Extra footage: kzread.info/dash/bejne/d2ih1KVsadarf7Q.html Matt's new book is Humble Pi: bit.ly/Humble_Pi More Matt videos on Numberphile: bit.ly/Matt_Videos

@mrJety89

5 жыл бұрын

Can't you just ask what numbers give you 277777788888899 when multiplied, and then that number would have a persistense of 12 by default.

@ErixTheRed

5 жыл бұрын

@@mrJety89 Or really you could look to multiply out to any permutation of the digits in 277777788888899. Maybe it's easier to end up with an even number like 997777778888882.

@jackingbowl5678

5 жыл бұрын

can you make a downloadable program for those codes?

@greyduck4965

5 жыл бұрын

interesting seeing python in a Numberphile video, as I just started learning python a couple days ago

@mrJety89

5 жыл бұрын

@@ErixTheRed Yeah, I was thinking abou that too. Something tells me that they've already tried both of those ideas.

"5 times 4 is … uhhhhh….20." The deeper into math that you get, the harder the easier things become sometimes. XDDD

@raimonwintzer

5 жыл бұрын

preach

@GoProGuyHD

4 жыл бұрын

He is obviously joking

@timirkantisom7833

4 жыл бұрын

Nope

@mmeister8582

4 жыл бұрын

This is actually super accurate. U stop using numbers at some point when u do math, so u lose basic skills

@SirNyanPanda

4 жыл бұрын

@@mmeister8582 What do you mean you stop using numbers?

As a programmer, what gets me is that he went back and modified his code, but didn't remove the redundant print statement.

@CorwinAlexander

3 жыл бұрын

Definitely, I barely coded ever and haven't coded since the 80s, but even I spotted that that was the problem.

@DarkKyugara

2 жыл бұрын

I knew he would simply remove 1 from the total number, because the code gave him +1 because of the entra last step.

@jpdemer5

2 жыл бұрын

It's a Parker Program: almost right.

@Lodinn

2 жыл бұрын

What got me is print statements in the first place. Python2 is strong with him.

@KarstenOkk

2 жыл бұрын

With a little bit of extra interfacing it could make logical sense. Like the final number gives an additional string "Final entry: X". But yeah, he said he "could just" remove it, he never said he would.

Matt: *writes code* Matt: "That can't go wrong." Me: *waits to see how that'll go wrong*

@wtfiswiththosehandles

4 жыл бұрын

That's something we would have called a *Parker Code*

@GlobalWarmingSkeptic

2 жыл бұрын

Every programmer writes perfect code while they are staring at it. Nothing can ever go wrong.

I love how Matt is willing to think and even make mistakes on camera. That kind of security in one’s intelligence probably makes someone really easy to get along with.

@F1amingDeath

2 жыл бұрын

Never trust a perfect person

@efulmer8675

2 жыл бұрын

Except Matt isn't perfect, he makes tons of mistakes all the time, he's just secure that his mistakes don't reflect on his actual abilities. Otherwise we wouldn't have the brilliant "Parker X" banter that makes his channel and Numberphile's channel so entertaining.

@chriswebster24

2 жыл бұрын

@@efulmer8675 I think that was the point. A person who claims to be perfect is likely to be fake, and you can’t trust someone like that. A person who doesn’t mind getting caught making mistakes, because he never pretended to be perfect in the first place, is more likely to be someone you can trust.

Mathematician small talk: “So what numbers are you into these days?”

@qwertyuiop-cy5en

4 жыл бұрын

ahh uhm i personally like 12

@theterribleanimator1793

4 жыл бұрын

@@qwertyuiop-cy5en i could go for an exponential today.

@AdelaeR

4 жыл бұрын

@@theterribleanimator1793 It's been the number 91 again for the last few weeks.

@Cream147player

4 жыл бұрын

32 is a number I find inherently attractive for no apparent reason (other than being a power of 2). I don’t find 16 as attractive but I do love it being the only number that can be described as x^y and y^x where x and y are differing positive integers (2 and 4, for the record). Overall I just love powers of 2. Numbers like 12 and 24 are cute and all, but that factor of 3 feels like an imperfection.

@jeek3452

4 жыл бұрын

3, take it or leave it

*uses calculator* "2 × 7.... equals 14" Literally me when I write an exam. Can't go wrong lol

@LundbergMeja

5 жыл бұрын

Stuka don't forget to double check it!

@The_NthGineer

5 жыл бұрын

It was me in engineering school... I was double checking simple multiplications because I was more stressed to get it wrong because of them than with the reasoning of the math!

@RedGallardo

5 жыл бұрын

He's a mathematician, he does it in a sequence, it doesn't matter how simple is an action. It's the order inside your mind. Because the moment he says "nah, I don't have to do it, it's obvious" he starts to make mistakes. From small to bigger and for math these are all the same. He's learned the hard way to be patient and correct. So it's now a reflex. =)

@Peter_1986

4 жыл бұрын

I had a weird habit of refusing to accept a calculator when I took math tests in junior high school in the late 90s. My math teacher was always like "shouldn't you have a calculator, though?" and I said NO, and insisted on calculating everything by hand. Not sure why, but maybe I wanted to prove to myself that I could do it without a calculator or something.

@M4RC90

4 жыл бұрын

Well he wanted to multiply all the digits together, so he started with 2 x 7. Sure he could have typed 14 straight away and saved two button presses, but he didn't.

I love how “Suggested: The Parker Square” pops up in the corner when Matt says, “I’m always one to give it a go.”

@titiksulistiyani8133

2 жыл бұрын

2777788888899?

For some reason, I always like videos about really big numbers. It seems it’s more interesting for a large number to be special.. because it’s so specific!

@happmacdonald

Жыл бұрын

Googology has entered the chat

The base 2 version of this game is pretty sad

@nowonmetube

5 жыл бұрын

You can only use 1s

@nowonmetube

5 жыл бұрын

1 11 111 1111 11111 Now play the game backwards..

