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More about Pebbling a Chessboard - Numberphile 

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You really need to have seen the main video for this to make sense!
More links & stuff in full description below ↓↓↓
MAIN VIDEO: • Pebbling a Chessboard ...
CONTINUATION: • More about Pebbling a ...
AND EVEN MORE: • Pebbling a Chessboard ...
PLUS CUT FROM PART ONE: • Pebbling a Chessboard ...
Featuring Zvezdelina Stankova - Professor of Mathematics at Mills College,
Director of Berkeley Math Circle, UC Berkeley
Spreading clones across a chessboard and escaping "prison" - commonly known as pebbling a chessboard.
Check these papers:
bit.ly/pebblech...
bit.ly/pebblech...
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19 дек 2013

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Комментарии : 252   
@yellowmeerkat97
@yellowmeerkat97 10 лет назад
I love Ms. Stankova. She explains everything with perfect clarity, the perfect pace, and admirable enthusiasm. Please do more videos with her.
@SuperAngryPacman
@SuperAngryPacman 10 лет назад
This is an extraordinary series, Brady. Zvezdelina explains everything with such enthusiasm and clarity.
@demoham42
@demoham42 7 лет назад
What do you expect Zvezdelina Stankova is a legend!!!!!
@anadice9489
@anadice9489 8 лет назад
"You're just being paid to have fun" I love the truth in that
@Qladstone
@Qladstone 7 лет назад
and allow your results to be used by any other branch of science or engineering for eternity.
@Mightylcanis
@Mightylcanis 5 лет назад
If you love/enjoy your job, that's always the truth.
@KurtSchwind
@KurtSchwind 10 лет назад
"Back to square zero" Thumbs up for zero based numbering.
@numberphile
@numberphile 10 лет назад
I liked that!
@qwertyuoip1234
@qwertyuoip1234 4 года назад
Woot
@jesusfkingchrist6591
@jesusfkingchrist6591 10 лет назад
When you said to try it in the first video, I immediately wrote a very simple program to test it. Just a square that checks to see if their is a square above and right of it, if not it creates them and deletes itself. Then i put the starting 3 in the prison and set it to randomly run the check constantly to imitate someone making random moves I made the squares single pixels and watched them try to fill in my entire screen while just creating tons of rectangles of pixels and making no progress in freeing the prison Obviously this doesn't prove anything, it was just fun
@haydentallon9730
@haydentallon9730 4 года назад
I wish I could see a video of this !
@Drachenbauer
@Drachenbauer Год назад
i also wrote a simple program to play around with it. i can do moves my self by clicking on the clones in my one.
@freshrockpapa-e7799
@freshrockpapa-e7799 Год назад
​@@Drachenbauernobody asked
@kwanarchive
@kwanarchive 10 лет назад
I can imagine her in a James Bond movie. "Ah, Mr Bond. I have placed you in a prison, with no means of escape" "Do you expect me to talk?" "No, I expect you to clone yourself"
@NoriMori1992
@NoriMori1992 8 лет назад
"Infinitely many times!"
@IMortage
@IMortage 10 лет назад
She is a very good guest, keep bringing her back!
@beejblud
@beejblud 10 лет назад
just admit it you dont know why but you find her attractive
@BenjaminAlexander
@BenjaminAlexander 10 лет назад
beejblud Please take this feedback in the spirit intended: I genuinely only want you to be viewed as the person you really are, and I think your comment doesn't reflect that. Perhaps you should stop for a moment and contemplate the larger environment where you are commenting. Lots and lots of people talk about how our culture values women for their looks over (or, just as bad, in addition to) any and all of their other attributes. You don't have to agree with this perspective to acknowledge that many other people have it. So when you make a comment like this, so short and context free, I think you'll find that many people will assume you are referring to her physical (or visual) attractiveness rather than any relevant attribute to a number focused RU-vid channel. It's your choice to care about that interpretation. But that choice will say a lot about who you are as a person. I don't know you, and I can't judge you. But this comment, in this context, is part of a larger problem of not recognizing the value women bring to the human world. Perhaps you didn't intend the comment to be taken as insulting and demeaning. (You just wanted to have a little bit of rudeness? You thought it was actually complimentary? Intention is so hard to determine online, which is why I don't judge it.) But your voice is part of a cacophony on RU-vid in general, which detracts from the conversation, in my opinion. You thought it was appropriate to randomly comment on Prof. Stankova's attractiveness. I think it is appropriate to give some feedback on that, for future reference. Best Wishes!
