The Game You Can't Win

John Conway’s work stretched from nearly-inaccessible math theory to fun children’s games, and it defined how we thought about recreational mathematics in the 20th century. Conway’s Soldiers is the perfect example of a Conway-esque math game: the rules are simple, the gameplay is easy, and it becomes very hard very quickly… and in this case of a basic checkers game, it packs a surprising punch of becoming literally impossible for a reason that isn’t even close to obvious.
But the mathematical importance doesn’t end with an unexpected reveal of impossibility. Conway found that the secret to why it’s impossible depends on the Golden Ratio of 1.618, which has fascinated mathematicians since Pythagoras and Euclid. We see the Golden Ratio in aesthetically-pleasing magazine layouts, flower patterns, and pretty faces, but John Conway showed us that it’s at the heart of why we can’t reach the fifth row of a checker game.
Play the game yourself with the online simulator and check out Zvezdelina Stankova’s proof on Numberphile. It’ll make sense. John Conway may be gone now, but we’ll be playing his games and poring over his ideas for centuries.
Conway Checkers (proof), Numberphile2 | Zvezdelina Stankova: • Conway Checkers (proof...
Conway’s Soldiers Interactive Game (Clever Learning): www.cleverlear...
** SOURCES **
Berlekamp, E. R.; Conway, J. H; and Guy, R. K. "The Solitaire Army." In Winning Ways for Your Mathematical Plays, Vol. 2: Games in Particular. London: Academic Press, pp. 715-717 and 729, 1982.
Honsberger, Ross. "A Problem in Checker Jumping." Ch. 3 in Mathematical Gems II. Washington, DC: Math. Assoc. Amer., pp. 23-28, 1976.
Tatham, Simon and Taylor, Gareth. “Reaching Row Five in Solitaire Army.” tartarus.org/g...
plus magazine, “Mathematical Mysteries: The Solitaire Advance.” plus.maths.org...
Bell, George. “The Peg Solitaire Army.” www.gibell.net/...
Bell, Hirschberg, Guerrero-Garcia. “The Minimum Size Required of a Solitaire Army.” arxiv.org/pdf/...
Taylor, Jasper. “Conway’s Soldiers.” sites.math.was...
John Conway’s obituary, New York Times: www.nytimes.co...
Roberts, Siobhan. “Genius at Play: The Curious Mind of John Horton Conway” (2015). www.amazon.com...
** LINKS **
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Hosted and Produced by Kevin Lieber
Instagram: / kevlieber
Twitter: / kevinlieber
Podcast: / thecreateunknown
Research and Writing by Matthew Tabor
/ tabortcu
Editing by John Swan
/ @johnswanyt
Huge Thanks To Paula Lieber
www.etsy.com/s...
"Binary Max Escape" by Basswaite: distrokid.com/...
Select Music By Jake Chudnow: / jakechudnow
Get Vsauce's favorite science and math toys delivered to your door!
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#education #vsauce2 #maths

[@anythingg00394]

My guy really drew us a whole board just to tell us that he cant use it. The dedication.

[@comradepeter87]

Was about to comment the same.

[@Noctu_ary]

It's not about the board, it's about sending a message

[@nickcru5637]

Not stonks

[@DMFM71]

@@catwpants beautiful

[@PhaseControlDNB]

also - he wanted to show that 5th level is impossible but drew a 7-level board :D

[@jmzlolo]

Thanks for making a tribute to John Conway, I'm sure he would have appreciated it

[@kkTeaz]

@@OzoneTheLynx i didn't since i had sort by newest

[@recklessroges]

I'm not sure that he would have, but I certainly do.

[@OzoneTheLynx]

@Gaytony It wasn't originaly... When I looked there were quit a few comments before it.(many of which I suspect were from bots).

[@gamingworld8355]

R.I.P. John Conway

[@AlexPBenton]

It’s even better, because Conway hated being known only for Conway’s game of life, so discussing something he did that is lesser known is probably what he would have wanted.

[@bunsenn5064]

I actually managed to win this game, I used a strategy called “cheating whenever I’m at a disadvantage”

[@rayzorblader9198]

XD

[@TimThomason]

Yes, we can solve this if we bend the rules a little bit. Specifically the rules that say you have to jump other pieces. Or that you can't just put any piece on Row 5 from wherever.

[@DotDotEight]

did you use wemod?

[@wertwert225]

lol nice

[@quedoom]

Good job 👏

[@brighton2862]

"The game you cant win" Me: pretty much every game i've ever played.

[@dwijnapal4615]

Lol

[@gaby8706]

Lol

[@Vota_]

Lol

[@TheUnderscore_]

Lol

[@evanderyorrel3549]

Lol

[@thomasfieschi-rose3705]

Rest In Peace, John Conway. The man that gave us life.