@J374338

5 жыл бұрын

Both 1 and 0 are the BOOM 🤣🤣🤣

@samodelkini

5 жыл бұрын

nowonmetube It‘s always 1 step whatever the number is 111111111111111-> 1*1*...*1=1

@Smittel

5 жыл бұрын

@@samodelkini yea i think they knew that thanks for clarifying tho

lot of people saying 327 isn't prime, I think he means the individual digits are prime

@numberphile

5 жыл бұрын

Yep, I think so.

@stardustreverie6880

5 жыл бұрын

@@numberphile nitrogen-infused coffee ☕

@Garbaz

5 жыл бұрын

He said "Primes" (plural), so yes.

@JamesSpeiser

5 жыл бұрын

that was obvious to me immediately and I'm an idiot

@hgjfkd12345

5 жыл бұрын

It's a parker prime

I think Matt hit on an important bit when he mentioned the base-ten-ness of this problem. Consider that in base 2, you can never have a number that multiples to anything other than 1 or 0. Has anybody checked for patterns across bases?

@douggggggg

2 жыл бұрын

i would think base 10 is definitely the reason for 11 being the maximum probably a proof if you generalize a base 10 number as a sum of multiples of powers of 10 where you can manage to pull out a "10" after 10 steps and then you will get the 11th step always resulting in 0 and there being no way to continue

@VynceMontgomery

2 жыл бұрын

@@douggggggg I don't think it's that clean, quite, but I do think the attrition of possible branches gets too fast

@markhughes7927

10 ай бұрын

111 - the number of the star-gate?

I loved watching him code along with showing the math problem. Please do this more often!

At first I thought that Matt was extremely brave to be so confident in his coding skills that he would be willing to do it live on the internet in front of an audience of nerds. Then I realized that Matt is not ashamed to be caught making mistakes. In truth, that's one of the things I admire most about him.

@YourIQDoesntMeanShitToMe

5 жыл бұрын

I entirely agree. I deeply admire and envy that about others, while I despise my own fear.

@HN-kr1nf

5 жыл бұрын

these numberphile regulars are really great.

@totheknee

5 жыл бұрын

He makes mistakes live on the internets for breckfist and doesn't give 2 Fs! XD

@GhostGlitch.

5 жыл бұрын

Mik he was talking about the individual digits being prime

@caleblewis8169

4 жыл бұрын

Parker square

"i'm always one to give it a go" *parker square shows up in the i-card*

@benstapleton5319

5 жыл бұрын

Just came here to see if anyone said the same thing.

@jakadirnbek7141

5 жыл бұрын

timestamp?

@jacobcoring1635

5 жыл бұрын

12:53

I love that thumbnail. The way he looks, with such fascination, at the number 277777788888899 as if it's the most attractive thing in the world 🤣🤣🤣

12:52 "I'm always one to give it a go" (i) symbol recommends The Parker Square *savage*

12:53 Matt be like "I'm always one to give it a go" Top right corner suggestion: *Parker Square*

@vanillaannihilation5871

4 жыл бұрын

Best punchline ever

@circlonianmapper

4 жыл бұрын

Richard Yan LOL

@krystofdayne

4 жыл бұрын

Yeah that was super passive aggressive xD

@oz_jones

3 жыл бұрын

@@krystofdayne Nah, it's just cheeky banter.

@mariafe7050

3 жыл бұрын

Coincidence?

I paused this at 3:40 and thought "I could code this!" So I did. Then I came to the video...and watched him decided to code it.

@DanielBrownsan

5 жыл бұрын

You get points for "doing the work". Kudos!

@kryo2k

5 жыл бұрын

Did exactly the same. Ended up without bugs.

@Faaaaaaaaaaaaz

5 жыл бұрын

5 points to Gryffindor

@anandsuralkar2947

5 жыл бұрын

Cool i m not in my room or i would have also coded it

@anandsuralkar2947

5 жыл бұрын

@@kryo2k lol

The reverse approach might be better - instead of looking for numbers that result in most steps, look for steps and reconstruct the number that should give these steps. For instance if the last step is 20 then we should go for number whose digits are divisors of 20, like 225 or 45, and so on

@capjus

5 ай бұрын

Clever

that is the world's best thumbnail

9:42 Matt with a Mohawk does not look right...

@RonJohn63

5 жыл бұрын

That's a buzz cut, not a Mohawk.

@WrenAkula

5 жыл бұрын

@@RonJohn63 Look at the shadow on the door.

@RonJohn63

5 жыл бұрын

@@WrenAkula I choose to not understand!

@forstnamelorstname4169

5 жыл бұрын

Matt is secretly an anime protagonist with a fancy transformation sequence.

@bcn1gh7h4wk

5 жыл бұрын

me: "Matt with a moh.... ?" _spots the joke_ ".... omg..." _facepalm_

> print(n), return "done" > pastes code in the terminal Inspiring.

@terner1234

5 жыл бұрын

you just can't comprehend his high IQ and thinking skills

@globalincident694

5 жыл бұрын

he was using python 2 as well

@Lovuschka

5 жыл бұрын

He forgot to add "Hello World"

@thexavier666

5 жыл бұрын

I know it's a joke. But let me educate others. Matt is a mathematician, not a coder. He is not expected to know the tiny nuances of coding. What matters is whether his logic is correct. So returning "DONE" is perfectly fine. Also, using Python2 is also fine. It's not like this code is some multi-client multi-threaded huge application which needs to maintained for a long time. It's just a simple script to crunch some numbers. No need to bring Python3 here as he is comfortable with Python2. But it's encouraged to shift to it. (I myself shifted to Python3 a month back)

@NightsChapterSeven

5 жыл бұрын

Sumitro Bhaumik how is returning done fine? It makes no sense

At 12:51 Matt: "I'm always one to give it a go" Numberphile suggested video: "The Parker Square"

I love these videos because they inspire me to code programs that do this myself. Eventhough I’m watching this 4 years later it was a great video

9:40 - u have nice hairstyle on your shadow)))

@DaBoss-sl3dr

4 жыл бұрын

Egor Strakhov 😂

@gluelover1239

4 жыл бұрын

He's trying to take over the tri-state area

@jazzabighits4473

4 жыл бұрын

Freaky Fred vibes

@eddiejohnston1853

4 жыл бұрын

The Weeknd

@maybecrazy6934

4 жыл бұрын

Goku hairstyle

0:14 "277,777,788,888,899" - written on the paper "277,777,778,888,899" - said by Matt Don't think we wouldn't find a Parker Square in this one too, mister Matt!

