SEQUENCES that keep getting HARDER | How far can you get???

[@giangnguyen-hh3zo]

6:50 I have done it a little bit different: 8 = 2 x 4 15 = 3 x 5 24 = 4 x 6 35 = 5 x 7 48 = 6 x 8 And I came up with the same answer. At first, I was about to do the same as yours but my calculations are kinda odd so... :D

[@jikkohelloua5922]

Actually makes sense, bcuz x^2 -1 = (x+1)(x-1) so that's why you actually did the same thing!

[@TomatoGuy-737]

​@@giangnguyen-hh3zo hey I know it’s digressive but can you tell me how did you obtain that emoji?

[@leqrit]

@@TomatoGuy-737 ye

[@ElizabethBrendaLo]

Identical method here.

[@ElizabethBrendaLo]

@@jikkohelloua5922 Got it right! It is this general formula a^2-b^2=(a-b)(a+b).

[@aidan-ator7844]

Level 7 was honestly a genius pattern.

[@andreyfom-zv3gp]

For your interest, I'll say, that this sequence was invented by the genius John Conway, who described it and some od its really nice properties.

[@gaurishbanik3281]

Approximately how much time do you think this took you to solve

[@Less0331]

Nah, not really, it's pretty dumb imo. I noticed it without pausing the video.

[@letitgrow6553]

I went the completely wrong way I guess and got the answer of 2211111211. I thought I was being smart but I was just overthinking it.

[@user-pr6ed3ri2k]

​​​@@andreyfom-zv3gplook and say! the limiting ratio between 2 consecutive numbers being a solution to a degree 71 polynomial is insane

[@redestroyer7994]

Those `n-1`s are one of the very reasons for why we, programmers, index from 0 rather than from 1 (another reason is pointer arithmetic).

[@DimkaTsv]

And then Fibonacci sequence says hello with it's t[n]=t[n-1]+t[n-2] So by your argument index should start from [-1] like in BlueBird, right? Formulas for sequences are written as to find [n]-th member, and there is no such thing as 0-th sequence member. They start from 1-st.

[@jjpswfc]

​@@DimkaTsv Really depends on what the context is, for some the first term is the 0th term like x0

[@siddanthvenkatesh2744]

No, the sequence would start at 0. f(0)=0 and f(1)=1.

[@someguy7110]

I'm pretty sure the reason why programmers start with 0 has no relation to sequences.

[@levels23]

I love these types of videos so much, it tests my knowledge as well as teaching me new things to learn. but next could you do "ALGEBRAIC TRIG EQUATIONS but they keep getting HARDER" or something along those lines?

[@Fire_Axus]

your feelings are irrational

[@akshithvasa4116]

​@@Fire_Axus Huh???

[@matthew28z_85]

For the last one I thought it was •5-4-4 were always the last three of any sequence •If the row is an even number, its first number will be the sum of all the numbers of the previous row and it will have 3 numbers other than 5-4-4. •If the row is an odd number its first number will be the first number of the previous row minus the first number of the previous of previous row and it will have 2 numbers other than 5-4-4. •For the rows that are an even number if they are between two other rows I saw that Its 2nd number will be the first of the next row minus the first of the previous row,the third will be the 2nd of the next row minus the 2nd of the previous row. •For the rows that are an odd number because they have one less number than even rows, their 2nd number will be the 2nd number of the next row minus the 2nd number of the previous row. I kinda just assumed it would work like that for the last step but with this I explained every number in there except the first two numbers of the first row which I assumed were random, so with this I got that the last numbers are 34-19-11-5-4-4

[@wavingbuddy3535]

You can also write Fibonacci non-recursively the following way: F_n = (ϕ^n - Φ^n)/ (ϕ - Φ) where ϕ = (1+√5)/2 and Φ = (1-√5)/2

[@MareykForsythe-pb1qu]

w h a t

[@JoeShow762]

Great vid! You can approximate any sequence with a polynomial of the same order as the number of terms. It will give you a valid result, just maybe not the one you're looking for.

