??
6:36 “E is banned” - Math dad joke confirmed. 🙄
Wait, what? What's the joke?
Ebanned sounds in Russian like a swear word
😤
Rules are simple
"Make ur own rules " 😲😲
Exactly.
I really congratulate the ones who were able to solve most of these sequences, these sequences are more of code cracking.
+Patrick Salhany
My guess on the first sequence was that I took the last digit in the previous term and then the whole term before that, and put them together - like for example 4 and 8 make 48, 8 and 48 make 88, and 48 and 88 make 488.
That actually did give me the answer 888 for the next term, but that was obviously very different from the method in the video.
"are you getting the idea? let me continue: 60, 62, 64, 66, 2000, ..." hahaha
😂😂😂😂
Me s
Me too 😅. Also, I thought his ”eban numbers” -sequence was missing something: 1000, 1002, 1004, 1006, 1030, 1032,…; and then I got the catch. What is it? I’ll let you work it out.
@@ensiehsafary7633 Seems a bit _ad hoc,_ but I’ll roll with it, ’cause what the heck 🤷🏼♂️.
Continue the sequence: 1, 3, ?
(It's the Tree sequence)
7:21 Well obviously they're primes
Me: cries in corner
I didn't notice it either. I got hung up on the fact that only 1 3 and 7 appeared
62, 64, 66, 2000.. that escalated quickly
I shall call it the PMS series, because from 66 goes up to 2000
1, 3, TREE(3),...
2002, 2004, 2006, 2030, 2032, 2034, 2036, 2040, 2042, 2044, 2046, 2050, 2052, 2054, 2056, 2060, 2062, 2064, 2066, 4000, 4002, 4004, 4006, 4030, 4032, 4034, 4036, 4040, 4042, 4044, 4046, 4050, 4052, 4054, 4056, 4060, 4062, 4064, 4066, 6000, 6002, 6004, 6006, 6030, 6032, 6034, 6036, 6040, 6042, 6044, 6046, 6050, 6052, 6054, 6056, 6060, 6062, 6064, 6066, 30000...
Wait until you see the Dutch equivalent...
5,8,12,20,50,80,5000000000,...
Isn't 1000 a number without an e? It's thousand tight?
1, 2, 48, 46, 37, 2000, 48, 48, 48, 27, 19, ... what's next and why?
Answer: 18 because that was the list of the numbers I randomly came up with when I wrote this comment, and 18 is the next one I'm thinking about.
I'm not sure that one will get on the OEIS?!
Though I found some that start with 1,2,48
oeis.org/A098694
oeis.org/A053290
oeis.org/A203305
@@numberphile This encyclopedia is amazing! We need to build something like that in physics.
Pretty much sums up the video.
my teacher be like
I feel like this is the kind of stuff the Sphinx asks you before it eats you.
These are like the mathematicians version of Dad Jokes, and I love them
Ha ha. I like the idea of mathematical dad jokes.
@@numberphile I don't think it's possible to have mathematical jokes without them also being Dad jokes.
German eban sequence:
5, 8, 12, 20, 25, 28, 50, 55, 58, 80, 85, 88.
That's where it ends.
If you write Ü as UE, Ö as OE, then it's even shorter: 8, 20, 28, 80, 88.
But you can also add a few elements by calling 2 "zwo" instead of "zwei".
If there are are not other language versions of eban already on it, you could submit them to the OEIS? I don't know if they'll be approved, but you'd think they must be a chance?
btw. Germans save their space bar, they don't use it until one million :)
In Dutch we have:
5,8,12,20,50,80,5000000000,8000000000,12000000000,20000000000,50000000000,80000000000,5000000000000000,...
I don't have enough knowledge to know whether this goes on forever :p
Italian: 1 4 8 11 12 14 15 18 41.... too many
From now on I’m using my own font where none of the numbers has any holes. Always leaving a hole in the loop.
See? I found the loophole in the first sequence.
Ah, but if you found a loophole, than that still leaves one hole
Perfectly engineered pun!
@Just A Random Dood easy! Just erase the middle bit
Use an LCD based number font so there are no connecting parts.
@@Tytoalba777 So that's a loophole inside their loophole... But then there is no loophole to find a loophole inside of. Is this a loophole inside your loophole inside their loophole?