@beejblud
@beejblud 10 лет назад
i see your point but its just a savy observation
@IMortage
@IMortage 10 лет назад
Antonio Craveiro Unless you are really slow writer... no. That should have taken at most 5 minutes of his time, 2-3 if he is a decent touch-typer.
@IMortage
@IMortage 10 лет назад
Antonio Craveiro Not sure why you think this needs that much mental preparation. If you can type it in 3 minutes, you can think & type it in three minutes. It's not Ulysses, but a fairly straightforward argument.
@RakeshPGopal
@RakeshPGopal 9 лет назад
Thank you Prof. Zvezdelina. This video really sparked a strong interest for Mathematics in me. It was truly fun. More fun because you elegantly didn't assume anything about the viewer's knowledge and explained an elegant proof of how problems are solved.
@BackPocketChange
@BackPocketChange 10 лет назад
She'd be a good teacher because she made me feel guilty for not pausing the video and playing the game.
@BenjaminAlexander
@BenjaminAlexander 10 лет назад
"You're just getting paid to have fun!" = the best kind of job you can have. Brady, you should try finding a job that lets you have fun sometimes ;-)
@AdeptusSteve
@AdeptusSteve 10 лет назад
I work in the vfx industry and my job is fun too... People can get really jealous if they see you dont consider your job annoying or exhausting... but its their fault.. they were just lazy and didnt work for their dream job... or they never had one... But brady.. you are a youtuber.. honestly, no one becomes a youtuber if hes not having fun at it :)
@Tfin
@Tfin 10 лет назад
They do need to eventually produce something of value if they intend to continue having someone pay them to "just have fun." Writing it all down and saying how it's useful in the real world is a bit less fun than playing number games all day.
@kayvee256
@kayvee256 10 лет назад
Stefan Ehrenhaus I'm a Software Developer, and love it. Which is fortunate. This job would be SO BORING if I didn't love it to pieces.
@MrChet407
@MrChet407 5 лет назад
Fucken weirdos
@QuannanHade
@QuannanHade 10 лет назад
"Why do you do this?" "Because it's fun" C'mon, that was a silly question...
@porkypine1888
@porkypine1888 10 лет назад
He asks those types of questions to get reactions. As you can see it was a good one.
@GretgorPooper
@GretgorPooper 8 лет назад
I love these combinatorics videos, I wish there were more of those. Professor Zvezda is awesome.
@NeedsEvidence
@NeedsEvidence 10 лет назад
Zvezdelina Stankova belongs to seven UC Berkeley instructors who are listed among the country's 300 best professors in a book published by the Princeton Review (www.dailycal.org/2012/04/03/seven-uc-berkeley-professors-selected-as-princeton-reviews-300-best-professors). IMO she does also a great job in the Numberphile videos.
@electroguy02
@electroguy02 9 лет назад
So using the logic that you only end up with one clone on the bottom row if you start with one clone, if you go back to the original game with the three clones in prison, it's still impossible even if you had an infinite amount of moves since you would only ever have two clones on the bottom row. Is that right?
@davidwilsch4668
@davidwilsch4668 9 лет назад
electroguy02 I had the same idea.
@jeremypnet
@jeremypnet 4 года назад
Absolutely right. You need to fill the whole of Greenland, but you can only ever have two clones on the bottom edge (and the left edge) so you can’t do it even with an infinite number of moves.
@MrDpsc
@MrDpsc 10 лет назад
this is quite possibly the most educational video I ever watched on youtube. It really showed an extremely elegant way to go about solving some problems.
@jellevm
@jellevm 10 лет назад
Is it weird that I really love her accent? xD
@OjesYobe
@OjesYobe 10 лет назад
i respect her, but I kinda can't stand it
@VioletTheGeek
@VioletTheGeek 10 лет назад
I was thinking the same thing. I love her accent. :)
@hglundahl
@hglundahl 10 лет назад
if you like russia, it is not ... unless it is perhaps lithuania ...
@NoriMori1992
@NoriMori1992 8 лет назад
Nope. I love it too. :D
@JamoWaffleSponge
@JamoWaffleSponge 8 лет назад
It's Bulgarian
@NoriMori1992
@NoriMori1992 8 лет назад
Haha, "You're just being paid to have fun!" Truer words were never spoken; everyone on Numberphile looks like they love what they do and have maybe just a bit too much fun with it. ;)
@Wildpfad
@Wildpfad 10 лет назад
Thank you for these interesting videos.
