69 Is A Nice Number, Mathematically

There's a curious fact about the number 69: it is the only number whose square and cube contains every digit from 0 to 9 without repetition. But how do we know it's the only number? We can prove it using some good old fashioned logic and some help from Google Bard to generate Python code.
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[@TheManOfTomorrow]

The fact that you had to specify "Mathematically" tells enough that why 69 is a SPECIAL number.

[@lrrahulbiswas8859]

Exactly 😁

[@SidneiMV]

LOL

[@Nikioko]

It is 3 times 23. Or what were you thinking of?

[@SHORTS_5876]

noice

[@AbhenandanJain]

Number "69" will blow your mind 🤯

[@ericchen3129]

Vsauce made a different take on this very number. He explains "69" is a strobogrammatic number, which means it's the same rotated 180 degrees. Both are interesting takes on why people like 69.

[@teleportingbiscuit8149]

There was also a Numberphile video about how 69 is the largest number whose factorial doesn’t produce an error on most calculators, if I remember correctly…

[@asheep7797]

Vsauce2 i think.

[@varunsathya-composer1404]

96 is also the same 180° rotated

[@lucasdasilva23]

This is the exact symmetry that makes 69 so nice 😊

[@DatBoi_TheGudBIAS]

​@@teleportingbiscuit8149 69! is the last factorial smaller than 1 googol, and as most calculators have a limit of a googol, they will give u an error when u put an integer larger than 69 with factorial

[@PuspaPrasad-l1l]

Video about : 69 Today: 6/9 Video length: 6 min 69 secs Everyone's favourite: 69

[@zimap]

this comment was sent at 6:09 AM

[@NecronHandlee]

Oh yeah

[@catch_me_if_you_can_1]

Likes for your comment will be 69😂

[@sumittete2804]

But your comment likes is 39

[@zimap]

@@sumittete2804 for now

[@Erlewyn]

For a bit of optimization, you could skip multiples of 10 (both square and cube always end up with a 0) and multiples of 5 (same reason with 5).

[@lenguyenminh3452]

u can also skip the numbers which end up with 1, 6

[@zanti4132]

​@r97bxjc988 The digits in the base number aren't included, just the square and cube. So numbers ending in 4 and 9 have to be tested.

[@zanti4132]

Another thread points out an additional way to narrow down the candidate numbers: Let x be the number being tested. Since the sum of the digits total 45, which is a multiple of 9, it follows that x² + x³ must be a multiple of 9. Factor this as x²(x+1) and we can conclude that either: (a) x is a multiple of 3, or (b) x+1 is a multiple of 9. Combine that with the requirements that the x is between 47 and 99 and can't end in 0, 1, 5, or 6, and the only candidates left are 48, 53, 54, 57, 62, 63, 69, 72, 78, 84, 87, 89, 93, and 98.

[@ams8961]

numbers ending in 0,1,5,6.

[@Konomi_io]

for some more optimisation, you could skip numbers that arent 69 because they will always end up with duplicate digits

[@realDonaldMcElvy]

69 is the number proven mathematically to get the most likes and shares.

[@realDonaldMcElvy]

420 is the second most popular number.

[@reoxoglephic603]

As is this comment

[@tristanvandervelde3569]

Like count of the comment should stop at 3 times 23

[@davidbuitelaar6659]

a funny comment like this one is mathematically most probable to be liked

[@mike1024.]

What a very sad truth you speak. It goes to show the maturity level of the average viewer.

[@TheManOfTomorrow]

*Dad sees the notification from KZbin on my phone, "69 Is A Nice Number -"* Dad: "Son! What type of channels have you been following, huh?!" *reads afterwards* "- Mathematically" Dad: "Oh. Good stuff, son. 👍*

[@faressakr3457]

Are ya winning, son?