I’ve watched this like 10 times and I keep coming back and watching it again. Same with all of his videos. I love this guy so much. Please keep doing more with him.
"There's an invisible zero" (2:37). Yeah. Right. Spotted that straight away. Not.
It makes sense when you think of it as removing any zeroes at the front of a number, which is a pretty normal thing to do!
So ... I can introduce any number of "invisible" leading zeros anywhere I like?
@@stuartofblyth 0023400.00=23400, but not the same as 2340 or 234.
I didn't accept that invisible zero either :(
@M. de k. No, but he should have not added a random 0 in the middle of the sequence.
Neil has the brain of a professor and the cheeky enthusiasm of a 7 year old. Always a pleasure to watch 😊👏.
This video makes me angry.
Me too. Obviously those puzzles aren't about the numbers themselves. Instead they're about different representations of numbers. THOSE ARE TWO DIFFERENT THINGS! oh so angry.
Your comment lacks subtlety. You can't just announce how you feel!
@Drunken Hobo That makes me feel angry!
CGP Grey wants to
Know your location
turnipy88 because you are a kid
Anyone else really want EMIRPS to be SEMIRP?
Yes. That was his second mistake.
I think putting the s on the end emphasizes that it's a prime backwards but it's forwards.
EMIRPS is actually correct. It's "PRIME" backwards then put in plural. It's more accurate because you can then say "an EMIRP" to speak of an element of the "EMIRPS sequence"...
I agree with fares gaming, but it also should IMO be capitalized as "EMIRPs".
Nope. A "prime" number is a singular, "primes" is all of them. Same here. An emirp is one, collective they are emirps.
at 3:52 where he makes a biiiig grin and says "what's the rule?"
Many people are really taking this too seriously. Numberpile isn't a channel for rigorous mathematics, it's a channel for having fun with math and numbers.
Of course people are interested in unexpected and mysterious patterns but not every video has to be about that and this one clearly isn't trying to.
Numberphile also shouldn't be your go to source for learning about mathematics. I think Neil has a very nice style and the sequences were cute.
Cheers. Variety is the spice of life.
Which is fine, but like the last video on moon numbers it doesn't make it even remotely clear this is the purpose. it started by saying 'these numbers might be taught in school" and then goes on to say "well we just made stuff up, it has no practical purpose whatsoever in your daily life"
And this video aren't (to me) interesting rules. It's extremely narrow usage of numbers. erimps were somewhat interesting, eban numbers also, but even eban suffers in that it is language dependant, and that kind of shows the weakness of these things to me. It becomes so situational that pretty quickly this numbers tend to shoot up like crazy, and become so far and wide apart as to be meaningless.
Notice how Tadashi often showed toys or other interesting tricks or ideas, but they were are math related where the maths behind it is interesting. Not just "we took this arbitrary rule"
@@blazerer2424 These sequences might be arbitrary but studying them is not pointless.
You don't need to study an object because you expect an interesting outcome, you can study them mathematically just bexause you want to see the patterns that emerge! And evem though these sequences are highly specific to the representation of numbers they are (can be) nontheless well defined and non trivial.
Try finding a formula for the sequence "number of 'e's in n", you will have to figure out the rules how we combine our words to make new number words, maybe draw a graph laying out the grammar of this process, don't underestimate the maths you can do with specific objects.
@@blazerer2424 Since you mentioned the moon video I also want to comment on that.
Algebra is all about studying how different algebraic operations behave and what structures emerge, so I wouldnt underestimate it. Maybe you come up with a funny operation and end up showing that you can express it with algebraic objects that you already know (groups, rings, morphisms, actions), wouldnt that be cool.
Never use this approach if you have to pass a test during a job interview, cause everyday world isn't that creative.
Wait I got this : so if I translate the english words for those numbers into korean, then back , then into French then back and then wrote them on a wall, an armadillo would point at them in this specific order.
I get it now
these sequences remind me of bad video game puzzles
For some reason if you do that, 2 literally just disappears?? one two three four five six => 일이 삼 사 오 육 => Un trois quatre cinq six => One three four five six ???? Where did 2 escape 2?
Why is everyone acting so offended? I think this guy is adorable and his obvious love for math makes me smile. You all need to relax
I agree. Neil has a playful side... But you will see later he does some hard core math too!