[@rogen8094]

Uhh... I mean, he was a great man, but didn't give us "life" Unless he's your father - in which case - I'm sorry for your loss. EDIT: Yes, I get it now! Apologies for the dumb comment! ;)

[@no-ls7uj]

@@rogen8094 i mean technically he did cuz he made the game of life

[@rogen8094]

@@no-ls7uj Fair point!

[@tabbeyond311]

@@no-ls7uj yeha

[@tabbeyond311]

@@no-ls7uj i mean yeah

[@notsofast3748]

Right? Wrong! :(

[@qwertyqwerty9349]

Right!!

[@gamingworld8355]

@@qwertyqwerty9349 WRONG!!!

[@hugo4049]

Or is it?

[@gamingworld8355]

@@hugo4049 or Kinda just going with the flow

[@hugo4049]

@@gamingworld8355 Just forgot OR.

[@teridactyl1250]

‘It’s like trying to invade Russia in winter’ *laughs in Mongolian*

[@johnlang6500]

It's like trying to invade Russia in the winter - Impossible. Except for the Mongols!

[@justinross4109]

Cue the mongoltage

[@christianlambhtx]

Crash Course Gang

[@teridactyl1250]

@@justinross4109 well done

[@jovicagasic98]

I thought the exact same thing 😂😂😂

[@MrOvergryph]

Kevin: "You can solve it if you bend time" Also Kevin: "Using 27-digit-dimensional space" Still Kevin: "He called it the Monster" *boldy explains nothing to audience* More Kevin: "And as always, Thanks for watching!"

[@Piotr_Tokarz]

I am literally confusion

[@tyzonemusic]

The "you can solve it if you bend time" thing is a bit complex but very well explained in the paper in the desc tartarus.org/gareth/maths/stuff/solarmy.pdf

[@vincentvanzwietenOFFICIAL]

@@tyzonemusic what I find interesting is that the solution literally uses all of the infinite soldiers to reach level 5.

[@tyzonemusic]

@@vincentvanzwietenOFFICIAL Yep! In the paper they mention a general version of the problem for N-dimensional checker boards, and have similar results. For a 3D checker board, you'd be able to reach a score of 7 with finite moves, and 8 with infinite moves (once again using every soldier).

[@orlandomoreno6168]

@@tyzonemusic transfinite numbers?

[@ahuman3393]

Every time I hear about Conway the guy sounds cooler, his game of life is still one of my favorite things

[@Psi_Fan123]

Game of life or?

[@Calculuscat14]

“I heard this Conway guy is pretty strong! Where is he?”

[@mastermonke2413]

​@@Calculuscat14you cant win goku he's too strong

[@FrancisBSCR]

Kevin: “This video is spo-“ Me: *furiously taps right side of the screen*

[@evaporatedmilkee6263]

LOL

[@adyhottie]

Ngl mischif sounds really good for trolls.

[@manwithabagon]

*with having it 60 seconds every two taps*

[@garrylarry890]

What is the right side of the screen Oh. I got it

[@cjfdnqkn4374]

mschf: no!!!!

[@huhneat1076]

This feels a lot like Minecraft piston extenders

[@scottharbin1868]

Tru

[@Potatoboii2]

You can make it 24 pistons

[@cowch3916]

Jing RS Lin ᴍᴄ it don’t work 😭 (the link)

[@allovas]

@@cowch3916 remove the space

[@moonpaw8874]

Huh Neat omg so true

[@cr4ckem]

I can imagine Kevin bullying his future child with the whole "right? WRONG!" thing. Poor kid.

[@anduro7448]

and one time he goes "right? yea , its right"

[@Jayy-Paus]

He already has 23 babies

[@anawesomepet]

@@Jayy-Paus No, he has 70.

[@mryodak]

"To get it right you would need to bend time. John Conway had imagined a group in the 196,883-dimensional space called a monster. And now, go to bed!"

[@jackdaniels4968]

brutal

[@DrakiniteOfficial]

This is the first I heard about Conway's death. Rest in peace, my friend. You've done so much for us.

[@JohnJohnson-od6dd]

Well thats part of the game .. The game of life (Insert laugh track here)

[@ammaleslie509]

maybe he can see the beautiful additional dimensions now

[@cjfdnqkn4374]

R.I.P. Rest In Peace My friend Conway...

[@the-anhpham3364]

Conway's Game of Life and Death

[@Jst4vgApostle]

Tbh I didn’t even know he was still alive (in 2019) until now...

[@trackeralias1124]

2n+1 for the moves seems complicated.. if the goal is reached when the final piece hits the target level, and each move removes one piece, then you'll always make total pieces - 1 moves? as you can't have 'pieces left over' as any piece used effectively deletes itself.

[@jax6648]

“The goal of this game is to get these checkers to the other side of the li-“ Me: *shoves all the checkers to the other side of the board with my arm*

[@augustomoreira7441]

instant win

[@bogdan_ostaficiuc]

I know that this is a joke, but that's called cheating.

