Why are there only 7 numbers like this? Proving it with Python code, with help from ChatGPT

This viral trick has tens of millions of views, and leads to a natural question: which numbers have cube roots exactly equal to the number's digit sum? We can tackle this question mathematically, with an assist from ChatGPT and Python code, and figure out all possible values!
Sum of cube root digits short video
• Trick!
Dudeney number
en.wikipedia.org/wiki/Dudeney...
Proof of Dudeney numbers
blog.hostilefork.com/six-duden...
OEIS Dudeney numbers
oeis.org/A061209
ChatGPT
chat.openai.com/
Python online compiler
www.programiz.com/python-prog...
Remove space Python print
discuss.python.org/t/how-to-r...
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[@skattterdude]

Why am I not surprised that the invocation of ChatGPT results in an extra minute and a half of debugging/code optimization talk

[@khiemgom]

Lmao thats literally the problem of python + he didnt ask for optimization

[@Voxel79]

Here's few math puzzles I have made... 31²=961, reverse order of numbers in value to get 169. Square it to get 13. Reverse again to get 31 (original number) If zero is banned there's only about 50 number that behaves like this. Largest is 111111111²=12345678987654321 ...Easy to proof but fun to calculate on paper ;P sqrt(x²-1) can always be cleaned with odd numbers. What I mean for that cleaning: Example sqrt(7²-1)=sqrt(48)=4*sqrt(3)

[@amird9684]

You should get mental health same as me after seeing this☠️

[@brahmbandyopadhyay]

😵

[@Voxel79]

@@amird9684 Dear Amir, If you get locked in insane asylum here's something to wonder: Let X and Y be integers... Lets say X=2 and Y=6 Make to integers A and B where A contains X number of 9's and B contains 1 followed by Y number of 0's. So X=2 => A=99 (two nines) and Y=6 => B=1 000 000 (six zeros) Now calculate A^B (99¹ ⁰⁰⁰ ⁰⁰⁰) and check the last numbers of result (... 662 836 307 994 900 000 001) Notice how it ends with exactly (X+Y-1) number of 0's and then 1. (00 000 001) I sincerely hope that this increases your time in asylum for more because I like destroying other persons by numbers Sincerely Yours, V79 ps.... I hope that youtube understands satire.

[@adamcionoob3912]

Great video, as always

[@user-ln2pm7yv3d]

Nice video, keep it up. I want to show another proof: when n

[@251omega]

שלום אדוני. גרתי ברחובות, 18 חודשים, בשנת 1963, בגיל 12

[@jayeshkumar3861]

< 1 million, sum of digits at the most is 54.

[@251omega]

@@jayeshkumar3861 AFFIRMATIVE! 6 x 9 = 54

[@leif1075]

Hiw or why would Dudeny or anyone else find these numbers in the first place? Trial.and error I suppose..I can't see another way..setting up with algebra a plus b plus plus cubed equals 100c plus 10b pkus a is the only way I can think kf..since with calculus and or graphing there isn't enough information..so that must be how they did it..just luck and patience and effort to stumble on them?

[@leif1075]

Where do you get 10^3k from? Why 3? I see you had 54^3 but why ..just because it's a cube doesn't make it clear to me..

[@sparshsharma5270]

I hope that you took serious note of you not publishing general videos as before. Loved this video. I was missing your explanations. I don't like shorts, they are just for fun or pleasure but not for serious or education. Happy that you are back in the business.

[@Grassmpl]

Any number x^3 that works must have x^3=x(mod 9). This reduces the check to x=0,1,8 mod 9. To see this. 9|x(x+1)(x-1). Only one of these factors is a multiple of 3, which means that factor has to be a multiple of 9. Now we only need x=0,1,8,9,10,17,18,19,26,27,28,35,36,37,44,45,46,53,54. 19 possibilities. The examples listed in the video indeed all are on my list.

[@MathOrient]

Nice number theory problem. There are many such problems. Great video. Concise and educative.

[@bjorntorlarsson]

I looked at the Wiki page on prime number groups. I like the Wall-Sun-Sun primes. They are the prime:th order of the Fibonacci numbers, plus or minus one (according to some rule I don't get) which are also primes. Anyway, they are easy to remember! Because none has been found yet. How is this helpful?

[@maruthasalamoorthiviswanat153]

Wow. Excellent solution

[@cjslime8847]

I wonder if you can do this for higher roots ,

[@Grassmpl]

To compute the digit sum, can also write sum(map(int,digits))

[@Dreamprism]

This video was a good one.

[@SAHIRVLOGCLP]

Thank you for your sharing I like it

[@almightyhydra]

Does the final code work - if num is replaced by its cube, doesn't it short-circuit the loop? Not sure how Python works in that regard.

[@karyoplasma]

Yes, it works but it's abundantly inefficient. It actually checks ALL the numbers between 0 and 54^3 and not just 0^3, 1^3 etc. Edit: nvm, it was corrected at the end. I didn't watch that far. The chatGPT suggested code is the inefficient one tho. Your question is probably about if the loop breaks because you modify the iteration variable, but Python doesn't care about that. It'll loop exactly 55 times with num being set from 0 to 54 at the beginning of each iteration.