@tzkelley
@tzkelley 10 лет назад
More videos with her, please!
@Zhatt
@Zhatt 10 лет назад
Why do you make the extra content on unlisted videos instead of simply not publishing it to the subscriber feed? I'd imagine you would get more views over all if people could stumble across the extras too.
@AlexTheUruguayan
@AlexTheUruguayan 10 лет назад
Probably because he doesn't want people to unsubscribe because he's spamming them with stuff they don't want to see. If you like the subject, you can follow the links to see more of it (like I did), if you don't you don't have to do a thing.
@greyed
@greyed 10 лет назад
Because it is published, at a later date. Like, today. :P
@Tfin
@Tfin 10 лет назад
It's a math problem similar to the one discussed, but with humans making choices. Of those who got #1, how many watch others, and how many others? Of those who got #2 (me), how many go back to #1, and so on. #1 should get the most views, a portion of those who got it plus smaller portions of the other groups, and each one farther along should get fewer views, with those who got #4 needing to go to all the others first, while other groups follow the chain as long as they like.
@Zhatt
@Zhatt 10 лет назад
Greyed Makes sense. Thanks.
@villanelo1987
@villanelo1987 10 лет назад
The end of the video (the idea of "fun" for this woman) kind of reminds me about Dwarf Fortress.
@BlazingMagpie
@BlazingMagpie 10 лет назад
For dwarves, it's not mathematics if the result isn't burning elves.
@rukiddin0669
@rukiddin0669 8 лет назад
+villanelo1987 But Kicking, for goodness! (sorry had to)
@error.418
@error.418 8 лет назад
+villanelo1987 cats in Dwarf Fortress are just like these clones
@10mimu
@10mimu 10 лет назад
I'm in doubt between getting a PhD in physics or mathematics. Everytime I watch a minutePhysics video: Physics it is. Everytime I watch a Numberphile video: Maths it is. Therefore we have a paradox similiar to grandi series: infiniteSigma n=0 term is (-1)^n-->1-1+1-1+1. Using calculus proof: 1/2. Therefore, I must get a masters degree in both physics and Maths. But another paradox: I just watched a numberphile, so I will get a PhD in Mathematics. Because Grandi Series isn't 2.
@ErikOosterwal
@ErikOosterwal 6 лет назад
Human Effigy - Just like engineering is simply applied physics, physics is applied math. Since the three disciplines are so intimate, do the one that's most fun for you.
@joeytje50
@joeytje50 10 лет назад
Woah, at 4:00 she starts doing EXACTLY what I did to conclude that the thing in the first video is impossible.
@W4LL37SK83R
@W4LL37SK83R 10 лет назад
I just realized this when she first noted that it is impossible to fill the outer rows: it is also impossible to fill any of the other rows. So even if this game were infinite and you could make an infinite number of moves in a finite time, you still would not be able to win.
@DtWolfwood
@DtWolfwood 10 лет назад
brady, thanks for only showing 1 video on the feed instead of spaming it with multiple videos at once. I have unsubscribed to so many channels because they do just that. Your consideration is very much appreciated :D
@CoyMcBob
@CoyMcBob 10 лет назад
As soon as you limit the amount of clones in the first row and column to 1, you have to limit the amount of clones in the second row and column to 2, because the only way to have more than two clones in a column is from getting a clone from the column before it. Try it out for yourself to get more than two clones in the second column and row while keeping the clones in the first column and row in the fourth position. This will eventually lead you to figure out that the first column and row each have one clone, the second column and row each have two clones, the third column and row each have three clones, and so on, Limiting the amount of greenland significantly. Thumbs up so numberphile sees this ^_^
@MichaelPaoli
@MichaelPaoli 10 лет назад
Lovely closer :-) More about Pebbling a Chessboard - Numberphile Brady: Why are they doing this? Zvezdelina: 'Cause it's fun! Once you solve a particular problem, the original one, which in itself was so much fun, you don't stop there, you don't want to stop the fun. Mathematicians have fun the whole time, especially when they're doing research, that's why they're into this profession. They love it. But you're get... you get paid, like people are paying you money, you're just being paid to have fun!