[@coolj4334]

👍

[@Sci0927]

Rotates board

[@-petrichor-7263]

@@bogdan_ostaficiuc R/whoosh

[@kabirbatra]

I'm all sad now..I remember when I was super fascinated with Conway's game of life in middle school, and I remember when my 8th grade teacher told me she had actually met Conway in person and they were friends..and I was so amazed and wished I could meet him some day..what a weird feeling it is to know that he was just human, vulnerable to corona like the rest of us. May his beautiful lessons live forever in the mathematical community, and may his games continue to appeal to the interests of people of all ages, from cs students programming the game of life at school, to nerds watching Vsauce and Numberphile. Thanks for watching? More like thanks for making this video Kevin.

[@duk8227]

Wait he died from corona?

[@kabirbatra]

@@duk8227 10:06

[@duk8227]

@@kabirbatra wow never knew he was an alcoholic...

[@kaka88k1]

this is so emotional ):

[@observr-1]

@@duk8227 how on earth did you derived that he is an alcoholic by using fact that he died of corona? are you one of the corona-deniers degenerates or something?

[@dorukefeozkan]

every actual time i watch a vsauce2 video: kevin: yes me: yes? kevin: no me: no? kevin: WRONG

[@cjfdnqkn4374]

Me: brain explodes

[@bonuswastaken]

Second

[@Itz_Sophia19]

@@cjfdnqkn4374 same

[@sharif47]

On the second half of the previous year, one of my friends came to me with the idea of implementing Conway's Game of Life as a Software Development project and we ended up implementing a very basic version (i.e. not very optimized) in Unity. One day, I showed him a Numberphile video of Conway explaining Game of Life and he was like, "He's still alive?" and I was like, "Of course, he is." I didn't even know he died until this video. RIP John Horton Conway. We'll miss you.

[@weirdernow]

R.I.P We'll miss you Mr Conway... Never will we forget, the greatest minds, now we'll see, how are the greatest minds of tomorrow...

[@weirdernow]

We miss you already, If only you succeed to making a key of immortality, before it was too late, and the virus, beat you through the fight. RIP.

[@arcurifamily8525]

Level 1, dirt, level 2, wood, level 3, Stone, level 4, bedrock

[@macsidia]

Level 5 void

[@danieltreshner4955]

The main difficulty I ran into using the game in the link, is that as you progress, you slowly create a void behind your leading soldier. That void prevents other soldiers from progressing in that column purely because they can't reach it.

[@hadesciphernius5244]

Ah. The main difference between explaining something logically and mathematically.

[@wren_.]

It kind of feels like when you start running in a dream but you’re not actually going anywhere

[@dukeofshadows5211]

Yeah this is what I discovered to get one to the 5th row you need one in the 4th with one in the 3rd also but once you get one in the 4th row the remaining tiles are 5+ rows away.

[@dragonmasterlangeweg7625]

@@dukeofshadows5211ok, so the way to avoid the void is to have it be on one side, but it's not possible to get one to the 4th row without taking from both sides of the square that makes it to the 4th row, or if it is, then getting one to the third row below it is impossible. if it is possible at all, you would need to have a formation that looks like a set of stairs essentially, and that doesn't seem to be possible with the limitations.

[@budd8852]

Well of course you can't beat it. You haven't handed the controller to your older brother yet.

[@arielsproul8811]

I am the older brother, and this can be beaten by moving into hyperbolic space

[@CopyTheCompcom]

The disappointed chorus kid fits this comment

[@masonhunter2748]

Ariel Sproul nah you have to move into 12324587452 dimensional space and you need 2938737284 chips

[@EclipsaEldrich]

I’m the oldest, and I’ll tell you how. Ya gotta jump twice, duck twice, dash to the left then right then left then right, draw a b and a and write start.

[@CopyTheCompcom]

@@EclipsaEldrich That's cheating, dude!

[@Never_Always2]

“It becomes mathematically impossible which seems impossible” No way

[@christianbarnay2499]

I think you missed the meaning of this sentence. He doesn't say that "Mathematically impossible" is almost the same as "Impossible". He says that the mathematically proven fact "You can't reach as far as you want even with an infinite supply of soldiers" seems impossible.

[@Never_Always2]

Christian Barnay yep what’s your point?

[@eljot1092]

@@Never_Always2 his point is you missed the meaning of the sentence

[@elfro1237]

Oscar Ward he was not saying that something that was mathematically impossible was impossible. He was saying that it seems impossible that is is impossible, meaning it seems possible.

[@panferno3926]

Everytime i get here because the headline sounds like a bad app ad and everytime i get dragged into the abyss of math and it's true nature, and by that i dont mean bad school math. I'm talking about the pure fascinating logic behind every single formula, every single number and how simple math looks when you such cool way to bring in across.