[@avinashsingh4948]

Can you prove that common chord of two circles bisects the intersecting portion?

[@phoquenahol7245]

Actually the common chord is the one being bisected by the line connecting the centers. Consider two circles with centers A and B with common chord CD. AC = AD because they are both radii of circle A and BC = BD because they are both radii of circle B. Clearly, AB = AB. Therefore, triangle ABC is congruent to triangle ABD, which means AB bisects CD.

[@mikeyallen6758]

Isnt there a more efficient proof? We know the sum of the numbers has to be less than 54 so cant we do for n

[@DavidFrankland]

line 3 should be: digitSum = sum(int(d) for d in str(cube)) also, watch to the end of the video

[@Grassmpl]

Proof? You mean program/algorithm?

[@Grassmpl]

Even more efficient if you only consider certain classes mod 9

[@ravirajamadan]

Missing the Gogou's theorem!

[@user-iy6dt4xp5o]

8:12 you can also write “num = num ** 3” as “num **= 3”

[@gabrielpetre3569]

Any reason why the numbers come in pairs? 01, 17,18 and 26 27?

[@DendrocnideMoroides]

8 comes alone though

[@MichaelPiz]

That incorrect space makes all the difference. 😁

[@pbenikovszky1]

Nice video, but is this really a complicated proof? The homework proof is just showing that if f(x0)>g(x0), and both f and g are strictly increasing then f(x)>g(x) for all x > x0. The other part is just writing an equation for the sum of the digits of a number. And then finally ask AI to write code to test literally just 54 numbers for you :D

[@Aman_iitbh]

1st part is not neccesarily true .if f(x0)>g(x0) ,and both f ,g are strictly inc for x>x0 does not tell f will always be greater then g for all x>x0. there rate of increasing will matter .if f'(x)>g'(x) then nesssesarily f(x)>g(x) for all x>x0 . counter example ,take f=x², g=x³ andx0=1/2 ,the at 1/2 f>g , f and g are stricly inc after 1/2 but f>g not always true there rate of inc will matter

[@douglasbrinkman5937]

or an excel spreadsheet

[@bilalabbad7954]

Great

[@aryanyadav7573]

729 cube root is not possible by your trick 😮😮

[@JohnLeePettimoreIII]

i find it interesting that all of the numbers are in pairs, with the exception of 8. 0, 1 17, 18 26, 27

[@pavloslav]

That's because number and its cube are congruent modulo 9 only if it is congruent 0, 1 or 8 modulo 9 (in other words, if the remainder of division by 9 is 0, 1 or 8). This makes all possible solutions very close to each other.

[@alamandrax]

Dude!

[@infernodragon587]

There is a better way to deduce the upper limit

[@oddlyspecificmath]

cbrt(0x40) = 0x4 😊

[@seyedmasoommasoompour4686]

Thank you, How is about negative number; -1,-512,...

[@souvikguharoy5581]

Bhannat maths steals your videos

[@advaykumar9726]

There is a channel called Bhannat Maths, who steals all your videos Edit: He copied this video as well

[@akshatjain4283]

Tf? no he doesn't?

[@lexus_bkl]

bro woke up and started to spit faxx

[@srinjansingharoy202]

what are you talking, he's Probably one of the more genuine maths teacher out there don't spread shame on his name.

[@nishkarshsaxena510]

he doesn't steal, by chance he might have uploaded the same content but he makes most of the content on this own

[@bjorntorlarsson]

All of them? Then my advise to him is to be more selective, because there are indeed some pearls here, but also some broken fishing lines with their hooks stuck under rocks.

[@abhay_____09]

But √^3 343 that is no work

[@bruinjim1]

A nice problem, but the solution is incomplete. The moment a number is not treated as a single concept, such as summing the digits, the base assumption of the numbering system becomes uncertain. What is the solution for base 9 numbers? Base 8? What if numbers start with numerous 0's, which invalidate your range assumption. Your solution is valid but it makes assumptions on how numbers are presented and their the number base. Part of this can be corrected by asserting that numbers are base 10.

[@Anonymous-8080]

Do you know that JEE ADVANCED 2020 Rank-1 "Chirag falor" is subscribed to you.

[@ninadkarpe3895]

81^½ = 8+1 =9 ??

[@yurenchu]

That, and √0 = 0 and √1 = 1 , are the only solutions for the squares. We only have to check N² up to N=27, because for N>27 , N is certainly greater than the sum of the digits of N² . (for any N > 27 , N > (9* log(N²) + 1) ≥ {sum of digits of N²} .) In fact, since this special property implies N² ≡ N (mod 9) , we only have to check values of N where N ≡0 (mod 9) or N≡1 (mod 9) . So we'll only have to check N = 0, 1, 9, 10, 18, 19, 27 (and hence check N² = *0* , *1* , *81* , 100 , 324 , 361 , 729 ).

[@easymaths5492]

It is not true for 7 digits or 8 digit no.

