Exciting news everybody. Just a couple of

days ago I solved the 40 Rubik’s cube for the first time. Not many people have done

this so I thought I’d do a video on this to enable as many of you as possible to

do the same. I’ve got two warm up exercises for you. The first one is this.

What are you looking at here? Strange question, obviously a cube. But that’s not

the correct answer. What you’re looking at is a 2d image of a 3-dimensional cube. It’s

going to be very important this kind of distinction. Second thing so imagine a

cube which has kind of a solid surface. How many faces can you see max when

you look at it? And most people will answer three which is wrong.

If you actually imagine that the cube is hollow and you can step inside what you

see is five faces and actually you can even see six faces if you go into one of

the corners and kind of just look around you can see all six faces of the cube,

kind of thinking inside the box đ Now this actually is a view of a Rubik’s cube

simulator. So the Rubik’s cube simulator actually shows you the Cube like this. So

it’s a lot better than what you see normally when you look at something like

this, hold it in your hand. Here’s a couple of twists and now that one is actually a

when you turn the Rubik’s cube and that gets a straight away to our 4D Rubik’s

cube. So there it is comes in the form of a program it’s called Magic Cube 4d. So

you download this for free off the web. It’s a program that has been around for a

long time, has been developed for a long time. It’s it’s a great program, you

should use it. And this is the 4D Rubik’s cube. Well, no, it’s not the 4D Rubik’s

cube. What it is is well something similar to that right wherever you see

squares there you see cubes here now this one is a two-dimensional image of a

three-dimensional object now the four-dimensional rubik’s cube

actually really exists in abstract four-dimensional mathematical space but

of course we can’t really go there right so what we have to do is we have to

project it down to at three dimensions just like we projected our three

dimensional object to this two-dimensional surface so we can do the

same sort of thing this guy here for example

as six square faces that are glued together the edges this one here in

actual four dimensional space is eight cubes glued together along the faces of

the cubes and here where you see five and ones missing and here you see seven

of the eight cubes and once not visible here anyway so what this really is is

well what is it really it’s a two-dimensional image of a three

dimensional image of a four dimensional rubik’s cube can manipulate like a real

object in fact you don’t even have to know that it’s a four dimensional

rubik’s cube you can just take the program and just manipulate it based on

what you see there okay that’s what we want to do okay let’s have a look here

let’s some twists you can see it’s a lot more complicated than normal rubik’s

cube that’s actually turns of the rubik’s cube so we don’t manipulate

anything kind of just turn it around to look at it from different perspectives

and this is what it looks like solved if you want to actually be one of those

people who can solve it interested to scramble it scramble it looks like that

pretty intimidating first time you see this you think not this is just a mess I

don’t want to touch this but you probably thought the same the first time

you saw like a five by five by five and you know think you know I don’t want to

touch this one but of course then you realize well actually since I know how

to do that three by three by three the normal rubik’s cube well i can actually

solve this part of the five by five by five so I’m always harmful is there and

something similar is the case with the forty rubik’s cube so is the 40 rubik’s

cube at first sight at least there is no rubik’s cube inside you see lots of

these cubes but they all have the same color so where are the rubik’s cubes

well I’ll show you in a second now let’s have a close look at the individual bits

and pieces that are being manipulated here so in a normal room X cube you’ve

got three different types of cubies that are being manipulated around

so let’s first the face cube is they’ll just have one sticker so we also got

something like this here in the forty Rubik’s cubes

it’s the little cubicle stickers right in the center of these cubicles cells

that is one kind of a hypercube II now we’ve got cue bees that have two

stickers you also have cue bees that have two

stickers in the four dimensional cube here it’s edge cubies there it’s face

cubies so see those faces of those little cubes

well the sticker there’s one sticker there’s another sticker here right

opposite those belong together they basically form one hypercube a face

Peiper QV now we’ve got three stick-up pieces they’re the corner here they’re

on the edges here to see those those three cubicle stickers they belong

together as you manipulate the cube they will always stay together either vollis

like they can never be separated they form one hypercube E and then we’ve got

one more type of hyper cutie these are the corner hyper cubes and they have

four stickers and you can see them here highlighted now hyper twists as I said

there’s a lot more complicated twists in this puzzle then in the ordinary rubik’s