@wvhdogg
@wvhdogg 10 лет назад
2:05 "Back to square zero" mathematician's humor
@intuneknitter4220
@intuneknitter4220 6 лет назад
This problem blows my mind! Because every time you think "oh I bet this prison is possible, you realize that creating different prisons changes "Greenland" which then makes escaping impossible! This is an excellent way to introduce an invariant!
@samramdebest
@samramdebest 10 лет назад
free the clones, clones are people too
@CobyHerford
@CobyHerford 6 лет назад
Love your videos Zvezdelina Stankova! I especially liked the videos about your favorite geometry problems from 5th and 10th grade.
@hvdklauw
@hvdklauw 10 лет назад
"We're back to square zero", zero based indexes \0/
@sgdstb494
@sgdstb494 10 лет назад
Boy, you really weren't kidding when you said the editing was epic. Good job, Brady!
@FLPhotoCatcher
@FLPhotoCatcher 10 лет назад
Yeah, keep those clowns in prison where they belong!
@MrMadMurder
@MrMadMurder 10 лет назад
These two videos were really cool, very easy to understand while also enjoyable and interesting.
@goodwillhart
@goodwillhart 10 лет назад
Beautifully clear explanations. Some of the best exposition I've seen. Bravo!
@JazzyWhisky01
@JazzyWhisky01 10 лет назад
Can you make a video about p vs np
@mrhoeivo
@mrhoeivo 10 лет назад
I could listen to her talk forever. Fascinating stuff. Please have her on the show more often!
@bas_de_beer
@bas_de_beer 10 лет назад
I love how she talks and explain things, please do more videos with her!
@xBleach4Eva
@xBleach4Eva 10 лет назад
I really like this woman! :) Classy+ funny :)
@ThichMauXanh
@ThichMauXanh 2 года назад
"You're just being paid to have fun" *smiles* *video abruptly ended*
@NoriMori1992
@NoriMori1992 8 лет назад
I just realized that the research paper has Ron Graham and Fan Chung as authors! :O!
@kevinhart4real
@kevinhart4real 10 лет назад
At 4:40 she didn't explain why the clone had to be in the 1/8 box, the "first cell in the prison with the largest weight". I thought her explanation might have a flaw, if the pebble was moved to a smaller fraction like 1/64. However, I realised that my thinking had a flaw as well, because if a clone was on the 1/8 square of the first row and cloned, the total added fraction would sill add up to 1/8. (example: 1/16 + 1/32 + 1/32 = 1/8) I think that this explanation should have been added to the first problem of the first video so that the final sum of greenland will be 1/2 instead of 2, for the previous problem, to prove to those people who don't understand that the geometric series 1+ 1/2 + 1/4 + 1/8... doesn't really add up to 2 when there is finitely many terms. Good job, numberphile, I really liked this video, it was really enjoyable. Continue to inspire! :D
@Mercury13kiev
@Mercury13kiev 7 месяцев назад
Zvezdelina, in Kvant magazine (USSR, Jul 1982) the problem was solved completely, and there’s a computer-capable algorithm that says whether we can free the prison. 1. Allow two or more clowns in the same cell. 2. Make matrix (m+2)×(n+2). 3. Each clown should clone someday. So do moves regardless of order that will free the prison and/or sort out doubled cells. 4. If we did everything right → TRUE, and the only remaining feat is to reorder moves to prevent doubled cells. If we went outside the matrix and still did not sort out doubled cells → FALSE.
@legendgames128
@legendgames128 2 года назад
In the hyperbolic plane, with 5 squares around each vertex, you can free the clones.
@john_hunter_
@john_hunter_ 10 лет назад
I really enjoyed these videos. I also like her evil genius accent. It made me feel like we were planning to take over the world.
@meteordude44
@meteordude44 10 лет назад
"Release the clowns >:DD"
@LightningLizard1
@LightningLizard1 10 лет назад
Congratulations, Mrs. Stankova for making it into an episode of numberphile. It's an honor to see that a fellow bulgarian is being in such high position in life. Поздравления! С уважение, 15-годишен почитател от София.
@bccxcc
@bccxcc 10 лет назад
This was really interesting! Please make more videos with Professor Stankova if you can.
@h2_
@h2_ 10 лет назад
How would this game work on gameboards made of different cell shapes? Triangles or pentagons or hexagons rather than squares?
@DataCab1e
@DataCab1e 10 лет назад
Pentagons don't tessellate. ;p
@tothm129
@tothm129 10 лет назад
DataCab1e well actually a hyperbolic plane would allow 3 pentagons around each point.