@feronanthus9756

5 жыл бұрын

I had high hopes... and then we got 15 seconds into the video.

@cleteblackwell1706

5 жыл бұрын

Someone explain?

@stumbling

5 жыл бұрын

The Parker persistence of "277,777,778,888,899" is still 11.

@cone16v

5 жыл бұрын

PARKER SQUAREEEAAAAAA

@nicholas2113

5 жыл бұрын

@@Sodiumitis no, he said some numbers reached the same length

Every Numberphile thumbnail is a work of art, but some, like this one, are even better art than the rest

This was pretty cool. I spent some time starting with digits and increasing them until the proverbial 2,5 pattern or a zero started showing up. Once you start getting a significant number of digits it really is difficult to not get a zero into any position simply due to the law of large numbers having some zeros somewhere.

I love that as Matt says "I'm always one to give it a go" a link to the parker square video comes up in the top corner

wise word: never code in front of class matt: hold my square

@nateiverson8681

3 жыл бұрын

Honestly it's no more risky than doing mathematics in front of a class. Everyone makes mistakes at the board.

@MakisHMMY

2 жыл бұрын

I always coded in front of my class. Hours and hours per day

Matt could've fixed the duplicated single digit final value by removing line 3. that's my only contribution to this video

@GeorgeDCowley

2 жыл бұрын

I noticed that, too.

When you became so advanced, easy things are the hard things

I liked the coding part! More of that yes yes!!

@randomdude9135

5 жыл бұрын

Can I learn these Cscience things all by myself?

@artaway6647

5 жыл бұрын

@@randomdude9135 yea, fortunately there are tons of programming lessons on the internet

@anthonyhoffmann

5 жыл бұрын

Just say no to python.

@LiborSupcik

5 жыл бұрын

@@anthonyhoffmann why so?

@erikbmx478

5 жыл бұрын

How about subscribing to computerphile?

If you add 90, or a 3.24e-11% you get 277777788888989, which has the same persistence, but is also prime.

@Monitorbread

10 ай бұрын

woah

@fcturner

9 ай бұрын

It’s higher than the original, and just has the same sequence of numbers. Bit underwhelming.

@bable6314

9 ай бұрын

It's literally the same sequence of numbers lol, just in a slightly different order.

@MIKIBURGOS

9 ай бұрын

If you add 900 to yours, it also works (or 990, 9990, 99990....)

@fffmpeg

7 ай бұрын

any permutation of these digits have the exact same persistence and it's pretty obvious. changing two digits around and calling it adding 90 is a little weird

One of the things I would do if I were coding the search algorithm: Include a table of entries that have already been processed, a cache, which links the number being calculated to its persistence value Any time you complete a digit-multiplication, check if the result has already been cached, because if it has, you already know how many more steps are left in the chain Or, better yet: Organize digits by their size, since as they say, at the end of the video, any permutation of digits will give you the same result -- This will reduce the size of the cache because you won't have a bunch of permutations clogging it up So, if "n" is the input number, your program would have a rough flow of per(n): is n a one-digit number? TRUE: return 0 FALSE: proceed to next segment R = multiply_digits(n) -> sort(R) -> is (sorted) R cached? TRUE: retrieve cached value, add 1, this is the persistence value of n; save n and its persistence to cache FALSE: recurse, using R as the new n -> add 1 to returned persistence value of R to get n's persistence value This would be especially useful if you were iterating over numbers, as it would save time computing the same chain of numbers over and over again On the note of iteration: As they say in the video, avoid any combinations of digits that are known to create a 0; the first and easiest way to do this is to check if the number has both a 5 and an even number in its digits, in which case you automatically know that its persistence value is 2. If the number ALREADY has a 0 in it, you know its persistence value is 1. This check might end up consuming more processing power, though, it's hard to say.

Great Matt! You make math(s) so engaging. I am fortunate as I find maths 'easy' however many of my classmates many moons ago didn't have a clue. They would have benefitted from your enthusiasm and simplicity at explaining mathematical complexities :)

I wrote a small C program to brute-force output the numbers. I think it's correct, if I understood the problem correctly. It should go through all natural numbers through 18446744073709551615 (the maximum size of an 8-byte unsigned long long in C). It's been running for a few hours now and I have 1-10. Terminal output: 10-> 0 Number 10 has score: 1 25-> 10-> 0 Number 25 has score: 2 39-> 27-> 14-> 4 Number 39 has score: 3 77-> 49-> 36-> 18-> 8 Number 77 has score: 4 679-> 378-> 168-> 48-> 32-> 6 Number 679 has score: 5 6788-> 2688-> 768-> 336-> 54-> 20-> 0 Number 6788 has score: 6 68889-> 27648-> 2688-> 768-> 336-> 54-> 20-> 0 Number 68889 has score: 7 2677889-> 338688-> 27648-> 2688-> 768-> 336-> 54-> 20-> 0 Number 2677889 has score: 8 26888999-> 4478976-> 338688-> 27648-> 2688-> 768-> 336-> 54-> 20-> 0 Number 26888999 has score: 9 3778888999-> 438939648-> 4478976-> 338688-> 27648-> 2688-> 768-> 336-> 54-> 20-> 0 Number 3778888999 has score: 10

@roguechlnchllla6564

5 жыл бұрын

You can make it much bigger, if the original number is a String, and you just multiply the digits.