[@manudude02]

Got all except 11. For number 10, my reasoning was a difference of 6 is 1x6, a difference of 16 is 2x8, then it's 4x10, 8x12, 16x14 so the next one was a difference of 32x16

[@toastkenyer3488]

U either really experienced or complete ginius or idk

[@NaThingSerious]

Nice, I got all except 10. After sequence 6 they’re more logic puzzles than maths problems (apart from 10), and I do way too many of those, so 11 jumped out to me almost instantly as I’ve seen many puzzles where you need to think of numbers written out before.

[@sanjukumari7684]

One series can have many solutions

[@InDstructR]

yeah got it the same way haha

[@BlacksmithTWD]

@@sanjukumari7684 Sure, as long as the different solutions don't offer different results it's still a good problem to pose.

[@M1Miketro]

14:09 This is why I dislike questions with language barriers. What if you think about numbers in your native language instead of English? How would you solve it?

[@TheFryGuy2763]

It would be cool to see one of these dedicated to trig equatons if possible.

[@theimmux3034]

my solution to every sequence is 0. The general term a_n shall be defined as follows: a_n = a_k for the first k presented numbers where a_k is the kth one and a_n = 0 when n > k.

[@elementgermanium]

I was about to give up on 11, hit play on the video, and then that fucking “magic number” riddle beamed into my head. Paused at 14:05 and I feel way too proud of myself.

[@guigui0246]

I did the exact same thing (even paused at the exact same time)

[@Hanaa-d1q]

Got level 10 a lil differently...I just found the differences, and got a pattern with differences, *3-2,*3-8,*3-24, *3-64, and with this got 2+6=8. 8+16=24.24+40=64, but this matched up with the differnces first found, meaning the next differnce added is 96, then 96+64=160, so if *3-160, we get the last difference found, 224, so 224*3-160, resulting in 512, so added onto 383, we get 895. :)

[@jawaduddin4244]

Technically, you could also fit a polynomial to the numbers in level 10: Using some linear algebra, I got 11/60(x^5) - 2(x^4) + 125/12(x^3) - 24(x^2) + 29.4x - 13. And using this polynomial, we could say that the missing number could also be 869 (if you plug 7 into my polynomial)!

[@sm64guy28]

Fun fact, you can do this on any finite sequence and get a result

[@tjalle74]

I missed lev 7 and 11, but English isn´t my native language and I was looking for math solution. I thought lev 7 was a base 3 problem. 1*1=1, 2*2=11, 21*21=1211. But I couldn’t get from 11 to 21 in a logical way. Great video 🙂

[@jimmeade2976]

In level 11, the solution only works for numbers in English. Other languages would not work. You would also get a different answer if you used the number of characters in the number's name (in English), not letters. The bottom row would then be 11,6,3,5,4,4 and would also be correct.

[@humanterminator1056]

This is actually pretty cool thx man

[@bud5]

for level six i thought 3 to 11 is adding 8 which is 2*4 then 11 to 26 is adding 15 which is 3*5 so you add 1 to each and multiply those then add it to the actual number

[@dorol6375]

For level 10, I took the second order difference and got 10,24,56,128 That 128 looked odd since it's a power of two so I tried to factor them and after a bit of messing around I got 5×2 , 6×4 , 7×8 , 8×16 The first factor is increasing by one and the second factor is a power of two! So logically the next number is 9×32. From that you can get the next number which is the same as what you got

[@reeb3687]

i dont like the ones where it has nothing to do with number patterns and instead its a "think-outside-the-box" one like 7

[@cheetolord4008]

Man, those last few were tough. I eventually got them all though. No way I would have got pattern 11 though if I hadn't already seen that other video that talks about this pattern and how it always goes to 4 and stays at 4 in English, which is the detail that tipped me off. Same with the upside-down numbers thing, I think I only got that because I've seen it before XD

[@thaddeusjohnjacobs7149]

There's 11 Levels And I Got 11/11

[@PotatoSinghThe3rd]

I made it up to level 8, I love your vids bro!

[@ElizabethBrendaLo]

Same here. I only got Level 9 after hints were revealed. I started to get giddy at Level 10. Level 11 made me feel like I was in outer space.