This whole video just made me giggle... a lot!
He seems to be agitated or under effect and this can make people nervous
I figured the eban one out on my own. Now I am pretty proud 🙂
You have to guess which box they have constructed to think outside, to think inside.
"Why are they called Eban?"
Cue the nerdiest dad joke ever.
Watching Neil Sloane videos makes me feel like I'm hunched over the Fountain of Truth wild-eyed, drinking deep its Waters in fervent Gulps with bright and beautiful Madness shimmering in my Eyes, seeing the World not as It Is or as It Should Be, but as It Could Never Be.
Cringe
I loved this one:
61, 21, 82, 43, 3, 64
Because I got it right thinking of something completely different. I added 6+1=7; 2+1=3 and 8+2=10. So, since the next numbers are 43 and 3, both, when added, sum up to 7 and 3, I thought it was a recurring thing for the algarisms to sum in a loop 7, 3 and 10, 7, 3 and 10. So, the next one had to have a second algarism that was one value higher than the last (because it starts as x1, y1, z2, a3, b3... I supposed the c would be 4), it had to be c4 and c+4 had to be 10, therefore, 64.
genius
Picks 3 random numbers. What comes next?
These numbers were the first things that came to my mind. The next number I was thinking of was 6,008!
Is this even math?
It's kind of topology
TH-cam search
"88 is 4 circles"
.
Nvm I just continued watching and it's less mathematics and more just coincidences as it goes on.
Well the channel is called numberphile, so I guess doing things with numbers that are not mathematical isn't banned!
@@masat87 Unlike E's, which are banned.
Top ten questions scientists have finally answered
shut
Glad you made a career out of spamming comments on as many TH-cam videos as possible - that's really impressive and admirable, time well spent.
From pewdiepie to Numberphile, I present to you : JUSTIN Y
Anthony Nguyen back here againn
4 8 15 16 23 42
What about those who write/draw their zeroes with a diagonal slash thru them? Would that be considered two holes rather than just one.
And get this, I learned to write "2" so that it has two holes! Zero had only one, though.
I've stopped that practice since my thetas look very similar. Does help in coding or distinguishing them from Os.
My Dad used to do that because the original computer keyboards had the zero like that to distinguish it from a capital O. It meant when I lived at number 20 one item of my post got sent to number 21 because the slash looked like a correction, which confused the postman.
[It looks more like a phi than a theta!]
Topologically yes.
0:20 The next one is 888, then 4888. Because, after a 4-followed-by-n-8’s, you’ll have n+1 8’s, without the 4; then, you’ll add the 4 back in front.
2:51 I can't believe I paused the video and had that on my desk for a week. I feel sad
I got the one with the numbers written out. I'm obsessed with those numbers and wrote a function to convert to them, which used recursion!
After seeing him move the commas
"That's illegal"
"It's misleading, it's deceptive..."
Yes, it is.
I feel like this is the first time ever that I want to cry out of frustration and happiness at the same time. Nice job Neil.
I noticed immediately that he was careful to write the first "4". I didn't think much of it, but noticed that it may be important. I guess it was, to close the hole.
What number comes next?
1, 3, ?
You guessed wrong, it's Tree(3)
but that WAS my guess
That was my guess though!
@@GlobalWarmingSkeptic Well, guess i'll die?
I guessed right.
No it's TREE(3), tree is a different function and Tree not even a function.
When I was in primary school, I had always thought about that is it legit for a maths test to ask us what is the next term of a provided sequence? Isn't that you can somehow make a formula for any number to fit in the next term?
This is my brilliant sequence and the most elegant in all of mathematics:
1, 2, 3, 4, 5, 6, 7, 8...........
Trick question. The next number is not a number, but a game.
Bookworm Adventures Deluxe to be specific.
IT'S A MASTAPIECE
So, you frequent Numberphile and Dunkey? Are you sure you're not me...?
This is uncanny
Removed from steam
is this all you want to be known for? you're gonna make yourself a meme and perpetuate it forever? all right then
There's an inherent problem with "continue the sequence" puzzles: it's always possible to find a mathematical justification (indeed, any number of such justifications) for *any* continuation of the sequence. That's demonstrably the case (had thos theorem taught to my in my Calculus 101 class back in the day).