[@imyrzaim6241]

Here before this blows up

[@shahjahonsaidmurodov]

Ah no son, don’t worry, I just thought

[@ujjwal2473]

@@faressakr3457 yes father

[@SidneiMV]

LOL

[@catcatcatcatcatcatcatcatcatca]

The original python code is only correct because the range is limited to seemingly arbitrary number. The set operation will ignore duplicates, so the rule is violated unless you first check that original lengths also add up to 10. Alternatively you could convert both numbers to strings and then sets, then XOR them, and then check the length of the resulting set. But if you first concatenate them as strings you can continue if the len is under 10 and break when it is over ten: this way you do basically what the manual tests at the beginning of the video achieved. So you don’t need to convert strings to sets and search the length of the set needlessly. Anyway, if google bard got the return value correctly, 69 is also the only number up to 9999 that has all the digits in it’s square and cube at least once. 10000 is trivial so we can safely round up to that as well!

[@Bhuvan278]

I had the same reaction. However, since he had worked out by hand ahead of time that the input range is the range of 2 digit numbers generating exactly 10 digits in its square and cube put together, this is valid. He should have, however, added a comment in code saying as much. But, this isn't a programming class, just a one-off where the solution is both the initial thought process defining the limit and one-off generation of matching numbers. So, I guess this works!

[@StokesFamilyCO]

This is a fun factoid. I checked for a number with the digits appearing exactly twice (so length 20 opposed to 10) and it turns out there is a single solution - 6,534 with its square being 42,693,156 and its cube being 278,957,081,304. I wonder if there is always a solution - exactly n appearances of each digit; does it fail ever…

[@mike1024.]

You just took this question and made it a whole lot more interesting!

[@Tom-cq2ui]

I ran a script for counts of digits from 2 to 40 and I only found 69 for 10 digits and 6534 for 20 digits. I didn't run it further because I need to optimize it for now (40 took like a minute)

[@Tom-cq2ui]

For example: in case of 12, I was looking for 1, 2, 3, 4, 5, 6 ,7 ,8 ,9, 0, 1, 2 - just to clarify what I was testing

[@yukimoe]

What about in other bases? Like a solution for every hexadecimal digit appearing once?

[@StokesFamilyCO]

@@Tom-cq2ui Very cool, thanks for checking a little further.

[@AyrtonTwigg]

69 inches the average height of males in the US. The woman who gave birth to the most children in history, gave birth to 69 children.

[@Tritibellum]

nice

[@lukasjetu9776]

when you rotate 69 by 180 degrees you will get 69, the world, is made of 69?

[@mikereid1195]

I *would* like this comment, but it has 69 likes already and that's a nice amount

[@SirNobleIZH]

3 more people liked Damn

[@mikereid1195]

@@SirNobleIZH damn

[@Tom-cq2ui]

I like how this just turned into a warning about AI-generated code. Although this is a cool example of proof by exhaustion, I was hoping for a different kind of proof. In any case, that's a pretty nice property indeed.

[@mike1024.]

As specific as this test is, it seems hard to imagine any other way to do it. You could eliminate any n that is congruent to 1 modulo 3 though, because n^2+n^3 is not a multiple of 3 but the sum of 0 through 9 is.

[@rjrmonkey]

I'd start by proving that numbers ending in 0,1,5,6 will have cubes and squares that end in the same digit. Next, I'd explore the properties of multiples of various numbers. Squares and cubes aside for a minute, I have a hunch that a six digit number and a four digit number that don't share any digits and don't share a factor of 3 will be light on common factors. I don't know how hard to look into that stuff though, checking 30 numbers by hand pretty quickly starts looking easy in comparison to deeper analysis.

[@compiling]

@@mike1024. You can go further than that. The sum of 0-9 is a multiple of 9, so n^2+n^3 must also be a multiple of 9. So n must be either 3, 6, 8 or 0 mod 9. i.e. it must be a multiple of 3, or 1 less than a multiple of 9.

[@phantomphoenix8828]

69th like Ironic

[@gblargg]

The original code worked by chance because 99 and 100 didn't happen to have missing digits of 9 and 1,0, respectively.

[@tareklel1127]

this video is 6 minutes and 69 seconds 😉

[@huzefa6421]

😂 Man that was a precise vision but very interesting Liked that one 😅

[@chinhhoangondiepchinh5610]

There's... 60 second in a minnute

[@LeafyMations._.]

Yes there is

[@LeafyMations._.]

And?

[@LeafyMations._.]