[@alexfrozen8987]

​@@ElizabethBrendaLosame, up to 8 and 9th with hint... Also, found second solution in 7

[@bhluschrean]

level 11: bruh my main langage is korean 😂😂😂

[@bhluschrean]

i like how the comment counter says 169

[@bhluschrean]

13^2

[@CosmicButterfly2]

I lost at 9, but I technically used a hint at 7 (Paused after he mentioned see and say, which drastically helped me)

[@zombiemonke]

im surprised I got 6, yet everyone else is talking about how they got to level 11 A brief review of everything after 6: 7 made my brain explode I should've got 8 from the message "will make your head spin" as that's how I remembered what 5 was 9 just makes sense WHAT IS TEN 11 made more sense than 10, 8, and 7.

[@jamesruiz3910]

Level eight really did make my head spin! 😉

[@ElizabethBrendaLo]

Haha

[@xDanKaix]

I spent so long on the last one trying to find an equation that would grow when less than 4 shrink when greater than four and stay the same when at four only for me to finally give up and unpause the video. You immediately said let’s count the number of letters and I died a little on the inside xD. Solved all the other sequences, granted I’d have probably also failed the 7th had I not seen it as a kid and had an obsession with it xD

[@circadianizzy]

I got 9 out of 11! Levels 6 and 9 (nice) were the ones that stumped me, the rest I managed to get. For level 10, I found yet another different way. I noticed that each term was a little more than double the last, so I started with finding the difference between t and 2(t - 1). For example, with the 7, 7 - 2 × 1 = 5. These results gave 9, 17, 33 and 65 for the subsequent terms - all being one more than powers of two (5 being 2² + 1, 9 being 2³ + 1, etc). So I knew the next difference would be 129 (one more than 2⁷ + 1), meaning the next term would be 383 × 2 + 129, or 895. The formula for my solution, therefore, is as follows: t(n) = 2t(n - 1) + 2^n + 1

[@ilicktrains8304]

I got stuck at sequence 8, I feel like some of these are unfair because we don't know you are and aren't allowed to do to link one number to the next; and it kinda makes the solution feels un-earned because there's no possible way you would've figured it out from just your own intuition

[@Leoscacchi08]

I miss 7 9 11 About the ten i've found another way to find the solution I calculate all Number *2 and i calculate differences between the Number doubled and the next number 1*2=2 next number 7 7*2=14 next number 23 23*2=46 next number 63 63*2=126 next number 159 159*2=318 next number 383 383*2=766 next number unknown Differences: 5 9 17 33 65 ? I saw After a Little while that numbers are tied up by the formula 2n-1: 5->10-1=9 9->18-1=17 17->34-1=33 33->66-1=65 65->130-1=129 I have to add 129 to 766 (383*2) 766+129= 895 Now, i know that the other way seems very easier than that, but It was difficult to find that pattern

[@CardinalRed925]

I figured out 1-6 and 11 completely on my own, and I sort of got 8 as well (I let it play to the part where he called out the 2nd number as strange, and then I figured it out before he was able to continue)

[@BHGull]

Level 9 would have also worked in a way that you divide the next number with the current number and replace the answer with the next number. So 49 / 7 = 7, 97 / 7 = 13, 130 / 13 = 10 and 10 / 10 = 1. Not sure if it's coincidental or it can be mathematically proven to why the answer turned out correct, all I know is that I got it right lol. Loved this video, really excited to see the upcoming ones!

[@shazaanemir4585]

I had a different approach to Level 10 1,7,23,63,159,383,--- 1×2+5=7 7×2+9=23 23×2+17=63 63×2+33=159 159×2+65=383 383×2+129=895 Logic:×2 is common and the pattern in 5,9,17,33,65 is 5×2-1=9 9×2-1=17 17×2-1=33 33×2-1=65 So, 65×2-1=129

[@RubyPiec]

Ayy we used the same method!

[@llama079]

I did it like that too but if you look at their solution carefully you'll realise they also did pretty much the same thing lol

[@Trep3]

I did x2 and then 5+2^2 to get 9, 9+2^3 to get 17, 17+2^4 to get 33, 33+2^5 to get 65, 65+2^6 to get 129

[@koopatroopa051]

Level 5’s hint was genius.

[@keithle_]

So is there actually a formula for lv 7, 8, 9 and 11?