PS: I found the intended continuation for the second sequence without guessing the comma shift thingy. One more drawback of those puzzles is that you only get the output, without the reason for it.
True 🎯. That’s, why my mathematician Friend hates these sequences, and doesn’t consider them mathematics. Including every sequence. Like: ”1, 2, 3,…”, and: ”0, 0, 0,…”.
Actually, i know there exist a certain theorem that ANY number can be the next number..... (take for example, in a simple series like 1, 2, 3, 4, 5, 6....... and logically, we know the next must be 7, but indeed, according to this theorm, it could be 7, 8, 9, or indeed, any number.
Unfortunately, i cannot remember what the name of this theorem is...... Can someone help?
I actually came up with a different rule for that one and it works: 2:00
(0), 61, 21, 82, 43, 3, 64, 24, 85, 46, 6
(+61-40+61-39-40)(+61-40+61-39-40)...
A lot of angry gatekeepers in the comments all puffed up after seeing that they passed their calculus I midterm...
Underrated comment.
And psychopaths who need to state, that disagreement for logical reasons means inferiority. While they are the inferior ones themselves.
"ID" is not a legal Roman number?!
499 is actually written "CDXCIX"
I noticed that too
That's why he said it doesn't count.
@@ubertoaster99 No he said it does count, IDIV sis not count in the video. Though it is complicated with Roman numbers, there are several set of rules, some allow for IIII being four, some allow to subtract ones from big numbers...
@@TheLetterT511 no, on the standard rules for Roman number, the subtraction works only between 2 letters close in magnitude, so when the second one is 5 or 10 times the first. So:
IV = 4, IX =9, XL= 40, XC = 90, CD =400, CM =900
But ID, or XM doesn't make sense
Isn't 499 in Roman CDXCIX?
ID seems invalid, if you ask me.
Is that a pun?
Really loved this approach to numbers, quite unusual but still interesting
You acknowledge us people indifferent to base-10 and then continue to show us your 'subjective' math
Guys Im not sure if you have already figured thos out or seen it somewhere but I came out with this one myself. Number in sequence,n if you were to sum up is equivalent to the square of last number in the sequence and then minus all the numbers before it. e.g - 1+2+3 = 3^2-2-1, 1+2+3+4 = 4^2-3-2-1 and so on. Why. Look, number in sequence, n represented by dots and the likes,if you were to arrange in order will form a triangle. So if you square the number, it means you add x dots to form a square. The x dots are the numbers beforw the last number. Since the x dots are not really there, therefore the x dots should be substracted. So the square is no more, exactly what we are trying to find - the triangle. If you are unable to understand this, feel free to ask.
I hope this can be beneficial somehow.
For the second one I had the correct answer with a different method.
61,21,82,43,3...
The sum of the numbers make : 7,3,10,7,3...
Then the sum of the last one is 10. Considering that the 4 on the fourth term is 2 below 6 and 3 is 2 above 1, I use the same method : 8 → 6 and 2 → 4
That way you find 64 !
I did something similar, seeing the sum of the numbers. I also got 64 another way.
I saw that the first digit of each number was always a different even (6,2,8,4,0) and assumed the pattern repeated from there, so the first number is 6.
Then I saw that the second number was increasing regularly (1,1,2,3,3), so 4 must be the next second number.
Hence, 64.
@@BunchaWords I got 46. 61 + 21 = 82. 43 + 3 = 46
@@tomislavhoman4338 Same
Subtract 40. If *resulting* number could be subtracted by 40 add on 1.
If the number *you subtract currently* can't be subtracted by 40 add on 1 infront of it.
21 - 40 would 82
It freaking works out even further in the series. Idk when it breaks or if it breaks but every number shown works lol.
I'm not certain but I don't think is a valid Roman numeral either, even though it looks like it ought to be 499. I think that according to the rules only C can subtract from D, only X can subtract from C, etc. 499 is CDXCIX.
I get similar patterns which are completely unrelated. The 2, 4, 6 thing makes a bit of sense as only numbers below six, you get to 66 and break (obviously because numbers after it have 'e', but it looks like there is a mathematical definition).