@edderiofer
@edderiofer 10 лет назад
Mike Toth No, a hyperbolic plane would allow 4 pentagons around each point. 3 pentagons around each point would be a spherical geometry, which is finite.
@tothm129
@tothm129 10 лет назад
similar to a dodecahedron? Thank you for your corecton
@edderiofer
@edderiofer 10 лет назад
Yes. "Spherical geometry" here refers to anything that is non-Euclidean and non-hyperbolic; one with positive curvature.
@CursedAbsol
@CursedAbsol 10 лет назад
"Why're you doing this?" "Because it's fun." This is why I love mathematicians XD
@cfsscfsshk
@cfsscfsshk 8 лет назад
The first column only allow one clone. I have already came up this idea after watching part 1.Thinking that no need to use finite move to prove it impossible.
@venkateshbabu5623
@venkateshbabu5623 6 лет назад
They always talk about dimensions. Say if you have a line you have infinite points which represent length. The base is something that tells you how many points you can have within a length. Say base 10 means you can have 10 points within the length of one. Say this is going up to infinite length you have a line system. Now we take an other line and place it at right angles to represent something in 2d we are limited to right angles system of coordinates. The points within the frame represent a multiplication table. As you increase the right angles you are getting a cubic and power four etc. When you get to the end you are multiplying infinity into infinity. To represent you get only quarter of what you started with.
@venkateshbabu5623
@venkateshbabu5623 6 лет назад
You are trying to represent something which should be double within quarter.
@venkateshbabu5623
@venkateshbabu5623 6 лет назад
The missing is eight fold.
@noidexe
@noidexe 10 лет назад
She said "back to square ZERO". That doesn't sound natural.
@jimmysuperchannel1527
@jimmysuperchannel1527 5 лет назад
@Marcus Jones can't you differentiate between reality and a joke?
@15kalas15
@15kalas15 10 лет назад
please do more videos with zvezdelina she's brilliant
@azoughkarim
@azoughkarim 5 лет назад
I have a question. What is the diameter of the circle that the motorcycle makes ???? if we turn the steering wheel alpha degree? This "phenomenon" seems to me very complicated. Thank you
@k0r0z1f
@k0r0z1f 10 лет назад
You sneaked in an optical illusion at 6:28, nicely done Numberphile!
@nuevemillas
@nuevemillas 10 лет назад
I don´t see it...
@k0r0z1f
@k0r0z1f 10 лет назад
It's subtle but I can see the circle kinda move/change size very slightly.
@freshrockpapa-e7799
@freshrockpapa-e7799 Год назад
​@@k0r0z1fmaybe you're high?
@evans.4453
@evans.4453 10 лет назад
Love the math involved and her accent doesn't hurt either.
@aza11112
@aza11112 10 лет назад
the 1 clone problem that was said to unsolveable can be solved... by just making one of the tails shorter by one square, I didn't hear a rule that a prisoner couldn't move one he was out of the jail
@SeanRhoadesChristopher
@SeanRhoadesChristopher 10 лет назад
The application may come, just give it time. The use of the matrix was at one time just some crazy game.
@GrahamJenson
@GrahamJenson 10 лет назад
Great extra video.
@One_In_Training
@One_In_Training 9 лет назад
Such an elegant proof. Lovely!
@chrisdoherty9466
@chrisdoherty9466 5 лет назад
Ron Graham (of Graham's Number) appears on the Pebbling the Chessboard paper
@robl4836
@robl4836 10 лет назад
So hang on... If you do play till infinity and end up putting a Pebble on the top row, does it become a Stone? Just Curious.
@MarkKeightley
@MarkKeightley 10 лет назад
I feel I almost understand a little of this, but I know most of this is beyond me. I used to play around a lot with cellular automata, of which this is an example. I never really understood the maths behind them, but I did try to encode them in various programming languages (perl and C as I remember), maybe I should dig up this old work and try and get it working in something like Objective C or C#? Might be fun!
@SciFiDeath
@SciFiDeath 8 лет назад
so... what if i turn this into a super task. i will clone every clone that i can in shrinking intervals. first 1 minute then half then a quarter, ill repeat this infinitely many times and after 2 minutes ill finish cloning everything. i now filled the whole infinite bored in a finite amount of time. does this means i win?
@FranciscoRodriguez-ef2so
@FranciscoRodriguez-ef2so 8 лет назад
Yezzir. Hypothetically.in practice you would at some point be unable to program anything to perform actions at a rate sufficient enough to actual perform the task, since the number of actions would be doubling at double the rate every time they double.