cube you click on any one of the stickers here and the program will

perform a twist so let’s just do it so for example on that corner here we get a

corner twist right so basically we are turning around the diagonal that goes

through this corner now here that’s an edge twist and then we’ve got one more

kind of twist that’s a face twist so there’s the first very important feature

of this puzzle that I have to draw your attention to and that is that every

single twist can be replaced by face twist so you can really restrict

yourself to face was just to show you what I mean by this let’s just focus on

one of those corner twists okay and so there it is and now I’ll undo this

corner twist but a straight face twists so one and there is another one actually

does two to face twists can replace one of those corner twists also edge twists

here we go it is I’ll undo this with face twists so there and there okay so

what means for you if you start solving a

Rubik’s Cube you actually don’t have to worry about the fancy corner twists and

the edge twists you can just stick with face twists so now let’s see where those

3d cubes are hiding inside the 40 cube and how we can use them to solve the 40

cube now anybody who knows anything about cubes and I hope you belong in

this category knows that you need just a few algorithms and solve the whole cube

in fact four is enough so you need like one algorithm to two cycle three edges

of the Rubik’s Cube then there’s another one here

one dead cycles three corners then there’s one that just flips two edges

and then there’s one that twists two corners so you use those sort of

algorithms here to put the individual qubits in the right place and then you

use those algorithms to orient them and what I want to show you is how you can

translate those algorithms into algorithms for the 40 rubik’s cube so

for that we first find some rubik’s cubes in the 41 here we go so it’s just

a different way of looking at the 40 rubik’s cube and she actually when you

kind of pull things together like this but we’re actually looking at usually

it’s kind of an exploded view is just a rubik’s cube so for example click on

that face here you know just is the usual twist of course the 40 rubik’s

cube is also twisted in this case now what i do here is i’m actually executing

one of those elders and 3d rubik’s cube algorithms on it

was the one that flips edges and let’s just see what effect it had on the 40

rubik’s cube okay so we kind of expand things back out again and you can see

very few type of cuba’s of the 40 rubik’s cube are affected by this in

fact it’s just like two columns of hypercube YZ and every single one of the

hypercube is in there is still in the same place as before it’s just that the

two stickers have swapped over now what I like to do is actually I like to focus

on the middle of the puzzle to my surgery there and and rotate things in

and out on the outside so I’m going to change

this new algorithm into one that actually affects the middle but as

rotating things down to the middle like this and so there you can see the

columns of hyper cubes that are being affected right in the middle arm now

let’s do the same sort of thing for another one of our 3d rubik’s cube

algorithms the one that cycles edges it’s actually quite impressive when you

see that thing in action so that’s again just the 3d rubik’s cube algorithm what

do we get well again there’s just three columns of hyper cubes that are being

affected and actually they just get cycled around like this and if you just

look at what we’ve done now that already looks very promising in fact when you

look at it more closely you see that these columns that we’re talking about

here contain one phase hypercube each so what gets cycled here in particular is 3

phase hypercube is and here again every column has one of those face either Q is

in it these get flipped so what you can do is you can use these algorithm

actually to fix up all the positions and orientations of the face hypercube is

straight away you just kind of go for it and you don’t worry about the other bits

that get pushed around here which is all edge hypercube ease the second trick now

which makes things very clean ok so what I want to do is I want to have another

look at this algorithm and just refine it a little bit so that I get out a

cycle of just edge pieces edge hypercube ease this is look so what I want is

something like this so this edge hypercube me that one and that one

just those cycle around with nothing else going on and we do this with

commutator z’ and if you watch my other rubik’s cube video familiar is it

otherwise maybe watch it so what we do is we just twist the top so we just

press this sticker that will rotate things some bits are left in peace

now comes the thing I’m going to run this 3d Rubik’s Cube algorithm in

Reverse it’s going to restore all the pieces that

I’ve not rotted it away to wait away before okay let’s just do this so this

one here in Reverse go for it in case you can already see that looks a lot

cleaner and now the only thing that I need to do is untwist the top which I’ll

do and you see the overall effect is has is that it just cycles these three edge

pieces around so that’s very clean right a very clean solution and well it gets

us something different too you can just go back to this this column look and I

can also isolate a cycle of face pieces a very clean cycle of face pieces and

the way I do this is I do a slice move which this program can also do just like

with the Rubik’s Cube you can just take the middle slice and do it like this and

so I’ve just sliced away the middle and now I’m going to run this guy in Reverse

it’s going to restore everything else yeah it’s a bit of magic really okay

wait for it okay so it looks very good now undone slice the middle and just

have a really really close look at it and what you get is a clean three cycle

here that just affects those face pieces and now we do the same for all the other