[@roostercubed]

very happy about finding level 9 as well

[@Black_Cat4]

бро пытается не придумать закономерность, а пойти хитростью

[@noelwalterso2]

Level 4 is also the number of possible pairs that can be chosen from n items. n×(n+1)÷2

[@jacksonbarnes8882]

Alternate answer for 6: each time, you’re adding 1 to both numbers being multiplied; ex: 2x4,3x5,4x6,5x7, then 6x8, so it actually continues the pattern correctly. That’s at least what I got

[@lithograhp]

What is the difficulity of the whole prime numbers sequence?

[@jake6056]

like listing every prime?

[@noelsilvester-tz8ho]

6:00 19 can also be divided by 2! And 8!

[@mihaelniko]

Damn, I have never actually tried these and have never seen them explained. I really liked it and now Im all gored up about doing a whole lot of these to improve my thinking hahaha.

[@fabimaniak]

For level 10, I looked at all the differences and divided them by 4. I saw that the numbers (1.5, 4, 10, 24 and 56) were the differences of the differences of the differences before them (example: 10 was the difference of 6 and 16). So I just followed that pattern and came to the conclusion that the last difference is 128 x 4 which is 512. 383 + 512 = 895 :)

[@Qxe7]

"And in level 12 you might or might have not noticed but, *drags in a number* you may have noticed this number was off screen the whole time so every tlnew number has to be dragged from off screen to on screen to complete the sequence"

[@systematic-rl4jf7oz7v]

For lvl four, perfect numbers are a subset of triangular numbers

[@systematic-rl4jf7oz7v]

The two differences surrounding each triangular number multiplied together equals double the referred triangular number. This means the surrounding differences of 496 are 31 and 32.

[@sennpowerhv6922]

Level 4 is all numbers you can have that number of bowling 🎳 pins in a bowling game

[@ibrahimali3192]

well yes but actually yes

[@BrekekeReal]

Billiards too I guess

[@afj810]

Triangular numbers so yeah

[@torlumnitor8230]

​@@BrekekeRealfalse see example 9 ball.

[@RubyPiec]

This is the first time I've ever gotten all of them! Good video

[@lourdesmercedes1201]

All numbers in level 4 can be stairs too

[@InDstructR]

Got em all haha, knew most of the unique ones before 9 and figured out the rest

[@xvoidx_yt1723]

Sir can you please find the missing term in this sequence 1,2,4,20,? What’s the value for (?) Choices are:5000,375,44,420

[@leqrit]

375

[@kirahen0437]

I made it up to level 8, and also was quickly able to do level 11 because I remembered one Vsauce video about it 9/11, very fun! (although Idk how but I struggled a lot at question 3)

[@sherwyntan8194]

Obtained 7/11. Levels 8-11 are the most challenging.

[@dimitriskontoleon6787]

Lol the level 8 was super easy! Is one of the most famous puzzle on parking, Facebook puzzle

[@Alians0108]

​@@dimitriskontoleon6787So it's not easy. You just knew the answer or method beforehand

[@jake6056]

i mean i noticed the weird 06 and thought about seeing it upside down. i was annoyed that he said 87 was the answer as in the original sequence the answer would actually be 78

[@ElizabethBrendaLo]

For Level 8, the answer depends on how you write the number 7. For me, I write '7' with a stroke across.

[@jake6056]

i was kinda annoyed he said the answer was 87 because in the original sequence it should be 78 because the 1s aren’t flipped

[@nazartverdokhlebov]

This were it came from. From the Pattern of Patterns

[@massy__]

i got lvl 8 bcuz of make ur head spin and im so proud

[@guigui0246]

I got 10 in a different way: In here each line is the difference of the line above (I added the original at the end to do the final addition): 1,7,23,63,159,383, _895_ 6 16 40 96 224 _512_ 10 24 56 128 _288_ 14 32 72 _160_ 18 40 _88_ 22 _48_ _26_ When you choose to put in prime factors each value you get a arithmetic sequence of multiples of two: 2* *3* 2^4 2^3*5 2^5*3 2^5*7 2* *5* 2^3*3 2^3*7 2^7 2* *7* 2^5 2^3*3^2 2* *9* 2^3*5 2* *11* 2* *13*

[@_ZAOB_]

Another formula for lvl 4 could be tn=1/2n(n+1)

[@ElizabethBrendaLo]

For Level 6, the differences can be expressed as: 8=2*4 15=3*5 24=4*6 35=5*7 Thus the next difference must be 6*8=48.