[@scottgagnon7528]

math is truly beautiful sometimes

[@facundocadaa9020]

That's how mafia works. Download Mafia City NOW

[@edelweiss9467]

Almost everyone (myself included) don't fully understand just how greatly the math we know have been simplified and "dumbed down" that we'd even find the fact that there's extensive proof that 1+1 = 2 ludicrous.

[@Alvionalx]

spam

[@Alvionalx]

spam

[@spoopy2180]

It's Like trying to invade russia in winter, its impossible *_heh im just glad hitler didnt know that_*

[@SunflSeeds]

He did and so he did it 6 months before winter but then he was too slow

[@zettour.]

@@SunflSeeds Nah, he was just really confused that Stalin didn't surrender when Hitler marched into Moscow. Though, I guess Napolean was in the same exact situation centuries ago.

[@bypy3544]

@@zettour. napoleon waiting at moscow for tbe russiand to surrender A few montha later Brutal winter rekts napoleon

[@woodybrison]

There is a theory that Stalin goaded Hitler to invade. Fighting near your own land you don't have a long supply chain.

[@ILoveNigga]

Soviets and Mongols

[@joiscode3832]

Rip, john conway, may he always keep inspiring and fascinating people with the games math and legend he left behind.

[@WarDaft]

There's actually a pretty intuitive way to see why you stall out. I'm going to post this before listening to the explanation, and before morning coffee so I could (possibly) be wrong. Movement requires spending pieces. More importantly, it requires spending *nearby* pieces. Movement higher requires spending pieces that you had to pay to move up there, meaning those pieces themselves "cost" more. The cost ends up exponential in the distance you move, at least doubling for each additional square of range, but the number of pieces in your "accessible fuel pool" increases only quadratically with increasing travellable distance, and so you starve out. If everything was conveniently in the right place, it should exactly double for every step up, but nothing is ever convenient, so it probably costs more to really actually move them. You can obviously move at least 1 place, at cost 2 (using 2 pieces from below the line). There's 4 fuel available within 1 distance (orthogonally, or by Manhattan distance) of your starting point, so you can move at least 2 places (at cost at 4). There's 9 fuel within 2 distance, so you can move at least 3 places (at cost 8). There's 16 fuel within 3 places, so you can move at least 4 places (at cost at least 16). There's 25 fuel within 4 places... Not enough to move 5 places which costs at least 32. It gets even worse from there. 36 fuel within 5, but cost 64. 49 within 6, but cost 128. 64 fuel within 7, but cost 256. Distance 10 has 121 fuel but costs at least 2048. In 1 dimension, fuel is sparser and you can't even move up 2 places. In 3 dimensions, fuel is denser, and you can move father - but the cost is still exponential which eventually beats the cubic fuel availability of 3d. In fact, any finite dimension Euclidian space will eventually run out of accessible fuel. Even if you can move a piece by more than one space in a hop, or diagonally. In a hyperbolic space, you should be able to move an unlimited distance up, because you access to fuel increases exponentially with distance. Note: we live in a functionally Euclidian space, and it costs fuel to move things - including fuel. We live in a very complicated game of soldiers. Time to watch.

[@WarDaft]

Update: I ran through a simple thought experiment modification where you're allowed to stack as much fuel as you want on a given square, and the cost to reach a given height with ideally placed fuel is actually the Fibonacci sequence, rather than doubling! 1 piece at height 3 cost = 1 piece on height 1 + 1 piece on height 2. 1 piece at height 4 cost = 1 piece on height 3 + 1 piece on height 2. A piece at height n is height (n-1) + height (n-2), the same recurrence as the fibonacci sequence, whose successive terms (regardless of starting terms, as long as they're both positive) tend towards... The golden ratio! That's how that comes in. This is probably all explained right in the original paper proving it impossible. Which I should probably go read.

[@Bloodsong13T]

@@WarDaft nice! thanks for the analysis and explanation.

[@XIIchiron78]

Bruh (That was a fantastic explanation, you have talent!)

[@XIIchiron78]

This is actually an analogue for Tsiolkovsky's rocket equation 🤯 you have to carry your fuel

[@gayatribiswal5652]

My mind has grown hyperbolically!

[@samarthkhandelwal5263]

Every Vsauce2 video: Starts of as a simple game but ends with a life-changing quote. One of my favourite creator.

[@0newheeldrives]

*Beautiful tearjerker outro begins* "and as always tha..." *manscape lawnmower ad begins* "WHEN IT COMES TO TRIMMING YOUR BALLS ..." KZbin, I beg you. Let us watch the outro in piece

[@commie281]

oh my god HA

[@pigman6954]

69 likes...nice

[@xarim4769]

Kevin: mentions the golden ratio Me, an idiot that read JoJo: I’ve seen this one!

[@Batmanman01]

exactly what i thought of

[@davidmagyar6093]

"It's like invading Russia in winter" Finland: Not impossible... Mongolia: Am I a joke to you?