3d algorithms in total we get out of this eight algorithms for the 40 Rubik’s

cube and for all the different hypercube ease so we’ve got a go reason for

positioning the face hypercube is and for orienting them

we’ve got algorithms ford edge hypercube ease and we’ve got algorithm for the

corner hypercube is actually here in the middle you see we’ve got actually lots

of other reasons for for the edges and it seems that we’re doubling up things

here so we’ve got two algorithms for cycling edges but actually doing

slightly different things so I’m going to create them create both of them okay

so now how do we use these algorithms to solve the 40 rubik’s cube well you can

just kind of go for it in fact you can go for any of the different sorts of

pieces straight away because all those algorithms that we’ve created work on

the and hypercube is in isolation you could

either go straight for the corners or for the edges or for the faces well I

recommend you go for the face hypercube ease because they only have two stickers

and here you know stickers highlighted where they belong

they are also fairly easy to locate so for example if we look at the cell here

in the middle there’s going to be in a sticker of a certain color in this case

it’s some sort of blue and in this guy here you know sticker I love another

color purple so we know that this face hypercube e that goes here has to have a

blue and the purple sticker okay so pretty easy so let’s go for it

and also this way it’s very easy to kind of get used to the interface and how

this thing moves and all that so you finished with that at some point in time

move on to the edge pieces those have three stickers a little bit harder to

orient also so far it seems like we only need those 3d Rubik’s Cube algorithms to

do the whole thing but actually here at this point we can encounter a surprise

something works for the 40 rubik’s cube that does not work for the 3d rubik’s

cube on a 3d rubik’s cube you can never twist a corner in isolation you can

never flip an edge in isolation anybody who knows anything knows this with a 40

rubik’s cube that’s possible so you can have something like this happening so

the whole 40 rubik’s cube is solved except for one of the edge hypercube is

it’s in the right place but the stickers are circular around it’s twisted around

in fact all six permutations of those three stickers are possible that comes

as a little bit of surprise and you actually need a separate algorithm to

take care of that and what I’ve done is I’ve actually created a second video for

all those people who really want to tackle this thing and that video I

described the interface that you’re dealing with how to create lock files

how to create macros how to you know create those algorithms eventually

hopefully you get to fixing up all the edges and

well only the corners remain and with the corners a similar kind of surprise

waits for you at the end you may have solved the whole Rubik’s Cube and the

only thing left over is this one corner hypercube we hear the stickers have been

permitted around so you also need another algorithm to take care of that okay what’s next

so you’ve solved your 40 rubik’s cube what else can you do well scramble it up

again like so and now try to blind solve it so how does that work well you’ve got

a scramble to you can look at it as long as you want then you put on your

blindfold and type in a key no that’s not going to work so they’ve got an

alternative setup for this what you do is you gray out what you see here and

now you try to solve this thing for memory and once you think it’s all in

place you ungraded nobody else has been able to do so for blinds of a 40 rubik’s

cube one person has been able to do the 2 by 2 by 2 by 2

nobody has been able to do this one something slightly less challenging

quite a few people have been able to do this to the 4 by 4 by 4 by 4 looks like

this or well nobody’s done that one bit tedious I suspect the nine by nine by

nine by nine or you could try this one here which is the 5 dimensional Rubik’s

Cube or if that’s not insane enough you could try this one here which is the

four dimensional counterpart of the megaminx 120 colors some people have

done this crazy okay but now here’s the real challenge ok here’s the real

challenge and I really want as many people as possible to go for this

challenge solve the 40 rubik’s cube and get yourself into the Hall of Fame so

the people who maintain the program also maintain a Hall of Fame and everybody

who solves the Rubik’s Cube can send in the log file and have their name

recorded in the Hall of Fame so Hall of Fame starts in 1988

it’s a fairly short list considering the time so it ends at 230 and that’s

actually me here the last entry on the 27th of May 2060 anything will count as

long as you get to the end you will get the mythology seal of approval and it

will be very remarkable achievement you

its not really a 4d hypercube though its just annother false perspective of 4d using 3d using 2d

ERROR 000 4rth dimetion not found, please restart your brain, for more information contact :www.omgwtficantimaginewhatimseeing.helpme

7:22 yes, it's called grabbing the corners of a flexible cube and twisting them after getting irritated because you can't solve it

I can solve an eleven dimensional Rubik's Cube it will only take me 456,000 years

so 2d dimensional projection of 3 dimensional cross section of a 4d hypercube

How about a 4D cube, which all the little cubes you can move individually.

those AND moving all the cubes and rearranging the cubes and then

I can't do this

I used this and his other video on this topic to solve the 4D cube – it helped a ton!! I had tried it before but had given up…but with this I managed to solve it!!!! Thank You Mathologer!