[@WilliamWizer-x3m]

no formula for level 7? and level 8 is quite a trick you pulled since that's not a sequence. it's a riddle. nice with the last level but I didn't see them end in 4,4. I saw them end in 5,4,4 doesn't matter much for the solution but it's something others may also notice.

[@blue_birb]

It's called arithmetic and geometric series btw iirc not sequence. Maybe they are synonyms btw idk

[@justinbrentwood1299]

The funny part is that every answer is correct. One can mathematically find a polynomial that would satisfy the given numbers and the arbitrary answer.

[@MuhammadTheOld]

Made it up to level 7, that level 11 was very brutal

[@Brandywackyman188]

Level 4 is actually just a quadratic sequence Is is expressed as an^2 + bn +c

[@strawhaaton]

I lost at question 9 because my dumbass forgot about happy numbers. thanks for the reminder

[@moderately4794]

Level 5 should have had 1, right? I initially thought it was prime, but then I looked at how 1 wasn’t there and was thrown off

[@vastabyss6496]

1 is not considered a prime number

[@rtch7105]

Got em all except 10, but I already knew some of them. For 11 I struggled though I had the right intuition, then I realized I counted the letters in my native language (French) instead of English 😅 Great puzzles!

[@rtch7105]

And today's useless information is: in French the final loop is made out of 4 digits: 4 (quatre), 6 (six), 3 (trois), 5 (cinq), 4, 6, 3, 5, 4, ...

[@harveyclay7793]

Got all of them eventually!! A couple were tough though. And my method for question 10 was really obscure. I looked at the difference between each term and 3 times the difference between the two previous terms, giving 5, 15, 39 and 95. From there I looked at the difference between each term and two times the previous term, giving 5, 9 and 17. I then noticed that each of these was one more than a piece of two, so the next of these was 33. This means the next number in the sequence 5, 15, 39, 95 should be 95*2 + 33 = 223. Then the final number in the original sequence should be 223 + 3(383-159) = 895. Very complicated but somehow worked 😂

[@Tribalchief69690]

I cant beleive i rotated the phone at 9:29 🤯

[@ClashWithKepler]

I got stuck on level 7

[@aidanhennessey5586]

Got them all eventually - funnily enough, I think I got stuck on the cubic the longest

[@Pictoo-ID]

Bro tries to find the pattern of every sequences by feeling when he can just use a general formula and find an infinite set of general solution for each sequences💀

[@stultar]

couldnt do level 9 and so on

[@massy__]

for lvl six i thought it was getting the diffs and then 2x4 3x5 4x6 5x7 was the pattern of the differences

[@ponypapa6785]

Fun, but level 11 shows that when using this kind of sequence, language is important. For example, use german. the sequences qould have been 7, 6, 5, 4, 4 | 20, 7, 6, 5, 4, 4 | 13, 8, 4, 4 | 34 14 8, 4, 4 which are vastly different apart from the final "four four" parts. take spanish it would have been 7, 5, 5 | 20, 6, 4, 6, 4, 6, 4... | 13, 5, 5 | 34, 14 (or 16 when counting spaces), 7 (9), 5 (5), 5 (5) As there are viewers from other countries who may or may not think about numbers in their native language, the given sequences are quite unintuitive.

[@RealitaetsverweigererDerAmpel]

I started struggling at number 7 and got max points at the math part of mensa IQ test and also max points at maths during university in almost every test😂 at least i noticed there probably isn‘t an arithmetical sequence but some sort of concatination of the previous two numbers or so but i overthought it.

[@deepuniverse4840]

Somehow , I found the same result in level 10 but with a different pattern which goes tn= [(Tn-1)-(Tn-2)] * 4 - 1 (n-1 and n-2 are the indexes ) basically like (7-1)-4 -1 =23 , (159-63)*4-1 = 383 and it gives 895 as a solution But with that equtation , we get [(Tn-1)-(Tn-2)] * 4 = n(2^n) , but how ? Maths is magic man....