[@papertom]

Germany: cries while doing so

[@iamdivan7368]

Poor Napoleon

[@DiogoCoutoooo]

Kevin: Right? Me: ye... Kevin: WRONG!!!...Kinda Later Kevin: so this is the perfect algorithm right Me: of cour... Kevin: WRONG!!!! Me: ... *of course it was wrong* ...

[@Etrehumain123]

Lol !

[@TuxMan]

Kevin : right? Me: *pauses* ... Me: r... i- Kevin: NOPE

[@weirdernow]

John died? The conway himself? 😥

[@SCP--gr3pd]

Kev: right? Me:... Kev:... Me... Kev:... Me:...y Kev:WRONG

[@Johnny-Joseph]

I was looking forwards to how he would explain the 5th level by removing time... alas, maybe next... time

[@adb012]

It can be done in an infinite number of moves. But is a "not so large infinity" (because infinities come in many sizes, like there are as many natural numbers as there are rational numbers, but quantity of real numbers is infinite times larger than those even when all these sets are infinite to begin with). So you can set up an algorithm (at least in theory, because in practice it can't be realized) where the first move takes one second, the second move takes 1/2 second, the 3rd move takes 1/4 second, the 4th move takes 1/8 second and, in general, the n-th move takes 1/2^(n-1) seconds, and by 2 seconds you are done in infinite moves. It's like the famous paradox: You can never reach a place that is 2 meters away because you always need to reach the half point of what remains first. So you first move 1 meter, then 1/2 meter, then 1/4 meter and so on and you never get there. Except... if you do the first 1 meter move in 1 second, the second 1/2 meter move in 1/2 second, the 3rd 1/4 meter move in 1/4 second and so on, you've made all the required infinite moves to reach 2 meters in 2 second. And that is how you actually can get from the bed to the bathroom at all. It is called "supertasks". Note however tat you can get to the bathroom because it does actually take less time to walk 1/4 the distance than 1/2 the distance. So that is a "possible" (in the real word) supertask. But in real life you cannot make that each following checker move takes 1/2 of the time it took the previous time forever, so solving this puzzle in infinite moves and finite time is impossible in practice. And by the way, reaching row 6 is impossible even in infinite moves. Infinite moves is barely enough to take just one soldier to the 5th row. Eve 2 soldiers to the 5th row is impossible (I think).

[@Geigenzaehler]

@@adb012 Two soldiers on the fifth row is impossible. In fact, you have to use every single one of the soldiers below the line to get a soldier to the fifth row. After the infinite sequence of moves, there is only one soldier remaining.

[@alexandrubragari1537]

@@Geigenzaehler or you can divide the infinity in two equal parts and make run 2 algoritms at the same tims 1 for 1 half and the other for the other half of soldiers and you have 2 soldiers on 5 lel

[@Geigenzaehler]

@@alexandrubragari1537 I know you are probably joking, but I still want to give a short analogy why that's not possible, if anybody is wondering: Imagine an infinite row of soldiers. First soldier is valued 1. Next one 1/2 then 1/4, 1/8, 1/16 ... If I add all the soldiers values, I get 2. But no soldier can be ignored. By your method we could now divide the infinite row of soldiers into two infinite parts. But guess what, the sum is still limited to 2. This is analogous to why there can only be one soldier on the fifth row.

[@serraramayfield9230]

Geigenzähler Set theory doesn't follow common sense....wait a second. Aleph-0 number of soldiers = 1 soldier on level 5. What would aleph-1 soldiers get?

[@raveneagle9117]

The dedication in this dude he drew a board just so he can’t use it

[@irrelevant_noob]

And at 12:17 we get a glimpse of how LONG it really took to fill it up too... @-)

[@pauldacon828]

The color of game pieces that he used makes me believe he was making a reference to Buddhist monks who spend hours, sometimes even weeks, making sand art just to sweep it all away in order to embrace the acceptance of the inevitably of the passage of time and the futility of trying to fight it.

[@wunba]

You can explain it all day, but I still won’t believe level 5 is impossible until I do it myself. 😂

[@FabbeNJ369]

Didn’t expect to see you here Wunba, love your videos

[@Cowtymsmiesznego]

Well, that's understandable, as he didn't actually explain anything

[@brotonnorgrinson7651]

Why are you here?

[@loverofcattz932]

I sort of figured it out myself before he explained it, the soldiers will eventually run out of being close to the center line and you will not be able to get to that center line and keep going back and back until your too far away to do anything.

[@3xtremelamborghini]

What are you doing here mister wunba

[@georgijmaksimov5415]

For the third it is (2x2)+4=8, and for the fourth it is (2+4)x2+8=20

[@aarryasaraf]

That man deserves this tribute and more rip JH Conway

[@luis_leitao]

This video got insanely emotional all of a sudden, it was already really deep once you start feeling the frustration and the passion in Kevin's voice but the whole thing with John Conway got me real bad. I'm tearing up man, thanks for that.