@defectus1769

5 жыл бұрын

@@roguechlnchllla6564 Even better, notice how the result of the multiplication is always of the form 2^a × 3^b × 7^c, since you're just multiplying lots of digits together. The 4's, 8's and 9's can be broken down into multiple 2's or 3's, and the 5 never appears with any 2's without instantly giving a multiple of 10 and therefore a zero at the start. Now, the problem just boils down to finding three integers, a, b and c, such that 2^a × 3^b × 7^c is a number with a multiplication persistence of 11.

@wg_spiritomb

5 жыл бұрын

I have written a simple one in python . Upto 6-7 its fast, but after that the time it takes grows exponentially

@eilonlifshitz7302

4 жыл бұрын

i got them all to the last one as well

@X3MgamePlays

4 жыл бұрын

@@defectus1769 You beat me to it. I too was thinking about that. I also thought of reverse engineering the next number. Ex. 2, 12, 34, it ends at 34, since it needs 2*17. 17 is a 2 digit number and a prime. Ex. 2, 12, 43. Ex. 2, 12, 223 or 232 or 322. Some of which can go further. Ex. 2, 21, 37. Ex. 2, 21, 73. I tried 6, and got myself a little tree of options to start from. They all end with 6. But I don't know how to write a program that looks for reversed engineer all options. If someone makes that, you could use that 11 parts number as a start. All possible answers would roll out. And perhaps even more. Since you are right about 2, 3 and 7. You could easily weed wrong answers out for the next step.

I paused at 1:50 and gave it a try. Went with 999 so: 999->729->126->12->2 4 steps, not bad.

@Ascordigan

5 жыл бұрын

I tried 3927 and got five (378, 168, 48, 32, 6) steps.

@SgtSupaman

5 жыл бұрын

@MilesTisserand , if you mean any number has an equal chance of being chosen, I have a feeling the odds would lean heavily to 1 and 2 steps because of how often 0 comes up. It would be interesting to see the odds if you automatically exclude certain numbers that you know will drag down the average (like any that has 0 from the start).

@tabletoparcade4203

5 жыл бұрын

@@Ascordigan Then 679 (2x3) would have the same steps. Now you know after watching the rest of the video, that the aim is find the lowest number.

@plplpop1

5 жыл бұрын

@MilesTisserand Interesting idea. If I wasn't a busy undergrad, I would definitely try it out and graph the probability distribution. It'd be crazy to find a hidden poisson or something haha

@megamuumi7859

5 жыл бұрын

I got six steps with 888888888

Love this video! Finally ... some programming on Numberphile. :) It's one reason I enjoy John D Cook's blog posts on mathematics. Your video and his posts reinforce to me the usefulness of Python and numpy for math.

Love how when Matt says "I'm always one to give it a go" a card for the Parker Square video appears...

Tutorial on how to convert your computer into a bonfire.

@whatisthis2809

4 жыл бұрын

Step 1. Run complex problems that nobody has answered! Step 2. Wait Step 3. Wait ... Step 9. Wait Step A. Wait Step B. Wait ... Step FC. Wait Step FD. Wait Step FE. Wait Step FF. Wait Step 100. Boom! You got an answer and a fire!

@MajorMandyKitten

3 жыл бұрын

Are you running a 90s processor without a cooler? Lol

@Tsutomu6

3 жыл бұрын

Made my day.

@boboften9952

3 жыл бұрын

@@whatisthis2809 Brilliant .

Hey mate, after watching this video I have spent hours upon hours trying to figure out a formula. I haven't come up with an exact formula, however, I have noted that if you start *backwards* you can go around in circles for ages. Take the single digit number 6, for example. Now 6 has 4 factors, 1-6 and 2-3. With this, we can make 4 number, from the 4 factors... 16 23 32 61 We know two of these are primes so they are irrelevant, bye bye 23 and 61 now, with 16 and 32, one is the double of the other - ill come back to this. So, like before, 16 has 3/single digit factors, 2-8,4-4 from this, we can make 28, 44, 44:) and 82 We can continue this sequence until all our remaining factors and their combinations only have primes as factors, and then this final number we can put into the program, or calculate yourself and figure out the steps, coming back to the final figure/our figure, 6. I'll leave you with one last thing. 23 earlier, was a prime number and we could not continue it in the sequence, however; 2*3=6 but so does 1*2*3, and 1*1*2*1*3*1*1 This is the difficulty I am facing with my current formula, as there is nothing against placing 1s into a prime number solution or just any solution in general and then continue on from there-doing the same thing over and over again. It does just mean one thing - your final solution will be longer than the current record, however, we can break the record and set a new one. I'll let you break the record though, is too tired now :)