[@ClashWithKepler]

Great video again, can you do finding area that keeps getting harder

[@stechuskaktus8318]

Unfortunately I didn't find a number looking like an upside down seven. Aside from that, surprisingly, I got it all right :o

[@cw6990]

Level ten I calculated by an=(a(n-1)-a(n-2))*4-1 For example ,23=(7-1)*4-1

[@professorx9932]

As a 12 year old with a WISC-tested score of 145, I got 6/10.

[@sonicwaveinfinitymiddwelle8555]

This is more of an philosophy problem than maths problem and therefore takes absurdly long time to solve as you can't just apply every single possible mathematical equation and have to think outside of the box

[@KasyapH]

The triangular numbers is one of the quadratic sequence

[@l0v0l78]

For level 8, I already felt it was rotated by 180⁰ when I just saw the 8, and then I remember the thing I learnt when I was small (I solved it) For level 11, it would be unfair to those who don't speak English as their native language (like me), but I realised that 7+5+4+4=20 and 13+8+5+4+4=34 I solved 7 sequences, level 9-10 are just too hard for me and level 7 I thought it would be 1112211 (I realised the numbers ends with a 1 and two 1s alternatively and every number becomes longer than the previous one)

[@johannesvanderhorst9778]

Levels 1-5: I didn't need to pause the video to solve it. Levels 6-8: I solved it after pausing the video. Level 9: I didn't solve it. It turns out I don't like properties that work only in decimal rather than that it is a property of the number itself. Level 10: I solved it using t_n = 2*t_(n-1) + 1 + 2^n. Level 11: I didn't solve it. It turns out I don't like it when it works only in a certain language the numbers are written.

[@meepsoleruler444]

I figured out a formula to solve any sequence. The difference between any two numbers is equal the distance between those two numbers.

[@JARG-Random_Guy]

I lost at lvl. 6. lvl. 7 is really funny though! I got lvl 8. lvl 9 and 10 seem unfair. I did lvl 11 in a different way, but I think it is true. this video is underrated.

[@taito404]

I was wondering why I feel deja vu in level 8, couldn't guess it in the end and when I press played I audibly sighed lmao Edit: level 9 was pretty easy tho Edit 2: last one made me cry :(

[@Klungklung123]

the irony that in the thumbnail the sequences get easier

[@roostercubed]

missed number 7, which i was kind of upset about, but figured out 8 in a matter of seconds lol

[@Astrophysicst.007]

We want part 2 please 🙏

[@arthasmenethil1526]

I love maths, but i lack of creativity. Im good in functons, equasions etc. , but im bad at geometrics. It makes me sad, because i dont know if i can still become great mathematician.

[@Niromica]

"absolute value of negative thirty nine." has 39 characters including spaces and the period. its not just 4 that has the same amount of characters as it's value.

[@thezwierz5563]

All except Woodall's number, it was easier than I expected though

[@adw1z]

Managed to complete levels 1 to 9 from the top of my head, gave up after that ahah

[@Ashwiindj]

I was able to solve 1 - 6, 8 and 10. For level 6, I did: 3 + (4×2) = 11 11 + (5×3) = 26 26 + (6×4) = 50 and so on... For level 10, I did: 1 + (3×2¹) = 7 7 + (4×2²) = 23 23 + (5×2³) = 40 and so on... In level 7, I thought the digits of the numbers add up to form Fibonacci sequence but I was wrong... To sum up, I think I have good mathematical thinking but not logical thinking.

[@50upss]

I was lost at level 9, although I didn’t spend much time looking at it

[@UnfunnyGaming99]

Got all except 10. I knew 11 because I knew something that 4 only had was that it has the same letters as itself

[@GoldenBoi507]

I was kinda expecting a binary sequence at some point

[@Imposter7777]

I got another answer for number 10, which also worked.

[@Imposter7777]

Nevermind, I redid the same calculations and got 895

[@mrblakeboy1420]

my foolish self saw the thumbnail, out of the corner of my eye thought that 1 was a list of primes, looked back up, realised it was linear, then saw the second one, a list of primes