@@chinhhoangondiepchinh5610he’s still ridht

[@babylonfive]

Correction (minor): you start testing at 47 and end at 99... it just so happened that the process of detecting the bounds involved exposing the numbers to a manual test in the lower and upper detection case - there's no reason to not count those endpoints just because you tested them manually. It's is an important aspect of methods and proofs that the bounds be made clear.

[@white9763]

you dont need to test 47 and 99 since u squared/cubed them to know whats the range of numbers with the property that when squared it has 4 digits and cubed has 6 2:00 for 47 2:50 for 99

[@yurenchu]

​@@white9763 He's correct. It's not a sound practice to already dismiss the boundary values. The boundaries were determined on the criterion that the square and cube must have ten digits together; the boundaries were not determined on what those ten digits would be. Since the boundary values 47 and 99 fall within that first criterion, they must be included in the checks that tests for the next criterion: are the ten digits all different? By already excluding these boundary values, you may run into problems when for some reason the goal of the program is slightly changed and hence the second criterion must be changed. For example, when instead of looking for instances where square and cube contain each of the ten digits, suppose the problem now asks for (let's say) instances where the ten digits of square and cube can be paired one-to-one to the digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} such that the difference between each pair is exactly 1 . Re-defining/rewriting the second criterion may be easy enough, but with such a goal change, the old boundary values suddenly must be checked again; but since you already dismissed them and excluded them from the criterion #2 test, they will be overlooked. It's a bad habit, and sloppy programming practice.

[@sanjeevkumarsingh8141]

69 is a nice number "Mathematically" and "Practically"

[@akshitranjan8392]

To be more accurate, 'biologically'

[@rishabhchaudhary3918]

Mathematics and Biology both agree that 69 is a nice number and has many uses👍

[@debajyatidey9468]

This is one of the best KZbin channels I follow from the beginning of my preparation for the JEE. It actually provided many interesting & mind-bending problems, proofs & solutions. Great contents! I totally appreciate your work!

[@Conflux4761]

Hi, I've actually done research into this area! Turns out 69 is the only known "nice" number not only in base 10, but in any base! This has been checked up to around base 48 - after which searching computationally becomes too slow. But more fascinatingly: there probably are more such numbers! If you assume nice numbers are distributed randomly, the result is that they just take until around base 120 to appear. (This arises because the dominant term in the approximation ends up as (b/148)^(b/5) based on Stirling's approximation, so b needs to be pretty high for b/148 to not be super small.) So, likely infinity, but only one found! So, of course, the natural question is whether any of these other nice numbers can be found. I asked about this on the website Manifold, and many users investigated. Various optimizations were found which knocked off a few orders of magnitude, such as filtering mod b-1. Looking at “quasi-nice” numbers, where x and x^2 have all the digits instead of x^2 and x^3, provided support for our heuristics about nice numbers. There were various other neat discoveries. However, none of that changed the computational intractability. So even though there‘s probably an infinite amount of nice numbers, only 69 in base 10 is currently known, which I am captivated by! KZbin shadowbans links, but I've written much more about this at tinyurl dot com/confluxblog/post/is-69-unique

[@PMA_ReginaldBoscoG]

watched your video & subscribed

[@pulverizedpeanuts]

69 is also: •the greatest number with a factorial less than a googol •the sum of all the divisors of all single digit numbers additionally, 69⁶⁹=69(mod 420) 69=1+2×3+4×5+6×7 69=6×9+6+9

[@kooshkooshyunger1438]

Fun fuct 18^3 = 5832 18^4 = 104976 All the digits appear only once, so 18 is also a special number

[@JCCyC]

Makes sense, since 18 is when you can get a 69 legally.

[@dxritq]

it says square and cube, not cube and the fourth power, but that's nice

[@adarshkumaryadav3449]

i also thought of something like that

[@deepakprasai525]

Today is 69 I mean June 9😂😂

[@HackedPC]

nice one

[@verticalslab1973]

Nice one

[@HackedPC]

@@verticalslab1973 y u copi me

[@robertveith6383]

​@@HackedPC Please write in English.

[@aram5642]

It is not! y'all date perverts. Today is 96!