@ZournUnleashed

2 жыл бұрын

this dude wrote all of that only to get 3 likes

@user-rv9vk8by5i

2 жыл бұрын

​@@onehotseat You... missed the point. Ethan started on a random single-digit number, and created a sequence that would go to it (28 -> 16 -> 6) by factoring it. It's transparent how this method works - you find single-digit factors of a number, and string them together to create a new number (factors of 16 are 1,16, 2,8, 4,4, so 28 and 44 both go to 16 which goes to 6). Using the same method we continue - single-digit factors of 28 are 4,7. 47 is prime, and 74 has no single-digit factors. However, 4 is 2x2, so we also have 227, 272, 722. And none of them have single-digit factors, so we can't continue this sequence past length 3 (47 -> 28 -> 16 -> 6) Adding 1 to the _starting_ number is pointless, but we don't _have_ a starting number. However, a 1 in an intermediate step is not harmful, and only expands the number of possibilities for reversing a sequence. We can't continue the sequence from 23 because 23 is prime - nothing will multiply to it. However, by inserting 1s, we could end up with a number that contains only a 2, a 3, and a ton of 1s, with single-digit factors. From these, we can construct a number that multiplies the number we found with 2, 3, and 1s, and that number will multiply to 16. At the extreme, there's the number from the video. That one ends at 0, and there's infinitely many numbers that can lead to 0. Picking one at random, 20, gives us more factors to play with. 20 factors to 4,5, giving us 225, 252, 522, 45, and 54. Continuing in this fashion, we get to 438939648, which has factors 2^12, 3^7, 7^2, all single-digit. However, you may notice that there's no way to arrange and combine those factors that gives us another number with single-digit factors, _unless_ if you slot in a 1 and end up with the number 4996238671872. That number _does_ have single-digit factors - a 2, 6 7s, 6 8s, and 4 3s. I'm just not sure whether this number theory method is faster than brute forcing. There's already a plethora of ways to rearrange and combine factors of large numbers, and you have to find the ones with single-digit factors. You then have to account for the fact that every combination could have any number of 1s put into it, in any position, and factorise those too, all of which sounds computationally more expensive than just multiplying down the digits of most numbers from 1 to 10^320

@9891904317589

Жыл бұрын

Toying with this for a while, I think I found a way to get to higher numbers. If you check the steps on each number, they always repeat the lower steps. Like, 277777788888899, results first is 4996238671872, then later is 438939648. While the one beneath it, 3778888999, the next step is 438939648. This could mean that a way to find the 12th number, maybe the second step of it is the first step of the 11th one. Not a rule, since the smaller ones seem to break it, but bigger ones a very consistent.

@bhante1345

9 ай бұрын

Have you gone insane yet? Sitting around your town recording the numbers of car plates as they pass, guarding a shopping bag filled with Easter eggs?

4:42 Thats a weird way if saying if(n < 10)

Just to add, they can also remove any numbers with "1" in them for the smallest number search, since that number will always yield the same number of steps as the same number but with all the '1's removed, so any smallest number cannot have "1" in its digits

Soon in comments, new world record with number that has 15 steps and Matt playing it on piano

@ErixTheRed

5 жыл бұрын

Play it on today's google doodle

@zmaj12321

5 жыл бұрын

Soon on 4chan, someone asks a question about an anime and someone else mathematically analyzes it to find a 15 -step number.

@ehsan_kia

5 жыл бұрын

It does indeed seem like 11 is the limit. I calculated up to 1500 digits and there aren't any solutions. Similarly, I computed limits for bases 2-10, Base 2: 1 Base 3: 3 Base 4: 3 Base 5: 5 Base 6: 5 Base 7: 8 Base 8: 6 Base 9: 7 Base 10: 11 They all reach this "cliff" after which there's no answers as far as I computed, so it's probably fair to conjecture they all reach limits.

@theonetruepath

5 жыл бұрын

@@ehsan_kia Base 11: 13 23777777777777777778888888999999aaaaaaaaaaaaaaaaaaaa

@bencrossley647

5 жыл бұрын

@@ehsan_kia Any chance you could do this for bases up to 36? I have a conjecture I'd like to test and I cannot code. :(

Your shadow at 9:46 is epic - you look like Julius Caesar. :-)

@bijeshshrestha2450

4 жыл бұрын

Nah, no knives

@heatheretaithaha

5 ай бұрын

​@@bijeshshrestha2450 et tu, bijeshsrestha, et tu

When the calculator is tilted to Landscape you know it's serious math

Can't you just get a number that when you multiply all its digits makes the record holder? Wouldn't that just add 1 step? Or is the record holder impossible to multiply into?

@dhycee8215

2 жыл бұрын

fact, but what string of digits multiplied will get you that number.... figure that one out

@notnoah154

2 жыл бұрын

@@dhycee8215 thats the problem lul

While the Parker Square is always amusing, this video leads me to a nice new constant: Brady's Number = 2

@woodfur00

5 жыл бұрын

Vihart already did that

I think it would be important to consider other base counting systems. Ten is a weird number, so start with smaller (or maybe larger) bases to see what might be going on underneath all of it. Certainly, larger bases will have larger persistence measures because a randomly chosen number will have a smaller chance of having a zero in the product of its digits.

love the shadow of his head at 9:41 lol

Love this episode!

Matt, we love you but please it's time to upgrade to Python 3.

@recklessroges

5 жыл бұрын

He's got 9 *whole* months before python2 is EOL ;-) [Yes! *stop* using python2; maybe try golang?]

@VaibhavKarve

5 жыл бұрын

I came into the comments to say this!

@nowonmetube

5 жыл бұрын

Lol

@nowonmetube

5 жыл бұрын

What's the difference though?

@mursie100

5 жыл бұрын

Or maybe use a decent programming language.

I love how Matt is both hosted on Computerphile and Numberphile.

Actually seeing the live programming was pretty cool

I discovered this trick when I was bored a school and started to multiply persistently numbers in the calculator. I always found it a very intriguing trick, didn't know it was actually a mathematical curiosity

@keksitzee1094

5 жыл бұрын

Judging from the videos in this channel, anything and everything is a mathematical curiosity when the simplest problems can be scaled up, and up, and up, until it isn't trivial anymore. There are quite a few other videos like this where the game is pretty simple, but then when you continue to play it, it gets more difficult. Then they whip out the brown paper

@thedavecwright

4 жыл бұрын

So rightly, the Guarracino Number of 277777788888899 is 11... etc... 😊

You need a string of digits that multiply out to 277777788888899. ... Oh, bummer, all of its prime factors are greater than 7.

@PsychoMuffinSDM

5 жыл бұрын

It's not just a string of digits that multiple out to that number, but any combination of the digits in that number.