[@Pugs]

Is there ever going to be an actual POSSIBLE game?

[@robertmorrison4457]

no

[@kkTeaz]

*NEVER!!*

[@maxsteinbeezly7904]

VSAUCE! Today I’m going to play Solitaire.

[@shambosaha9727]

Brussels Sprouts

[@kkTeaz]

@Tangent of circle. IMPOSSIBLE

[@Magicastor]

6:00 SAYONARA, PUNY CHECKER BOARD!!!

[@MiguelLopez-tj1br]

Got an essay to write about this for my calculus class thank you!!

[@axlcodes]

Absolutely loving that 12:34 video length!

[@zsivkovicsmate8747]

Because 5 is impossible

[@confus.d]

WRONG!

[@snl9500]

it's 11:16 though

[@adilloco6261]

If a smart guy like kevin promotes an app it must be good Edit: just came back from the appstore the app is not available in my country so that is nice

[@demerion]

Same here :/ Gotte find an IPA or create a new account

[@kkTeaz]

@@demerion sad

[@8o8inSquares]

Same here..

[@Johnny-Joseph]

They must have paid him a tonne to drop his credibility like this

[@syrialak101]

@@Johnny-Joseph The app looks like it fits his style though.

[@elucinadoboy4967]

wow, that ending really got me. Conway's death didn't really hit me until now. Thanks for helping carry on his legacy, Kevin

[@JohnWarosa999]

That ending almost got me crying. May you rest in peace John Horton Conway.

[@Mr_Tophatt]

"think of them as soldiers, trying to penetrate as deep as possible" well at this point I think I have won without playing

[@ScibbieGames]

Conway would be proud seeing something other than his Game of Life being talked about.

[@aldothelizard6669]

Me: mom can we have "right" at home? Mom: we have "right" at home "right" at home: WRONG ! 1st thought, can you do it backwards, started it on a square at the 5th row 2nd thought, what if, the plane is 3 dimensional, so you have multiple column, row, AND layers; 1 checker can jump forward, backward, right, left, AND up and down

[@YOM2_UB]

On the second thought: level 5 would be fairly simple, just do level 4 like you do on the plane, then jump enough checkers down to do level 3 in the same spot. You could then jump enough checkers up to do level 4 again to get to level 6.

[@רפאל-ב]

Right? WRONG!

[@adb012]

"1st thought, can you do it backwards, started it on a square at the 5th row" You mean doing it in reverse? Like starting in the 5th row, jump back to the 3rd row and add a "soldier" in the 4th row? You can't make it in a finite number of moves. You will end up with soldiers "hanging" beyond the line and not being able to return.

[@רפאל-ב]

that's a really smart way to find a solution

[@zsivkovicsmate8747]

Actually if its over 2d, over 3d etc like 60d, its infinitely possible

[@SigmaGamerProzst]

i'd like to get that "collar that swears when your dog barks "

[@cornesalvo9366]

I have a really strong feeling that even though it's implied that the feet pic sending AI is worthless, a lot of people would think otherwise.

[@michaelestrada1972]

"The game you can't win" You're telling me there's games I can win?

[@DaxSkrai]

Instead of "2n+1" you could just say that it takes one less move than the number of pieces it takes to get to that level.. 8 pieces takes 7 moves to get to level 3.

[@kandyappleview]

"The answer is beauty...and taxis." Sounds like me answering a word problem about trains on my math test

[@AverytheCubanAmerican]

Even if it doesn’t make sense, you have to admit that it’s kind of fun to do the impossible. Walt Disney said it best

[@kkTeaz]

Yup

[@razdahooman]

WHAT???? he died??? I didn't even know and he was one of my favorite mathmaticians..... Really sad now :( hey, it was still a good video tho XD

[@Mitiya__ua]

I didnt even know this guy before this video and now he is dead! Oh man! What is wrong to the world?need to cancel death for at least couple months

[@saddlebag]

@@Mitiya__ua I mean the main reason I knew about him was because of “Conway's Game of Life“ which he created.