@fofys55
@fofys55 4 года назад
This explains how 50 clowns fit in a tiny car. Cloning
@TheGreatSteve
@TheGreatSteve 10 лет назад
To me "Pebbling a Chessboard" sounds like a really dirty euphemism.
@nolanaubuchon7015
@nolanaubuchon7015 10 лет назад
Can you do a vid on Euler's formula?
@jeremymcadam7400
@jeremymcadam7400 10 лет назад
can you have this lady on the show more? she has a really nice voice
@jroru
@jroru 10 лет назад
"we start with one clown" :D great vid
@Dalroc
@Dalroc 10 лет назад
Do more configurations for us! :D It's wonderful to listen to this :)
@iamalexkempton
@iamalexkempton 10 лет назад
Loving this!!
@antwerp7970
@antwerp7970 9 лет назад
Even with an infinite amount of moves and time, the last problem isn't possible. Look at the second row. The only way to move a clone to a spot in the second row is from below or the left. Cloning something from the left leaves the amount of clones in that row the same as before, but cloning from row 1 lets us add 1 to the amount of clones in row 2. BUT, since we need the single clone on the first row to be equal to 1/8, we can only clone the bottom clone three times. Since we can only add +1 clones to the second row three times, it's impossible to fill the entire board since those three need to fill an infinitely long row of squares, which is obviously impossible
@AhsimNreiziev
@AhsimNreiziev 6 лет назад
And thus you have provided an argument that actually proves the impossibility of the problem, unlike that which was presented in the video. Restricting the "game" to a finite amount of moves is, after all, a completely ridiculous limitation. But, since you have proven that even with an infinite amount of moves you can't fill up enough of Green Land to get every clone out of the 6-cell prison, you have proven it is impossible to empty the entire prison while not imposing arbitrary, silly restrictions like finiteness. So, you have proven to be better at Maths than Numberphile! Well done!!
@JRLarsen
@JRLarsen 10 лет назад
Her voice makes me think of a character from a show or movie. I can't think of who or what though...
@PixelButts
@PixelButts 10 лет назад
Is it possible to apply this to a cube and have it be solvable? My only thought is that if you do this, the cube's orientation will need to change, for example, the cube can be rotated 90 degrees to the left, making the top face now the left, right face is now the top face bottom face is now the right face, and the left face is now the bottom face. and now you can move the "clones" the same way, up, and to the right and they can reach every face. I'm not sure if that makes sense, but if the board (or 6 boards) was made into a cubic shape that can change its orientation, can it be solved? I ask because we have a finite amount of space, but now we can fill it all more. I'm also not good enough at these types of math subjects to get an answer, but it SHOULD be possible, right? Actually, if the orientation of the board used in the video was able to be changed, and still have the same movements, being up and right, this is able to be done on that finite board, because now gaps can be filled. Yes, if the board was rotated like 90 degrees, the movement of the "clones" would no longer be up and right, it could then be Left and Up, but the board's orientation changed, so the pieces are still being moved like the rules stated. I just want to see if that makes sense to anyone, because I'm confident that if board rotation is allowed you CAN solve this.
@Hythloday71
@Hythloday71 10 лет назад
Classic.... as the penny drops - 'so like, your just being paid to have fun" (paraphrasing I know). Reminds me of "if mathematics is the queen of the sciences, then the theory of numbers is, because of its supreme uselessness, the queen of mathematics" HARDY.
@mantkcmantk8717
@mantkcmantk8717 6 лет назад
Very nice. Thank you. But again, can you free the clones in infinitely many moves?
@MarianoPeterlongo
@MarianoPeterlongo 5 лет назад
" but you get paid?" so the people paid you for having fun? LoooooooooooooooooooooooooooooooooooooooooooL extraordinary
@robbiedart7422
@robbiedart7422 10 лет назад
I love this video, but it makes me wonder what other great numberphile videos I've missed because they've been unlisted! :(
@BenjaminAlexander
@BenjaminAlexander 10 лет назад
Guess you have to watch them all over again and look for end screen notes! ;-)
@hugolabs
@hugolabs 8 лет назад
So... would this mean that if we start with lighter clones we will surely have a solution? Let's say columns 1 and 2, row 2, total weight 3/4. If the weight of Green Land is X, any Y
@glarynth
@glarynth 8 лет назад
That particular starting prison is solvable, but in general it is not sufficient that there be enough space in greenland. There is also the question of how efficiently you can fill it.