@owensilberg2966

5 жыл бұрын

and you can add as many 1s as you want anywhere in the number

@kevinr.9733

5 жыл бұрын

True. That would potentially make the search easier.

@owensilberg2966

5 жыл бұрын

@@kevinr.9733 I agree with that, but couldn't it also exponentially increase the number of numbers that would have to be checked?

@MIKIBURGOS

5 жыл бұрын

@@Stefan-ls3pb Oh i just realised :( you destroyed my life

It's been more than a year since this experiment. Has the record of 11 steps been beaten?

@sobeeaton5693

2 жыл бұрын

I found one, but the KZread comment section is too small to contain it.

@kurzackd

2 жыл бұрын

@@sobeeaton5693 isn't Numberphile gonna do a vid on it? :P

@KaptenKetchup

2 жыл бұрын

@@sobeeaton5693 Nice reference haha

@jamesmnguyen

2 жыл бұрын

@@sobeeaton5693 Get Outta here Fermat!

12:52 "I'm always one to give it a go" "Suggested: Parker Square" Numberphile you did it again

I really like these types of videos that combine coding and number stuff

@bhante1345

9 ай бұрын

Would you pay for this on onlyfans?

Loving Matt's shadow at 9:42 :)

@nowonmetube

5 жыл бұрын

Interesting...

@barraman.

5 жыл бұрын

Very lol

I just learned more about coding in this simple video than i ever had before

I liked this because it sort of demonstrates problem solving and developing strategies.

“You never wanna have two threes, cause that could be a nine”

I lost it when the Parker Square video popped up in the suggestion card when he said "I'm always one to give it a go."

9:44 Loved the mohawk in that shadow.

I like this guy. Watched several videos by him.

Dr. Brady, we need more live coding in Numberphile videos.

Every time I watch these kind of videos, I find myself convincing myself that I would be so good at math if it would be taught to me this way back in school. But then I think, I am a potato when it comes to math. Fun to watch it anyway

@Loki-

2 жыл бұрын

Nothing wrong with giving it a go

I really like the doing programming on the video, helps me know what to expect when I’m programming.

"this is so much quicker!" said the inventor of calculator

This is a common problem on MBPs caused by the trackpad ribbon cable being too long, being bent to fit, and failing after time at the kinks. Replace the trackpad ribbon cable (£7 or so) and your trackpad and keyboard should work again. Did mine a few months ago. Good luck.

@standupmaths

5 жыл бұрын

Julian Pinn Thanks! I plan to take a screwdriver to it soon.

@gartinmarrix8484

5 жыл бұрын

Did it myself recently and I was surprised at how easy it really was.

@Zolbat

5 жыл бұрын

Just go to the genius bar and get them to fix it practically for free (probably less than 2000 pounds at least)

@gartinmarrix8484

5 жыл бұрын

@@Zolbat It's 7 pounds for a cable, over 100 for the genius bar.

@Zolbat

5 жыл бұрын

@@gartinmarrix8484 so practically for free, which is amazing since the problem isn't even apples fault. Obviously all the users don't know how to treat their hardware... Opening and closing a laptop multiple times is nothing short of careless.

4:00 the trackpad having problems along with the keyboard is a known mac issue from what i can tell watching louis rossmann

@jtlundberg2381

5 жыл бұрын

Yeah it is. It happened to my computer. The trackpad cable just needs to be replaced. You can get one off amazon for $10. Super easy fix

@jeffreymontgomery7516

5 жыл бұрын

or he hit the shortcut to turn them off and hasn't realized it yet

@ceruleanfish6703

5 жыл бұрын

Or RE trackpad on a Mac laptop... If it's an older machine, take the battery out and make sure it isn't swelling. My LithIon MacPro battery up and swelled so bad it crushed the trackball circuitry.

@weirdal3333

5 жыл бұрын

I just came here from his video 😂

Every time enjoyable. But in this case a technical question: How do you manage to paste code that contains empty lines into the console. That always fails on my machine as python tries to execute what it received so far after an empty line.

You can reduce the sample spaces even further. You can eliminate all numbers with a 1 in it (since it has no effect on the result), and can eliminate all numbers that start 34.... (you can start 26...) or 36..... (similar to 2....9). edit: Also just realised it could never have more than 1 six in it, as two sixes allows 4....9 for a smaller number. And it cannot start 44 since it allows 2....8...

@Luxalpa

5 жыл бұрын

You can also calculate the thing backwards (i.e. start from the smallest number, then work your way upwards), which would probably make the thing much faster.

@manudude02

5 жыл бұрын

@@Luxalpa I thought some more about it, and I think that any numbers beating it will have to start with 2,3,4,6,7,8,9 or 26 before we hit the wall of 789s (and obviously kept in digital order). If we cheat and count 26 as one digit for the purpose of recording length (obviously we multiply by 12 still), then we only need to check 210680 numbers to check all numbers of length 230, and even that is double counting some numbers.

@Luxalpa

5 жыл бұрын

@@manudude02 I would like to know how you got to that idea. I myself found a way to get up to length 1600 with fairly realistic effort (without requiring a super computer that is). Basically, the realization is that all chain numbers (i.e. all numbers except for the starter) must be N = 2^x * 3^y * 7^z. So you just need to go through all the x, y and z, find a number that doesn't contain 0 or 5, and then see if the multiplied digits result in any other of those numbers. With x, y, z < 1000 you only need to check 1 billion numbers. Storing them all on a hard disk would take some 1.6 TB of storage, however I think if you exclude all the numbers with 0 and 5 in it, the storage requirement will probably be much lower (I'll have to double check my math on that one or just learn Python and give it a try).

@senshi01

5 жыл бұрын

I tried to make it all the way around, the program ask the number of steps and then calculate all the numbers... didn't succeed...