Explain the hypershpere

In the year since you posted this video, that hall of fame has grown by over 100. As of this comment, there are 337 entries on it, with the most recent from 11 days ago. I bet you had a lot to do with more people working it out. I've known about Magic Cube 4D for 10 years now, and even though I'm an avid cuber, it always seemed like too much. I'm gonna give it a go again, because after watching this video and the followup I'm pretty confident I can do it.

This video actually was the only thing on the entire internet that helped me visualize a 4D hypercube.

FYI, Matthew Sheerin just became the second person to solve the 2x2x2x2 blindfolded, and the first person to do it without using macros. Here is his video proof using this special build of MC4D: https://www.youtube.com/watch?v=UbLPxuSDRk8. The first blindfold 3x3x3x3 record remains up for grabs.

Hi, I thankfully appreciate you for sharing your knowledge on how to solve this puzzle, I conquered it, now I'm in the hall of fame at #339. I totally used your method and had to come up with 2 algorithms at the very end to solve the puzzle. I encounter this puzzle around 2 or 3 years ago, but it was totally insane when I saw the movements of the puzzle itself that I was too afraid to tackle it. Lately I've been watching youtube videos about Math and came across this video who opened a world for me to not be afraid or intimidated by the 4D cube. Thank you very much.

Could you 3D print this? I know itâs 4D but you could print that 3D representation

U can't solve it because it's represented in our 3-dimensional world

In a 2-dimensional screen

In your 1-dimensional brain

B U R N3D World: first game created: 2D

4D World: first game created: 3D

5D World: first game created: 4D

Then if each world creates its games shown in the dimension lower than the actual world.

Then… how does a 2D world create a game? 1D? Wouldnât it be so boring?

If so? Then how does a 1D world create games? 0D games?

Wait wait, If a 2D image of a 3D object is how we se it, would someone in 4D see it as a 3D hologram of a 4D object? Albeit on a 4D screen phone thing device

i believe this is the starting point in makeing a time machince . when the cube hit the 4 d mode it can not be seen because we are in 3d world. and our eyes only can see 3 d with this method we can work out the movement of the cube when it hits the 4d world . this is the starting point in time travel which i believe see 4d toys and watch the toy disappear from view that show time travel as the toy has enter another time frame it leave our view john

Does the 120-choron have a name? I doubt that I could solve it; not only would my head explode, but I doubt that I could see 120 different colours anyway.

Going the other way, I wonder if any 4D twisty puzzle simulator includes what I have dubbed the Pentaminx; a 4-simplex whose five faces are each a Pyraminx.

GOOD NEWS EVERYONE

We can't go there yet. We need to build a spatial dialator to spread out to greater dimensions.

The 4d Rubik's cube has only 7 cubes, but the tesseract has 8.

Pretty good corner cutting.

When will this be built

Boooooooooooo

Looks like you glued a 3×3 to a skewb

I wonder what kind of 4D things exist in the world like are there 4D animals we dont know about? Can 4D animals see us in 4D and 3D?

its not 4d its still 3d, its littarly just a bunch of bend rubiks cubes attached to eachother

look at this: http://www.bilibili.com/video/av11061559

manually solving 4d and 5d rubik's cube

Wait, if you can describe said 4th dimensional rubik's Cube, in 3 dimensions, without ANY more things to add, isn't it an overcomplicated 3d puzzle? (spoiler: it is) . If you look at 3d object from 2d perspective, you can not describe it perfectly, because you need 3rd axis. and if you look at said "4d" object, from 3d perspective, you can give each point a place on xyz axis. And i mean EACH.

I would like to get this out into the public domain:-

At school in 1948 at King Edward vi Grammar School Morpeth

Northumberland, when boys were bringing to school memorabilia that their

Fathers and Uncles had brought back from the war in Europe. One boy had

what I now know to have been a puzzle cube that rotated in the same way

that Rubik made his cube revolve. It was made out of wood and we thought

it very unusual and then went to play with our marbles and swapping comics. Over the years this

memory has haunted me and I wonder, has Rubik ever divulged where he got

his idea of the cube from?

is that a 10×10

/r/iamverysmart

3cubic5me

Did you just solve a tesseract?

wait… a 4D megaminx what the fuck… also, 5D 3×3 good fucking luck m8 if someone solves that my faith in humanity will be restored.