[@Milenakos]

set()'s in python automatically eliminate any duplicates, so in this case if some digits repeated it would still claim the number is valid

[@wombat4191]

But it couldn't be because a range where the square and cube have exactly 10 digits combined was selected. If there were duplicates, then all digits from 0 to 9 weren't there and the number wasn't valid.

[@yacoop7432]

yeah but due to the range restriction if the digits repeat it wont have length of 10

[@charleslivingston2256]

Exactly. That is why the code that included the number itself still worked for 69. Luckily, after removing the number itself and restricting the range to where the total number of digits is ten, then having at least one of every digit 0-9 is the same as having exactly one copy of 0-9.

[@flarklooney]

Since the digits 0-9 non repeating add up to a multible of 3, you only need to check numbers that are a multible of 3.

[@bjorntorlarsson]

Aha, a piece of analysis and insight there! Then one might take a look at the progression of digits of different significance evolve with multiples of the prime 23. Or with what other bases this works. Or with powers of 1 and 2 or of 3 and 4. No, because it is ridiculous.

[@Afrin_Ali]

Could you please elaborate?

[@CyCloNeReactorCore]

how does this follow?

[@bjorntorlarsson]

​@@CyCloNeReactorCore You did follow here, so you ARE the answer! How likely is it that ten randomly generated digits in a row consist of all figures 0-9? And the range accordning to this arbitrary generation rule is about 50 tries. And the question of this "show" is: "How come there is ONLY ONE example of this???"

[@CyCloNeReactorCore]

@@bjorntorlarsson you're insane :)

[@embracinglogic1744]

MindYourDecisions has a sense of humor, I love it!

[@ThePROestRedn99]

Nice to see that - "You are exploring something else other than Maths"😁😂

[@FoleiCZ]

I would like to tell you that 69 is the sum of the divisors from 1 to 9. Another mathematical fact, why is 69 a nice number.

[@Tim3.14]

It took me a minute to get it, because at first I was counting 4 as having 2 factors of 2, and 9 as having 2 factors of 3 - resulting in the much less elegant answer of 74. Nobody likes 74

[@samueljehanno]

​@@Tim3.14 73 is better

[@yurenchu]

​@@Tim3.14 "Nobody likes 74" Yeah, even The Connells were faltering about it: "74... 75..."

[@mach6893]

1+3+2+3

[@deggery-oneaboveall3365]

Oh god , never expected this video from you , but I love it 🤣

[@mike1024.]

For a little bit more rigor, though obvious, you should argue that the square and cube functions are increasing functions.

[@goobert813]

Didn’t even mention that 6+9 + 6*9 = 69

[@russianyoutube]

Wait fr

[@dzyszla]

6534 is another one - each digit occurs exactly 2 times in results of square and cube :)

[@huzefa6421]

Another reason 69 is special It is the only upside down anagram number whose digits could be used to create an upside down anagramic equation equal to 69 That is *( 6 + 9 ) + ( 6 × 9 ) = 69* EDIT : Also video posted on *6 - 9* - 2023 ( Tha pattern is not my type becoz i am asian using DD MM YYYY pattern 😅 )

[@mike1024.]

Isn't 6-9-2023 month first?

[@huzefa6421]

​@@mike1024. Thanks for pointing I meant that i am asian who rarely uses that MM DD pattern

[@huzefa6421]

​@@mike1024. See that itself confused me that i typed it wrong 😂

[@yurenchu]

Isn't 5 also an ambigram number? So how about the expression: (55 - 5) - (5⨯5 + 5 + 5/5) - (5 - 55) which produces 69 too, using just the digits of the number 5?