61, 21, 82, 43, 3 - I guessed this one right because I thought the pattern was that if you add each of the digits of each number (6+1, 2+1, 8+2, 4+3, 3), you get 7, 3, 10, 7, 3... so I figured the next number's digits must add up to 10; next, I looked at the two that add up to 7 (61 and 43) and 3 in the pattern (21 and 03) and saw that the first digit just transferred a 2 to the second digit (6 -> 4, 1 -> 3 and 2 -> 0, 1 -> 3) and determined that the next number must be 64 (8-> 6, 2 -> 4).
I had a similar process, recognizing that the sum of the digits was a pattern, but I ended up seeing that the first digit had a pattern of subtracting four each time, starting over at ten when zero was reached (6-4=2, 2-4=8, et cetera) from that, I figured the last digit had to have a 6 in the tens place, and the sum had to be 10, making the ones a 4. Therefore, 64.
I got the roman numeral one right away!! The rest not a chance 😂
Same
Yeah, that one was sorta obvious because the camera zoomed in on the IX in "six" ... and the fact he was writing out the words meant it had to be something to do with the letters ...
Same here. Got that as soon as he wrote six
Same here
Found myself leaning in during this video. This fella is entrancing I'm his delivery and enthusiasm.
i saw the 1 4 8 as a binary problem
4 being 0
8 being 1
1 being some useless irregular number that shouldn't belong there
Same! But then I noticed it didn't work
The eban numbers in german would be....
0 (null), 5 (fünf), 8 (acht), 12 (zwölf), 20 (zwanzig), 25 (fünfundzwanzig), 28 (achtundzwanzig), 50 (fünfzig), 55 (fünfundfünfzig), 58 (achtundfünfzig), 80 (achtzig), 85 (fünfundachtzig), 88 (achtundachtzig)
"Don't think to complicated"
Rewites the whole series, and even adding a new number.
"now do you see it?"
FAM....
It's like Neil Sloane is the lone wizard who is custodian of all types of magical numbers, be they powerfully useful, or trivially entertaining. But he enjoys them all and will pass them on to any visitor that cares to seek him out.
The first sequence could be defined without using holes, if you take away 1 you get. 0+4=4, 4+4=8, 8+4*10=48, 48+4*10=88, 88+4*100=488, 488+4*100=888 and so on. If n is generic element of the sequence then n=(n-1)+4*(10^i), with i=0,1,2,.... The power can be defined i'll think about
Yeah, I had a similar solution. but I need given n1=1,n2=4,n3=8. then the rest comes with following algorithm: n[i] (with i>=4) = n[i-2]*10+last digit from n[i-1]. n4 = 10*4 + 8. n5=10*8+8. n6=10*48 + 8. and so on. well, the n1=1 isn't used here...
You could change i to be [n/2] where [x]:=min{k ε Z | k>=x}
The solution I had was that it was simply ascending binary numbers (4 being binary 0 and 8 being binary 1) the 1 at the beginning throws that off though.
Well in math therms it's a bit more complex, but if you want anche algorithm to use on a calculator you set i to be:if n is the index of the generic sequence element as i meant before, then the generic sequence number S(n)=S(n-1) + 4*10^(i) where (i=n-1 if n is odd number) otherwise (i=log((S(n-1) - S(n-2))/4) if n is even) with base 10 but probably doesn't work for first elements. I'd need some more time to work the first elements
I thought it might have to do with the sum of each number going up by 4 each time excluding 1.. 4 8 12 16 20
I used a different approach to determine the next numbers in the first sequence by using a substitution system.
The first digit of each number is replace based on the following rules to determine the next number:
1 -> 4
4 -> 8
8 -> 48
Which results in the sequence 1, 4, 8, 48, 88, 488, 888, 4888 etc
@ 0:22, I found the same number by using this method: take the second integer of a term and combine it with the whole previous number (starting from the fourth term which is 48, doesn't work with 1, 4 and 8).
Ex: So 48, take the second integer 8 and combine with the previous number 8 = 88,
88, take the second integer 8 and combine it with the previous number 48 = 488
488, take the second integer 8 and combine it with the previous number 88 = 888
888, take the second integer 8 and combine it with the previous number 488 = 4888
4888, take the second integer 8 and combine it with the previous number 888 = 8888 etc...
give me the Nobel prize.
Yeah i did the same!
@@bastiens5219 I did the same and I also got the 64 right without realising the comma stuff. I just thought the rule was -40 if the result was positive, else +61. I don't know exactly why but it works for the next numbers as well.