@manudude02

5 жыл бұрын

@@Luxalpa Obviously we are not going to have zeros or one and removing 5s (not checked, but I doubt you can avoid even numbers for long), but look at every 2-digit other case. I ignore any starts with a 7,8 or 9 in it since we are already in the "wall" in that case 22 -> replace with 4 for 1 less digit 23-> replace with 6 for 1 less digit 24-> replace with an 8 for 1 less digit 26-> unable to find a fault in it 33-> replace with a 9 for 1 less digit 34-> using 26 gives a smaller number with the same product 36-> using 2 and a 9 gives a smaller number with the same product 44-> using 2 and a 8 gives a smaller number with the same product 66-> using 4 and a 9 gives a smaller number with the same product I started up a program (in java) about 10 minutes ago to check, so far it is has checked every candidate under 120 digits, but at least it scales by an order of N^2, while checking 2^x * 3^y * 7^z is scaling by an order of N^3. edit: Actually, I think your way may be more efficient if you don't have memory concerns, going from k=1000 to k=1001 gives you another 3 million-ish numbers to check, while going from 1600 to 1601 digits is another 9 million-ish numbers to check. You do have the downside in that you'd need to actually convert the x/y/z values into an actual number, but that's a small price to pay

On my second attempt, I got 12 steps using 3,277,799,229,998,778

@magnummuskox958

4 жыл бұрын

That's 2 steps. 1,524,382,530,048 0

Alright. I like what you're thinking, AND... 2 steps.

You can do it in fewer lines using a map: def per(n): if n return 0 print(n) n_new = 1 for x in map(int, str(n)): n_new *= x print(n_new) return 1 + per(n_new) Using returns in recursion lets you return the depth. Also don't need to use str and len to check if it's a single digit, you only need to check if it is lower then 10. It's a pity that you need an import to get the folding function in Python, otherwise you could do it in a single line using lambda (and without printing) Haskell allows for an even cleaner version: productDigits 0 = 1 productDigits x = (mod x 10) * (productDigits (div x 10)) per x = if x Then you can map it over all the integers: pers = map (\x -> (x, per x)) [1..]

I'm a simple man. I see a thumbnail of Matt Parker possesed by the ghost of Hannibal Lecter and I click on it.

@CinnamonSandman

5 жыл бұрын

Cristian Baldi dudes aging fast

Math and Coding in one video. This is a good start to my day.

Well I had to have a go. The best I came up with was 66, 36, 18, 8 (3 steps), 77, 49, 36, 18, 8 (4 steps - 11:17 in the video) and 6677, 1764, 168, 48, 32, 6 (5 steps). Thanks Matt.

Set a programme to run backwards- start with any single digit then split it into its factors string it into a number split that into its factors (stop if double digit) string it up, and repeat. So 8, 2x4 24, 3x8 38, 19x2 (stop) 5, 1,5 15, 3x5 35, 7x5 75, 3x5x5 355, and so on

@PsychoMuffinSDM

3 жыл бұрын

Not that easy, you have to consider other permutations too: So 8, 2x4 AND 2x2x2, AND 4x2 So 24 AND 222 AND 42, etc Don't forget 1s may apply too, so 124, 214, 412, 2221, 2122, 421,142, etc etc etc...

I love how he always has to put in the Parker Square. Matt will never live it down...

I paused the video to try the challenge and went for 799->567->210->0 I beat you Brady, but only just... EDIT: after watching the rest of the video I'm quite pleased with my 3 steps 😁.

@Anders1314

5 жыл бұрын

Tha's atually 4. He counts the zero when he counts the 11 steps

@MEver316

5 жыл бұрын

@@Anders1314 I counted the 0 as well. I didn't count the 799 I started with though.

@Anders1314

5 жыл бұрын

@@MEver316 You're right. My mistake

@yesmannoman454

5 жыл бұрын

Mine was 7879

@anandsuralkar2947

5 жыл бұрын

Nice

i keep coming back to this video because the thumbnail is so damn spectacular.

to print the last number only 1x with your code, just remove the print command from the single digit check at the top. Also my pyton wants the print command slightly different: print("some value") It wants "()" around the content to print. in the version, that also tells the used steps, the print-line, that tells this, can replace your printline in the single digit check. I saved me the code as a textfile, so i can play around with it in my python software, whenever i want.

He didn't use stackoverflow? Matt is a genius!

@Attlanttizz

5 жыл бұрын

You misspelled Stack Overflow.

@wWvwvV

5 жыл бұрын

@@Attlanttizz you can't put whitespaces in URLs. Even the logo is stack*overflow* as one word:.

@Attlanttizz

5 жыл бұрын

@@wWvwvVUse your favorite search engine, search for Stack Overflow, you'll see.

@MrUwU-dj7js

5 жыл бұрын

@@Attlanttizz If this was a matter of you being able to find your page on Google, the original comment was already fine.

@Attlanttizz

5 жыл бұрын

@@MrUwU-dj7js Well obviously: no. Stack Overflow is the name of the site and it's written with two separate words, not in one word. Even the term stack overflow as is used in programming is written with two separate words. Just wanted to point that out, nothing more :)

Never a Matt Parker video without a Parker blooper within 20 seconds of the video starting.

@numberphile

5 жыл бұрын

It's all marketing for Matt's new book about math mistakes... Available now: bit.ly/Humble_Pi

@standupmaths

5 жыл бұрын

Numberphile Can confirm. All mistakes (for the rest of my career) are now officially deliberate.

@aozorakei5288

5 жыл бұрын

@@standupmaths You could say it's a Parker Mistake

I like how he says, "..today we're **doing** the number...”

The prime factorization of each number (>20) in the list at 8:03 can be written as 2^a * 3^b * 7^c (a,b,c >= 0) So the same will probably apply to the number with multiplication persistence of 12. But no idea how to get a computer to work out numbers with 200 digits...