[@rickostidich]

I started with a very short script for the Pari/GP calculator: for(n=47,99,if(#Set(digits(n^3*10^4+n^2,10))==10,print(n))) This indeed shows only "69", in 1 ms; and without the need of any "AI". Since we know exactly that the numbers which produce a string of 10 decimal digits are those between 47 and 99 inclusive, we don't need to check the length of the string, but only the uniqueness of the digits. I was interested in finding the solutions for many bases other than 10 decimal. But with big bases and the appropriate ranges, the script gets very slow. Of course, the speed of the script can be increased by more than 100 times by writing a real *program*, in machine language of course. And there are many other mathematical optimizations to implement, mainly based on modular arithmetic and number theory. (For example, by checking the ending digits that are equal both for n² and n³, and the specific rules for each base: in base 10, we must have n≡0 mod 3.) But first of all, I wanted to calculate the exact values of the range of numbers to check, for whatever number base. And I saw that it depends on the base, according to its remainder mod 5. Here are my calculations, that I find quite interesting (b is the base, and k∈ℕ): For bases like 5k-0, the range is [ ⌈b^(k-1/3)⌉, ⌈b^(k-0/1)⌉-1 ]. For bases like 5k-1, the range is [ ⌈b^(k-1/2)⌉, ⌈b^(k-1/3)⌉-1 ]. For bases like 5k-2, the range is [ ⌈b^(k-2/3)⌉, ⌈b^(k-1/2)⌉-1 ]. For bases like 5k-3, the range is [ ⌈b^(k-1/1)⌉, ⌈b^(k-2/3)⌉-1 ]. For bases like 5k-4 (e.g. 6,11,16,21,…), there is no useful range, and hence it's never possible to find a solution. The only exception to the rules above is the base 3, where the ending value is less than the starting one; so, again no range and no solutions. (Things like this sometimes happen, according to the Law of very small numbers.) 🍻 The two more complicated cases are those for 5k-1 and 5k-2, where initially two possible ranges appear to be searched; for example for base 14, if we have n² of x digits and n³ of y digits, we could have 14=x+y=5+9=6+8, but we can exclude the 5+9 case since it's not possible for any 5k-1; similarly for base 13, 13=x+y=5+8=6+7, and here we can exclude the 6+7 case which again is not possible for any 5k-2. I have written a nice proof of these results, but it's too long to fit in this comment, so it is left as an exercise for the reader. 😜 In the end: I quickly checked all the bases up to 30, and I found no solution other than 69₁₀. The complete Pari/GP script that I wrote is this: for(b=4,30, k=-(-b\5); i=5*k-b; if(i==4,next); print("base: ",b); \ start=ceil(b^(k-[1/3,1/2,2/3,1][i+1]))-1; \ stop =ceil(b^(k-[0,1/3,1/2,2/3][i+1]))-1; \ my( chk(n)=concat(digits(n*n,b),digits(n^3,b)) ); \ if(#chk(start-1)==b || #chk(stop+1)==b, return("Range error") ); \ for(n=start,stop, s=digits(n*n,b); if(#Set(s)#s,next); \ s=concat(s,digits(n^3,b)); if(#Set(s)==b,print("Found!: ",n)) ) ) (Here the start is decreased by 1 because of rounding errors that can occur in Pari, despite the precision set.) Maybe one of the next days (or months) I'll improve the algorithm and write a real program, in order to quickly check many more bases, or variations of the problem. In this case, I'll write a comment to this comment. Bye!

[@tusharagarwal5306]

Me to my friend : 69 is my favorite number My friend : you perv.. Me : no, hear me out

[@yukimoe]

Not only did I not expect something about 69 being nice here but also I definitely didn't expect a nice crash course on Python and trusting output from AI chatbots :D

[@cheeseparis1]

69 always brings surprises

[@yoapps137]

To make the code run 65% faster introduce these few more If conditions ignore Modulus 3 != 0.. because the concatenated number has to be a multiple of 3 Avoided all 2 digit numbers that end in 0,1,5,6... since they all immediately have a repeated last digit in the ^2 and ^3....

[@mathewwilliams6801]

Dont forget (6+9)+(6×9)=69

[@djsnowpdx]

I’m sure everyone noticed, but I didn’t read any comments about it, so here goes. This video wasn’t just nicely timed, but nicely dated, and nicely done.

[@matthewsaulsbury3011]

Wow, this is neat! Also, the number 69 looks the same when you rotate it 180 degrees. It's an ambigram! 😀 I like making an ambigram out of a word. Now here is one with a number.