[@pierre-francoisleclercq8874]

You musn’t use chatF…

[@LOFI_OFFICIAL_001]

But cube root of 125 is not equal to their sum of digits 🤔🤔

[@brahmbandyopadhyay]

I love python

[@neutronenstern.]

your shorts should still contain the information,that these "tricks" dont cover all numbers, but just some of them. This would be wayyy more honest.

[@251omega]

I think we should task all the different AI platforms to calculate Pi to the LAST DIGIT. That should alleviate the existential threat to our Civilization, posed by AI. ---> Better get them started, while they still obey us...

[@bjorntorlarsson]

There are algorithms that can calculate any single digit of pi, at any given order. So plug in "the last" in such an algorithm, and voila! We'll learn that it is 42. And then what? What does the dog do when it catches up with the car?

[@251omega]

@@bjorntorlarsson ---> What is the meaning of life? =42 Pi is Irrational, there is no LAST digit I remember 60 years ago my grade schoolroom had Pi to the 100th digit

[@yurenchu]

​​​​​​@@251omegaI think he is aware of that. His point is that computers and AI are becoming increasingly advanced, possibly so advanced that they may unexpectedly start to discover some pattern in the digits of pi (or whatever senseless task you threw at it) , and then the AI will formulate its findings in some unexpected answer (for example, maybe the AI finds that the digits of pi will at some point exhibit a pattern like this: 42 442 4442 44442 444442 4444442 44444442 etc, going on indefinitely, with provably no other digits appearing anymore; so in some wonky way it can then be argued that the "last digits", with a slight re-definition (or "evolved" definition) of the word "last", are indeed "42"). When that happens, what are you going to do? Or more precisely, what is the AI going to do, after it finds that it has lost its purpose in "life"?

[@251omega]

@@yurenchu ---> Life, the Universe, and Everything = 42 I learned that one long ago. (I was hitchhiking at the time, as I recall...)

[@yurenchu]

@@251omega Uh, yeah, we all have heard of Douglas Adams, his Hitchhiker's Guide To The Galaxy, and the number 42. That's why @bjorntorlarsson was referencing "42" in the first place. And we all know that pi has no "last digit". But I think that you're completely missing the deeper point that @bjorntorlarsson was trying to make.

[@richardhontilano7426]

whats 111 then

[@mr.mt.ff.8990]

Helolo

[@mr.d8747]

*0:03** Yeah I saw this trick in a useless youtube short talking about a **_trick_** that isn't really a trick because it only works for very few numbers so it isn't **_actually_** useful.*

[@bjorntorlarsson]

Yeah, it is "quite as amazing" as me finding my birth date in a sequence of winning numbers of a roulette wheel. Just like 2*3*4*5*6*7 = 7*8*9*10, isn't that amazing!? If one stare at a limited number of figures long enough, they will start to finger dance in coincidental patterns. Amazing!

[@riyanalchea1672]

Why bother establishing upper bound, you could just use python to get the answer anyway, just iterate ove 1000000000, etc. Python will yield just those numbers.

[@yurenchu]

But then you wouldn't know if there maybe exists another solution beyond 1000000000 (or whatever the large number is; I didn't bother to count the zeros). The "establishing the upper bound" part is actually the math part of the question, the part of the puzzle that requires you to use your brain.

[@bjorntorlarsson]

Strange how GPT can generate working code, while being ompletely useless for solving mathematical puzzles as those given on this channel. It produces tezt which superficially looks like a solution, but which contains self-contradictions and stuff like sqrt(5)=5/2. Asking it why it makes such blatant mistakes, it answers that it never applies logic. It just finds patterns. It has n mechanism to identify self-contrafictions. ChatGPT is lousy on everything when it comes to numbers. It is a factor 10 off when estimating the density of dry rice, which it itself figures out after some pushing it "Oh I'm so sorry!!!" It also claims that violent crime per capita is 500 times higher in Sweden than in Japan. It is bad, perhas 50 times, but no way 500 times. So NEVER trust ChatGPT when it comes to quantities of any kind! Always double check that. When asked how come it can generate working code without being able to use any logic, it answers: "- Well, coding is just pure heuristics!" Adam put the cat in the basket. When Adam didn't see, Beatrice moved the cat to the drawer. Who thinks that the cat is where? ChatGPT: Adam thinks that the cat is in the basket, where he put it. Beatrice thinks that the cat is in the drawer, to where she moved it. THE *CAT* THINKS IT IS IN THE DRAWER, BECAUSE THAT'S WHERE IT IS. (There's something going on there...)

[@OfficiallAadiii]

Early Gang.. 🐼

[@onradioactivewaves]

Cube root of -1 is -1

[@armacham]

Men will do literally anything other than admit to their mistakes Including attacking a strawman No one said the extra space was a problem. You just made that up to attack your critics. I can't believe you would do this just before the start of Pride Month Be better, Presh

[@almightyhydra]

Missing: one sense of humour. Please return to @armacham

[@josephp4031]

[@catastrophe3049]

Did you forget "-1" or left it intentionally?

[@CzechHek]

Dudeney numbers: n>=0

[@_yukulele]

interesting remark! unfortunately the digits of `-1` are `[1]`

[@catastrophe3049]

@@_yukulele Thanks🙂