5:36… just that massive leap from 66 to 2000 is just incredible… XD
That broke me! Lol
Why not just make it an easier sequence: 1, 0, 00, 000, 0000, 00000?
1, 01, 001, etc
@wise ol' man 0 is in the middle so you could say its both
the problem is that all of those (except for 1) are the same number, so it doesnt count
Got the 3rd sequence, he made it easy for us by spelling the names of the numbers rather than just writing the numbers, it was huge clue.
The second one
61, 21, 82, 43, 3 has an other relatively simple rule:
Add 60 to the previous one, take the rest of the division with 100 , if the sum of both digits is more than 6, add 1.
So it continues with .... 64,24,85,46,.... which is also correct with the comma shift one.
This video leaves me half-annoyed...and half-amused...
This is somewhere between serious mathematics and wasting precious time, closer to the latter perhaps
@@mikkokarkkainen2807 definitely the latter
I remember reading a Martin Gardener article in Sci Am many years back about "What number comes next". He said the correct answer is always 19. He said you can always find a justification for any following number if you try hard enough. It was a great article. (I wish I could find it again! (Sad Face)).
"How many holes in a polo"
-impossible quiz
how many holes in math
i gave up trying to figure out what comes next when he started moving comas, i just watched in awe and laughed with each solution
**Notices a striking number of downvotes**
One minute later...
**Sees why there are so many downvotes**
NEIL SLOANE! 🤟 Thank you for sharing this, I loved it. Great fun. Especially the reveal of "E is banned 😁" made me belly laugh haha
How is changing the sequence by moving commas and then adding random zeros *not complicated*? It goes against the very conventions that make a sequence a sequence.
Here the mathematical approach.
61 - 40 = 21
If the resulting number could be subtracted by 40 again, add on 1. If you go below 0 just keep on going (you know as if you take over 1) so 21 - 40 is 82 (20 - 40 wpuld be 10 then 00 then 90 then 80. I think you know what I mean.)
The graphic at 1:06 is correct, it says the number that divides the plane into n regions. 1 divides into 1 region, 4 divides into 2 regions, 8 divides into 3 regions. Am i missing something, I dont understand the need for the correction in the description.
The invisible zero one was complete nonsense. Why would numbers be having one invisible zero? Why didn't 61 have 061? Oh, it has to be only two digits? Well what happens when sequence gets above 100?
The problem of sequences is also that there are always multiple solutions anyway. My solution is at least consistent, unlike his:
61, 21, 82, 43, 3, 46, 7, 53, 13, 66, 27,...
Edit: the sequence start cycling once it reaches 55, it has a 36 number cycle. I just HAD to check.
We know that is infinite number of sequences that could be a consistent continuation of the first 5 numbers. And yet he picks one that is inconsistent and says others are wrong. :)
Subtract 40. If *resulting* number could be subtracted by 40 add on 1.
If the number *you subtract currently* can't be subtracted by 40 add on 1 infront of it.
21 - 40 would 82
X)
Formula for the first sequence: f(n) = n-2 concatenated with the last digit of n-1; works only for N larger than 3
Damn I did get that it would be 64, but mainly because I assumed that first digit would follow pattern 6,2,8,4,0 and last digit seemed to be increasing, but having third 3 in a row would be weird for the sequence...
Yeah I did a similar thing, I got it by adding the previous number to the first number 61. it should've been 05 not 03, but adding 61 to 03 got me 64, which turned out to be right for all the wrong reasons =P
This made me feel like I was trying to solve the cryptic clues on a crossword. That feeling is frustration.
Funny to see how angry people get at this video. I found it frustrating too, when the rules were a bit "creative" but what's the point of getting angry at it? It's just different.
It's like they've never seen a numberphile video before.
@@asystole_ Numberphile videos are about math. Wonky math sometimes but math always. And this isn't math.
@@Z3nt4 old numberphile is about number with arbitrary properties, not all about math
@@oldcowbb No. Old videos feature a lot of popular or funny numbers that happen to have wonky properties or features. Pointless ones often which you could find for just about any random number if you put the time in and get creative with your approach, but rigorously mathematical ones.
These are just silly, non mathematical rules one might come up with to blow the minds of some 12 year olds but hardly something you approach an expectant and somewhat mathematically savvy audience with. They will be met with blank stares and and an invitation to see yourself out.