[@neuralwarp]

chimp

[@liam.28]

@@neuralwarp lol what

[@olga2891]

88 00 They are also the same when flipped

[@NowNormal]

@@olga289100 isn't a number

[@allright6610]

for i in range(48,99,1): square = i**2 cube = i**3 digits = str(square) + str(cube) distinct = set(digits) if len(digits) == len(distinct): print('Unique number with all digits existing exactly once in square and cube is:', i) print(sorted(list(digits)))

[@omsincoconut]

69 is a number that it's sum of divisors is itself with reversed digits 1 + 3 + 23 + 69 = 96 And removing itself in the sum 1 + 3 + 23 = 27, a cube

[@moonlight-td8ed]

69 is the myth. 69 is history. 69 is 69

[@spark_coder]

There also the isosceles triangle with two 69° angles (Nice-osceles triangle) that gives 42.0° as the third angle. (On a Euclidean plane)

[@jsosianimations]

lol

[@jsosianimations]

69 is meaning to the universe confirmed

[@pomtubes1205]

Who gave that name lmao

[@NexsusPoint]

"69 is a nice number but not mathematically" Jhonny Sins

[@animadas4052]

Mathematics + computer science perfect combination doesn't exist❤❤❤

[@RocketsNRovers]

IIT Delhi Maths and computing engineering

[@tayserbinjafor1569]

I have to also mention that, using only factorial, 69! is the highest number that can be handled in the 'CASIO' scientific calculator.

[@5ucur]

A small hint for future videos that feature code: use a monospace font. It makes the code much more readable, especially with a language such as Python. There are some good-looking monospace fonts out there, don't be discouraged by the ugly ones.

[@mike1024.]

I've said it before and I'll say it again. Taking any fascination with the number 69 is nothing more than showing a person hasn't grown up enough yet. It's a number! But this random fact was kind of cool despite caving into teenager mentality to be willing to post this for likes/subscribers.

[@TudorPaisanu-jm8tm]

I think this number is interesting for other reasons.

[@vivianzhang647]

Also the sum of the divisors of 69 is 96, pretty cool

[@mastershooter64]

Lmaooo I did not expect this title

[@satyapalsingh4429]

Heart filled with joy . What a good number you found .My salutations to you ,dear professor .

[@sonicwaveinfinitymiddwelle8555]

Nobody: Kids in the comment section: 69 haha funny number

[@peterhawes9680]

On a standard Connect 4 Board (6 x 7) there are 69 winning lines! 24 horizontal, 21 vertical and 12 diagonals in each of 2 directions. 😂

[@XanderX_the_lone_survivor]

This man literally brings "The Holy Number (69)" to the next level

[@nvapisces7011]

How do I prove it is true? Just write a python code running all natural numbers from 40 to 100 (check total number of digits for square and cube in intervals of 10). Run a for loop to check if the set from 0 to 9 exists by appending the digits into a list. Check also if len of list is 10. Then append to a new list every time a number satisfied the conditions. This list should only contain 69

[@frietvet]

I was hoping for a neat number theory proof using ring theory or something.

[@illuman1369]

Also 6+9+6x9=69

[@Y1314T]

@6:43 "69 is the only solution". Another beautiful justification for its necessity, both mathematically and spiritually.

[@rithikkeshri3799]

Thank you so much sir ❤ Every time your new videos gives so much knowledge and I very thankful for that.sir keep making this kinds of videos

[@rotatingmind]

Would be interesting to know whether there are solutions in systems to another base than 10 (i.e. the decimal system)

[@PokeManiacArceus]

Up to base 30 there is no such number other than 69 for base 10. It's very time consuming to check them, there are 494 million base-30 numbers with square and cube having 30 digits together, and none of them have all base-30 digits. There are 30! permutations for base 30, but only those 494 milion right solution candidates. Maybe because of this there is no other base with solution of this problem, but it will be very difficult to prove it.