@htmlguy88
@htmlguy88 8 лет назад
+Angel Slavchev depend on prison size etc. if you only have 1 1/2 piece in the original prison to start the game can end in 1 move with both half pieces in the prison it can equate to the single 1 piece in the original prison etc.
@tacfan72
@tacfan72 10 лет назад
I was thinking about moving to Greenland, but now that I know the clones got out of prison no thanks!
@Maxence1402a
@Maxence1402a 10 лет назад
Is it possible to use another invariant, as the color of the board, changing at each move ?
@NetAndyCz
@NetAndyCz 7 лет назад
Why is the game finite? Why are you not allowed to do infinitely many moves?
@AhsimNreiziev
@AhsimNreiziev 6 лет назад
My question *exactly* ! Now if one could prove that, say, the more moves you make, the further the pebbles on the bottom row and left-most column would have to move -- although I don't think this is the case and thus not a factor -- or if you could prove that other rows and columns can't even be completely filled either.... then that would be a convincing proof that escaping from the prison is impossible. The way it's presented, however, relies on the unfounded claim that _"Oh, it's a finite game and thus we have a contradiction!"_ ; which, with it being an unfounded claim and all, makes the argument as presented in the video fall apart at the seams.
@nothefabio
@nothefabio 6 лет назад
Choose a job you love, and you will never have to work a day in your life.
@thom_wye
@thom_wye 10 лет назад
Doesn't the observation made from around 4:20 and onwards contradict statements made in the first video? In there, you can use exactly same reasoning to show that you can have at most two clones in the first row and column - thus you can't have the sum of Greenland of 2.
@SomeUser9753
@SomeUser9753 10 лет назад
I CAN SEE YOU, BUT YOU CAN'T SEE ME. DAMN THE HAND WAS NAILED TOO.
@MrQwefty
@MrQwefty 10 лет назад
Ummm, really, you could just show that (after a considerable amount of moves, obviously necessary to bring infinity closer) there can't possibly be a prisoner in some of the places close to the prison, which would mean that occupying all of greenland is impossible, QED.
@anticorncob6
@anticorncob6 10 лет назад
So, is there any way to prove that a specific variation of this puzzle is possible without giving an example of how to do it?
@tjrummel
@tjrummel 10 лет назад
It is like archimedes and the turtle. When you apply math to it, it seems impossible but in real life, it is possible.
@Ezechielpitau
@Ezechielpitau 10 лет назад
No, math actually works perfectly in both examples...
@unpronouncable2442
@unpronouncable2442 10 лет назад
I actually was wondering about this. There are algorithms that require infinite moves in order to give result like in the grand hotel paradox. can't the same principle be applied here? can't you just say that you make all these moves at once and say you won the game?
@yvesnyfelerph.d.8297
@yvesnyfelerph.d.8297 5 лет назад
Why a=2b? What is the link to the stones moving across the board? We are supposed to just accept this assumption or what?
@akhinambiar
@akhinambiar 10 лет назад
Hi Guys, could you do s video on conditional portability please.
@qoaa
@qoaa 10 лет назад
If its Pennywise clowns then they can stay in prison They all float down here, and when you're down here you will float too!
@lennartgro
@lennartgro 9 лет назад
i think a video about the weierstraß function would be interesting
@debasishraychawdhuri
@debasishraychawdhuri 10 лет назад
After a long time, something interesting.
@MrKyogre14
@MrKyogre14 10 лет назад
I just love her accent...
@MechaTama31
@MechaTama31 8 лет назад
It's even worse than that. The restriction on how far you can go up the first row/column also restricts what portions of the second row/column you can fill. The only way to increase the number of clones in a row/column is for them to come in from below or to the left. Otherwise, as mentioned in the video for row/column 1, you're just pushing that one clone along and leaving empty space behind. With row/column 1 being virtually empty, there are no clones from which to inject new clones into row/column 2, so it cannot be filled up either. And then the same goes for 3, 4, etc.
@chanalex3971
@chanalex3971 8 лет назад
Hope I can be another one paid to have fun like that! Great video
@il2xbox
@il2xbox 10 лет назад
Numberphile Episode II : Attack of the Clones
@smellmcguy
@smellmcguy 10 лет назад
Why is it that you are allowed to number the squares?
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