@AA-100

7 ай бұрын

If I knew how to write code so that it does this: Take the number 277,777,788,888,899, replace some of the 8s with 2 4 or 2 2 2, and some of the 9s with 3 3, then add an arbitrary number of 1s at the end, then rearrange ALL the digits in that number, to get another new number, which is an even number The digits in this number will still multiply to the same value and still have a MP of 11. Now check if that number can be expressed as 2^a × 3^b × 7^c. If not, repeat the process Surely by pure luck, the computer will find such a number that is in the form 2^a × 3^b × 7^c Which will be the digits of a number with an MP of 12.

What about using a different base? Let's say base 2; because those numbers only contain one and zero, the product will always be either one or zero. The max number of steps for base 2 is just 1. What is it for base three? 222 (26 in base 10) -> 22 (8 in base 10) -> 11 ( 4 in base 10) -> 1 Three steps is the longest I have been able to find so far. Is there a formula to find Max_Steps(base) = ?

@JimBob4233

5 жыл бұрын

Shouldn't 22tri be 8dec, since it's 6+2 and 2*2*2? Likewise, 11tri is 4dec.

@gregg4

5 жыл бұрын

@@JimBob4233 Yes, I did edit my comment to correct that.

I don't know why, but I love plucky little 77. 77->49->36->18->8 The longest run for a two-digit number.

@MusicalMatthew

5 жыл бұрын

Fun fact, in my 12th grade math class many years ago, the teacher had on the whiteboard (from a previous class) a complete the number sequence puzzle and it was 77, 49, 36, 18, ___ and I managed to get it in seconds. I've told so many people that one and very few have solved it without me telling them. So when I read out loud '77 - 49 - 36 - 18' I was like HEYYYYY I RECOGNIZE THAT PATTERN!

@gabrieleporru4443

5 жыл бұрын

It seems like it never wants to end

@gabrieleporru4443

5 жыл бұрын

@@MusicalMatthew well, okay, but it doesn't seem it was so difficult😂

@brightonpauli3916

4 жыл бұрын

@@gabrieleporru4443 It never seems difficult when you know the answer lol

@MrRenanwill

4 жыл бұрын

Factor this number in prime decomposition and then get the possible numbers that make 77 be true in their multiplication (arranging them in any order).

Here's the code if you wanna do it yourself (in progress) : def per (n): if len(str(n))==1: print n return "done" digits = [int(i) for i in str(n)] result = 1 for j in digits: result *= j print result per(result)

if len(str(n)) == 1 is for nerds -> if n < 10 is for engineering

@besserwisser4055

5 жыл бұрын

pretty simple

@blueskyredkite

5 жыл бұрын

That's definitely less stress on your processor. There are times I wish I knew languages other than Perl.

@erynn9770

5 жыл бұрын

len(str(n)) is what's directly defined ("if there's only one digit left"). n

@HyperSpify

5 жыл бұрын

If you compile the code, str(n) is faster because you're going to call str(n) later on line 6 so the compiler will optimize it to compute it once and keep the result. Of course you can get rid of str(n) completely by using "% 10" (i.e. modulus 10) and "/10" in a loop instead to calculate "result", which I'm guessing is even faster.

@charlieangkor8649

5 жыл бұрын

Mattia Conti hes a mathematician. cannot do common sense. only complicated abstract concepts.

I loved the coding part! Do that more often please!

You can decrease the search radius even more: - You never want a 0 or a 1 - You only want 1 number below 4 maximum - You don't want 2 and 4 together on the other hand: - 5s are actually ok, but only if you only have uneven digits (like 355)

Conversation be like "Let's add the counter to the program." "We could remove the second '0' at the end." "Naa, let's just keep it."

@Coldheart322

3 жыл бұрын

It kinda annoyed me that ALL they had to do was remove the very first print(n) statement to remove the duplication. I'm guessing if it wasn't being recorded live, Matt may have noted this. But yeah, why have the first print(n) when the previous call had already printed result.

Well, I gave it a go, but all I managed to do was confirm there indeed are no better examples with less than 100 digits. This took about 20 minutes to check with a bit of a clever search. I found a way to check up to n digits in O(n^6) time. I am planning to improve this to O(n^4) and maybe try some more heuristic search methods to get even faster. Then we'll see what I can find over night. For the curious reader, the O(n^6) comes from the fact that there are O(n^4) numbers of n digits for which the largest prime divisor is less than 10, because there are 4 such primes. The other O(n^2) comes from calculating the product of the digits of an n digit number. Since the numbers become way too large to fit into 64 bits, arithmetic operations can no longer be done in constant time. The O(n^4) is easily improvable to O(n^3) by disregarding multiples of 10, but this requires some technical details I haven't had the time for yet. The O(n^2) might be improvable to O(n) by some pre-computation tricks.

@adimadis

5 жыл бұрын

I tested up to 2.6E44 numbers or 45 digits using my best search. But just testing the number after that slowed my algorithm down. How did you get up to 100 digits ? Cheers

Python 2? In 2019? Well, I suppose you still have 288 days left to enjoy your habits.

@PaulaJBean

5 жыл бұрын

Python 2 will not suddenly stop working in 2020. There are gazillion companies still using Python 2.x codebases, and they won't migrate everything to Python 3. Heck, forty-year old COBOL code is still used, millions and millions of lines of code.

@Art-fn7ns

5 жыл бұрын

@@PaulaJBean You're right. Also, Pluto is a planet.

@leandrometfan

5 жыл бұрын

@@Art-fn7ns well, it is, a dwarf one.

@iqbalnash5748

5 жыл бұрын

@@Art-fn7ns Now this is important!

@Stiwoz

5 жыл бұрын

@@leandrometfan smaller than our moon? it's an ateroid, not a dwarf planet. its diameter is smaller than the width of australia cmon