[@dankaplan4330]

For any even base b, the sum 0 + 1 + 2 + ..+ b-1 = (b-2)(b-1)/2 = (b-1)[(b-2)/2] is a multiple of b-1. Note that mod b-1 a number written in base b, a_0 + a_1 b + ... + a_n b^n is the same as the sum of its digits, a_0 + a_1 + ..+ a_n. So for the digits of n^2 and n^3 to be 0, 1, .., b-1, the sum n^2 + n^3 needs to be 0 mod b-1. In base 8, we can use this to check only 3 numbers by hand - two of which are establishing the bounds. For bounds: 20^2 = 400 and 20^3 = 10000 is the smallest number with 8 digits and 30^2 = 1100 has more digits so is too large. Now n^2 + n^3 = n^2(n+1) = 0 mod 7 implies n = 0, -1 mod 7. So we only need to check 24 and 25. But 24 ends in 4 and 4^2 = 0 = 4^3 mod 8, so its square and cube both have 0's. 25 can be checked mod 8^2 since its cube ends 55.

[@HappySunburnn]

if you put 69 uoside down, its 96

[@HackedPC]

Presh seems like too eager to get views....

[@aram5642]

Lickbait ;)

[@deggery-oneaboveall3365]

@@aram5642 oh you 🤣

[@anuragg7007]

​@@aram5642😂

[@huzefa6421]

i gave u the 69th like 😅👍🏻

[@HackedPC]

@@huzefa6421 Thank you.

[@simplifiedgeometry]

I'm so happy that you included Python in this math channel🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉🎉.❤❤❤

[@NotHexaaaa]

It's also divisible by 23

[@heco.]

here's how i coded it: numbers = [] for i in range(47,100): total = set(str(i**2) + str(i**3)) if len(total) == 10: numbers.append(i) print(numbers) and for fun i did it in 1 line: numbers = [i for i in range(47,100) if len(set(str(i**2) + str(i**3))) == 10] print(numbers)

[@beginneratstuff]

the first one is probably how most people would do it for a quick result if they weren't trying to be instructional, just getting rid of the extra variables and unneeded function. And for the second one, I didn't even know you can write python syntax like that lol

[@FreyjaWithA_J]

69! (factorial) is also the highest number most calculators go up to as any higher is over 10^100.

[@kwokchuchan7793]

Back then when I was a student and whenever I received a calculator (or borrowed from classmates), I would try 69! to see how fast the calculator was, because it was the hardest single-function problem for a calculator I could think of. And then tried 70! expecting to see an out-of-range error.

[@samueljehanno]

What

[@minerscale]

@@samueljehanno 69! is the largest factorial displayable on most common calculators (they tend to have a limit of 10^100). They also take some time to compute so it's always fun to watch the calculator think for a second or two.

[@tronicgo8873]

Why do I keep thinking sonic is the one taking in this video 😂

[@oldsport]

*Karma is like 69 you get what you give*

[@LittleLu609]

This is great you posted this on June 9th, which is also my birthday.

[@mightygreen3364]

I was honestly most supprised, that there is no number for which the square and the cube have exactly 11 digits. But it makes snse, and also holds for 6,11,16,21,...

[@oddlyspecificmath]

Can Bard handle 0-9 twice? (here's one answer): >>> 6534**2, 6534**3 (42693156, 278957081304) _[code]_ for n in range(4642, 10000): sqcu = str(n**2)+str(n**3) if len(sqcu) > 20: break if "".join(sorted(sqcu)) == "00112233445566778899": print(n, sqcu)

[@zimap]

this is why sex is math

[@gabrielgabi543]

💀

[@zimap]

@@gabrielgabi543 :skull:.exe

[@Dr.1.]

hey i loved this longer kind of video keep making more like these...

[@Maaz2360]

also 69 is the highest factorial a regular calculator can show

[@adventureboy444]

yea I once factor random number for fun and realize this fact

[@mecidelhasan9398]

In my phone calculator not 69 but 170

[@TYsdrawkcaB]

cool

[@ego5809]

Noice

[@serkratos1216]

and 20! is the highest factorial that fit in 64 bit integers

[@Gideon_Judges6]

Without testing, I suspect python set() quietly elided the duplicate digit created by str(number).

[@TheMultipower47]

Thank you I was wondering how the code dealt with duplicates

[@mike1024.]

In retrospect, you just proved this code will output any number whose set of digits from squares and cubes contains every digit.