[@samraatplayz1607]

@@AbiGail-ok7fc Who

[@JaceyRbrts]

I don't understand any of this but I just listen to this man spit facts at my face

[@2carrots25]

Same

[@alihesham8167]

6:56 thing that makes me think that its less sense is that we can put a 3 behind a 4

[@jay-tbl]

fun fact: otters have a favorite rock they take around wherever they go edit: what? this comment is from two years ago and i neither remember making it nor watching this video. it isnt even relevant. did I just click the video for the sole reason of writing this one comment? why did i do that? what edit2: ?????? I have no memory of this its been 4 years what???? anyways i looked it up and they dont do this just for fun, sea otters carry a rock around to smash open mollusks like a hammer

[@БранимирНиколов-ж7ф]

I knew that already but being reminded of it made me smile so here is a like from me

[@jay-tbl]

@@БранимирНиколов-ж7ф Thanks

[@balintbosnyak3383]

And they hold hands in their sleep so they won't drift away from eachother

[@human-1223]

I learn this from a manga

[@nickf3242]

This was news to me... Decided to take a stroll down the comment path and was enlightened by this tidbit of knowledge. I knew about the hand holding, but not this. I will probably be obsessing over this for the next few hours. It sparked a bit of curiosity and now I wanna know what happens if they misplace their beloved rock or someone takes it, do they freak out? I'm afraid of falling down a unplanned Google rabbit hole with this question. I'm not ready for the time investment at the moment. Thanks for the future Google query.

[@Ykulvaarlck]

it's refreshing to see someone honor conway for one of his more interesting and significant discoveries, rather than the culturally-widespread one that i shall not name

[@YahyaFalcon]

In case anyone doesn't know what yuval is referring to, it's the game of life

[@wariolandgoldpiramid]

Conway's Game of Life. You are not allowed to not name it.

[@unhingedfrogspawn6715]

I am confusion

[@anduro7448]

@@wariolandgoldpiramid y tho?

[@sujatapatne9521]

@@unhingedfrogspawn6715 y tho

[@joshrobertson4900]

This is the first news I've seen on John's passing. Thank you for the kind words.

[@norman5917]

Bro i don’t usually tear up from stuff but for some reason I just started to get teary when he was talking about how Conway died.

[@DaellusKnights]

Conway's game of life has long since been one of my favorite hobbies for times when I just wanted to chill and not use my brain overmuch. I didn't know he had passed. RIP Mr Conway. You didn't know me, but you changed my life in many ways. 💖

[@ReezeZoronauto]

Anyone else just recently been getting recommended videos mere minutes after they're posted

[@coriae]

the algorithm is tired of recommending the old catalog of at least 3 year old videos

[@kevinmyers8325]

When you know kevin so well u can right wrong him before he does

[@רפאל-ב]

Right?

[@pikach336]

WRONG

[@fumpledump]

When you make a custom board only to realize that the game is impossible...

[@AllShakhov]

"It’s like trying to invade Russia in winter" Actually literally everybody invaded in summer, but fought until winter. Забавно :D

[@dragonmarble5779]

Да

[@robinsflight]

:D

[@simplifi-digitalart5571]

6:00 “i guess i gotta make my own board so sign off puny checker board”😂😂😂

[@TheDutchFighters]

That looks awesome, they should make this kind of game for two players. Like you both get a side and you have to jump over the other to remove his stone.

[@caspergotlost]

This is a joke, right? Ive not played checkers in so long I'm not sure if I remember the rules correctly

[@sebolarimore]

Me: Reads title Also me: Isn't that 𝘦𝘷𝘦𝘳𝘺 Vsauce2 game?

[@trbld5219]

“Right?” Me:Yeah! “ *WRONG* !!”

[@DoctorBones1]

Conway is my inspiration, i love the way he turns extremely complicated math concepts into interactive experiences.

[@markys_top1514]

4:20 I think about "number of soldier"--1

[@GabRioBlu]

yea its just 2^n - 1

[@Savant_Ananya]

My guy really did get emotional at the end. I hope Covid-19 goes away asap

[@carealoo744]

I had to drop out of univeristy because its online

[@SharayaYT]

I didn't know Conway passed away, I am so sad about this... I really liked his way to think, I tried to learn his Doomsday algorythm because I was so fascinated, and this video made me even more curious about his works.

[@livethefuture2492]

great video! and really loved the tribute to John Conway, R.I.P. truly a gem in this world!

[@RichTiger7]

"This is a one-player solitaire game." Thank you for the clarification. Otherwise, I might have become confused because of all the 4-player solitaire games out there.

[@cubingman4632]

"One must imagine Sisyphus happy."

[@SopranoCheese]

Kevin: *says golden ratio* People who know part 7 of JoJo: Ah, yes, infinity

[@jotarokujo6858]

Arigato Gyro

[@Infidak1ng]

i felt like a hero when i reached the 4th tile until i realized that 5 was the impossible one

[@zawsrdtygbhjimokpl6998]

:actually it us possible viewers: oh, nice. Now to hear about how it's possible :you need infinite everything and time manipulation viewers: darn

[@ericb3157]

this sort of reminds me of an old puzzle i have called "hi-Q" it has a + shaped board, you start with pegs in every space except the center, and you "jump and remove" pegs the same way, and to get the best score, you have to finish with one peg in the center.

[@MissSimsalot]

I know this is a 4 year old video but thanks for bringing me down memory lane. I remember reading a book 15 years ago about an autistic boy. And for some reason a large part of the book was him playing this game in his mind. I have no idea what the book was called, and thinking back about it, it was so random. And still 15 year old me absolutly loved that book.