I found a mathematical rule for the 61,21 etc. Sequence. The roman thing is actually very common x).
For the second sequence I got the right next term, 64 - but it was an accident: funnily enough if you simply look at the difference in value between each term, 61 -> 21 (minus 40), 21 -> 82 (plus 61), 82 -> 43 (minus 39), 43 -> 3 (minus 40 again)... so if one goes back to the beginning and follows the minus 40 with plus 61... 3+61=64 :) (the next one comes out as 25 instead of 24 though)
He looked so pleased with himself every time he presented a new sequence.
The man loves sequences.
I found a more complicated pattern in 61, 21, 82, 43, 3. subtract 4 from the left most digit and loop back if you go below 0, so 2 minus 4 would be 8. around increase the right most digit by one, which would give you 64 for the next in the sequence
I love OEIS for programming. Need to generate a particular sequence of numbers? OEIS probably has an efficient way to calculate the n-th number instead of brute forcing it.
This goes both ways. If you have an efficient algorithm for computing a particular sequence, you can add the formula or the program to that sequence.
for the 4,8,48... function you could do:
f(x)=sum{n=0 to x-1}(4*10^(floor((n+.1)/2)))
this works for every value of x except 0
desmos code:
f\left(x
ight)=\sum_{n=0}^{x-1}4\cdot10^{\operatorname{floor}\left(\frac{n+.1}{2}
ight)}
This video left me with less of an enthusiasm for numbers than other videos... lolololol
Absolutely love this guy. More videos from him please
7:47 you did it too fast, I didn't have time to count the zeros, now I am not sure if you showed the right number :)
The way I worked out the first one was start with: 1, 4, 8,
Go back 2 numbers (4) and take that number and multiply by 10 and add 8
= 4*10+8
= 48
and append this number to the end of the sequence.
Now, go back 2 numbers (8) and take that number and multiply by 10 and add 8
= 8*10+8
= 88
and append this number to the end of the sequence.
Now, go back 2 numbers (48) and take that number and multiply by 10 and add 8
= 48*10+8
= 488
and append this number to the end of the sequence.
Now, go back 2 numbers (48) and take that number and multiply by 10 and add 8
= 88*10+8
= 888
and append this number to the end of the sequence.
This makes a lot more sense to me.
My head hurts after watching this. Oh wait there’s still 6 minutes left....
OEIS is one of my favourite places to go to relax. I'm currently trying to find ways of making some of the sequences into music.
E🅱️AN Numbers
The Roman numeral sequence has appeared once on Only Connect, but with the.letters replaced by the digits - F4V, S1X, SE5EN, and they had to figure out the fourth element was E1GHT
"Smallest positive number that has N holes in it". Shouldn't it be 0 for N = 1 ?
0 isn't positive
@@AntisocialSocietyCub thanks, my bad.
Yeah, don't you DARE not follow this SPECIFIC rule !!
61,21,82,43,3
The first digit goes down by 4 each time
The second digit hits each even number once and each odd number twice.
The next number would be 64. This doesn't work with the "real" answer past the next digit, but it functions enough to work for this term and also requires the invisible zero
These were delightful!
Eban is my favorite by far ^-^
Glad you likd thm. :)
@@numberphile i c what you did thr
I just remembered a Chinese (admission?) Test that went viral. The parking lot numbers were mirror-imaged, and the test asked what number comes next.
misdirection by not giving all the information is just lying. what about all the other missing zeroes before all the other numbers screwing up your "simple" solution . does not make your 'simple answer' simple. there is an easier one than the one you provide.
And what is it? Did it not fit onto the margin of this comment? The suspense is killing me.
@@ludvercz Subtract 40. If *resulting* number could be subtracted by 40 add on 1.
If the number *you subtract currently* can't be subtracted by 40 add on 1 infront of it.
21 - 40 would 82
It freaking works out xD
This guy is the boss you have to fight after you have defeated all other dorks on the planet.
His Encyclopedia is amazing!
So great to see an interview of Neil Sloane
It was areal honour to have Neil on the channel - he has done a bunch more videos for us - some are really amazing!
That reminds me..must make a computer game that throws out a set of random numbers...the game would be to figure out the rule for that set sequence