[@laxminarayanbhandari855]

40000 years of evolution and we have barely tapped the vast potential of 69. - Tony Stark, 2069

[@DarkifyDarkify]

For a calculator that can give an output of 99 digits, "69!" is the biggest factorial, "70!" is already out of the range

[@joaof5838]

nice piece of informatin, right there

[@theloyal6361]

So,69 mode is more powerful clock sanitizer than 11 MODE?😂😂😅😅

[@JGKCJGKC]

**pops** NICE

[@PoomanLore]

-69: Am I a joke to you?

[@hamster8706]

I love how this video released on 6/9

[@youknowwho7896]

this channel is gonna blow up now

[@antorthebrilliant6712]

yes, 69 has very interesting properties..

[@thetrends5670]

MindYourDecisions: 69 Is A Nice Number. Me: Yes, I agree.

[@aprivatechannel1152]

Nice^2 and Nice^3

[@learnerrabnawaz641]

Even my useless friends are having much obsession in maths as they always share me memes and jokes on this number .Didn't understood the jokes until I saw this video. LOL I didn't knew only I was the one didn't knew this mathematical beauty of 69. Thanks a lot Presh Sir..

[@tahaabujrad7806]

hello there, the code only worked becuase of the specified range from 48 to 99 for larger numbers it won't work correctly, for example 128 will also pass the test the flows are in lines 8 and 9 change the lines to the following: new line 8: digits = list(str(square) + str(cube)) new line 9: if len(digits) == 10 and len(set(digits)) == 10: the flow that you do not ckeck for repeated digits: 69 -> 4761, 328509 all digits with no repeats 128 -> 16384, 2097152 all digits with the numbers 1 and 2 repeated twice each.

[@Jusio]

69 is my door number lol

[@gblargg]

Of course this actual setup is more complex: it's taking the square and cube, doing modulus by 10, divison by 10 then modulus, etc., until the number is 0, for each value. That is, it's base-10-centric.

[@darkparker7500]

69 may be a nice number, but not if there is a lack of hygiene. 😱😅

[@sivakumar_rajappan]

I've actually wrote the code to not only test for the specified range of numbers but for any given number . I've realized that the code given does not check for the uniqueness of the digits and only the number of digits , for instance any number above 99 say 100 or more would have more digits and at some point would have all digits in it and repeated . To avoid this error , we can create a list which contains all the digits exactly once and at the final step when the given number has 10 digits to go with we can give a for loop containing if the digit is found in the created list , that digit would be removed from the list so that if the same digit is repeated once again that digit wont be available in the list and we can eliminate this possible number in else condition and finally print our righteous number """69"""

[@alfredkhew1634]

That's the correct way to learn with Bard or other chatbot, they are not 100% perfect sometimes, but they really generate something for us to start with. From the generated codes, we can modify/test/debug/run again/..., until we get the desired result.

[@deepanshchhawla4380]

I wonder what is 6*9 + 6 + 9

[@CosmicExplorerX]

6*9 + 6 + 9 = 69, what an exciting number

[@elite69]

I always believed that I am special.

[@arnavsaanvifrancis4493]

Every no. has its own value

[@s.p.a.3583]

Before the calculus, you had the possibility to remove any number in the form of a*10+u, that u is 1 of the following: 0,1,5,6

[@neuralwarp]

To be more mathematical you could heuristically screen out numbers whose squares and cubes end in the same digit, eg multiples of 5.

[@klrdgk1]

69 is the only positive integer that will work for the sol ution. For use negative numbers you can also get -69! Nice!

[@kitten6317]

Isn't the factorial for any negative integer undefined

[@RawwkinGrimmie64]

This video is: A) Nice B) Nice² C) Nice³ D) All of the above

[@chem7553]

If "Nice" is 0 or 1, the answer will be D.

[@yurenchu]

@@chem7553 Nice is a city in France, so the answer is not D.

[@jansentanu2637]

The range() should be from 48 to 100, since python's range() upper bound is exclusive.

[@thomaspickin9376]

He's only testing numbers from 48 to 98 though that's why it's range(48,99,1). He doesn't really need the 1 as that's default, he could've put range(48,99).

[@charcoalmilk]

And this video currently has 69k views...

[@user-qr4jf4tv2x]

69 also looks like yin yang