[@heldersantos9928]

7:36 "impossible, it's like invade Russia in the winter". [Laughs in finish]

[@aarneheikinheimo1256]

I don't think Finland has ever invaded or even tried to invade Russia

[@BALegend1230]

​@@aarneheikinheimo1256 have you ever heard of WWII?

[@aid_as]

Isn't MSCHF's drops are like gambling or so...? I swear I saw something similar in the gaming communities where it later was punished by the law. Of course, you can have a science cover behind it, as a "experiment", but who'll confirm that a 100%? It's just my opinion and it's a bit weird tbh.

[@Jacob_Welsh]

Its only gambliing if you make it. You buy the box for $100. if you open it, you only get whats inside the box. But, they said, that if you didnt open your box, they'd buy it back off you in 12 months. So its not really gambling. more of an experiment.

[@Johnny-Joseph]

@@Jacob_Welsh If you were allowed to return a scratchie after you bought it, it would still be gambling :P

[@jacobmorejead8122]

@@Johnny-Joseph but it's unscratched and you get $1,000 for returning it. Like essentially the game is that one option is gambling while the other isn't.

[@barnabusowl4252]

Kevin lookin extra fresh in this vid 👌 👌

[@brunodaugrois3200]

My intuition for the golden ratio popping up, is that to get a chip to level N+1, you'll need one at N and one at N-1. So a fibonacci-like sequence pops up, and fibonacci numbers are closely connected to this ratio. Getting a chip to N creates a sort of void around it though, so getting a second chip to N-1 requires more moves than only getting one to N-1, yielding different (and much larger) values.

[@halamadrid7512]

Logically, we can visualize and simplify the explanation to this: any given checker can only move in 4 directions and with each move it removes (to be more accurate, it must remove) the adjacent checker in that direction (without this removal, it cannot move, following the rules). After 4 moves, it had removed all 4 checkers around it, thus making it impossible to take any more step in any direction. Everything we have done so far to make it move to the 4th row in fact is just to rotate that checker to meet our direction.

[@damamoot2291]

0:18 Two of the checker pieces swapped for some reason.

[@Mauripsu]

"Is like trying to invade Russia in winter" BLITZKRIEG!

[@bcn1gh7h4wk]

"It's like trying to invade Russia, in winter, of 1025, BC, with horse chariots, and you're the stables boy."

[@MrFram]

@@bcn1gh7h4wk laughs in Mongol

[@Chrischi3TutorialLPs]

Cause that worked out.

[@taiwanisacountry8221]

It isn't that weird to think about when you try to play it. The soldiers require other soldiers to be close to them in order to move. The further away they move the harder it is for them to keep moving

[@MrSpooner1985]

Playing the game, it quickly becomes apparent why you cant get to level 5; its so frustrating that each new tile you need is further back than use so you are always further and further away from the goal with tiles in front you can never reach again. Clever game.

[@shlimeball475]

I still have no idea what the golden ratio is even after watching dozens of videos on it

[@vorinz]

Bending time to get a chip 1 space foward.

[@ryangurnick]

Thanks for your contribution to remembering the amazing work of john conway, what an incredible person!

[@mr.jabbywock1830]

3:52 trust me, and now you can't un hear it

[@jammin1336]

The biggest voice crack ever

[@hoyyosoy]

One of the best videos I've seen, Kevin: we send you a big hug from Uruguay

[@michaelklog]

makes perffect sense you exust your reserves trying to get to 4 so there is nothing t oget youu to lvl 3 to jump to 5

[@masteryoda5931]

“It’s like trying to invade Russia in winter, it’s impossible” -Vsauce 2

[@epicadus8722]

Lol Napoléon Bonaparte and Hitler agreed 😳😀😂

[@dirkbastiaandejong997]

@@epicadus8722 the huns and mongols dont

[@user-uy6io8wm5e]

@@dirkbastiaandejong997 Well, they invaded Russia in summer...

[@GermanRumm]

@@epicadus8722 FYI Both of those guys invaded Russia in June

[@bcn1gh7h4wk]

so..... the trick should be to actually invade Russia in winter and turn the meme over itself! RIGHT! it's like the first test of Ready Player One: it's a race, so everyone just races.... nobody would have thought of going BACKWARDS!

[@GoodSmile3]

0:50 it doesn't if you HAVE to use Times New Roman

[@TheIndieGhost]

"get ready to social distance your heart out" me: that aged well then i see upload date me: oh

[@Zurdrex]

Imagine doing this with 1 million chips and still not getting to level 5

[@khaledshell507]

The calculation of the N first terms of the "Conway Sequence" was my baccalaureate practical CS exam. Only 2 people out of 150 in the exam hall could find the solution, plus another 8 people who made some effort granting them an average mark.