So basically, you put six force cubes around a force cube?

You made the 4d 2x2x2x2 yet? I already have trouble solving that.

I just put my head on a bucket to water cooling my cpu after watching this. :v

So to visualize 4 dimensions better, in a 3 dimension world surfaces are ''flat'' in ''2 dimension'' and in a 4 dimensional world surfaces are in 3 dimensions?

It's called a rubik's tesseract in the fourth dimension. (A tesseract is a 4d cube)

A 3d man playing with a 4d cube in 3d space from a 2d monitor.

Step one, throw against ground.

I would kill to see feliks zemdegs have a go at this!!

Hi

If only we had three dimesional vision so we could use it

Thanks, Mathologer! This video helped me solve the 4d rubik's cube. I ended up using some methods from blindsolving near the end of the solve as well.

Just realised, isnt the 2d rubiks "square" impossible?

1:01 I actually did that with my nearly cubical room.

Would it be solvable if you could only perform 3d moves on each individual cell? If you did a face-turn on one cell, you would cycle four columns on the connected cells, but would that be sufficient?

Is that a 10 by 10????

i had to skip around to prevent my brain from 'sploding Dx

STOP SAYING WORD EASY!!!

Just noticed I graphed your shirt: https://twitter.com/SumDumThum/status/958592169635434497

How do you do a slice move in Magic Cube 4D?

If it's a 4 dimensional rubik's cube, can't you just move it backwards in the 4th dimension to a point in which it's already solved?

Actually, not a 2d image at beginning… The led lights are not infinitely flat..

Interesting! However I really want to know Where I can get one of those T Shirtz??

Try to solve it xD

No

he's getting into understanding comics stuff here

for an simple human the difficulty number to solve the 3x3x3x3 rubiks cube is… 99999999999999999999999999999999999999999999999999999999999999999

and one thing toofrom today nobody have never done the one at 7:07

at 17:07

***************************sry i dnd't watch everything :xDThanks, I solved it with Your method! Although vastly ineffective, it works (with proper imagination).

The u perm u used is so complicated lol

I dont understand why it has 7 colors?

it takes me half an hour to solve ordinary 3x3x3 and now this… Impossibru!

a few weeks ago I had this graphic idea about geometric patterns of polygons …

A triangle….surrounded by a square…then a pentagon…then a hexagon…etc just like that one on his T-shirt….sharing the common center…. I've done it with a 2D CAD application.

This guy is great.

Just solved it today. It took 1329 moves.

At 7:33 the corners permutation is visually inaccurate

So under the stickers, there are other dimensions that are invisible so to speak? ( Dont worry, I'm not taking it apart. I get the point.).

Itâs easier to solve if you visualize it in actual 4d.

This video made me realized how this puzzle is not that far from a regular cube. I then gave it a go, and managed to solved it (after a few days)! I didn't use your method but I definitively thank you for allowing myself to consider that I can do it !

it would be really cool to see a transparent projection of the 8th folded cube

Fuck Rick and Morty, this just gave me 10000000 iq

These videos are ruining my recommended

But what is God's number for the 4D Rubik's Cube?

God level Math. I don't want to see 4d, Show us 8D.

Imagine living in 4 dimensional world, solving an abstract 5D Rubik's cube with 3D image of 4D image of this cube… xD

So the corner and edge flipping is the 4d equivalent to a parity

what would be harder to understand? women or this

So what would it look like if a 4 dimensional person was drawing on a piece of paper?

Illuminati: you better delete this f*cking comment.

Those intro chords sound like babushka. Is that just a coincidence?

Mathologer you should try Melinda's 2x2x2x2 puzzle; with that you can actually manipulate and solve a 3d version of the 2^4 hypercube!!!

the cube is wrong, a 3D cube has 6 sides then 4D cube has 8 volums/cubes

Now try to solve a cube in 4 dimensional

I have 80 dimensional house

444k subs

Like this because im begging fir likes cuz idot

Now here we go with the two dimensional beings that dont exist cant exist and will never exist…mumbo jumbo af

There are more billionaires than there are people who have solved the 4D Rubik's cube.

I'm impressed…..could you imagine earth and sun in 4d cause this is a fact …and we live in just one side earth and see on side of 4d sun…believe me…there are more people we didn't met yet!!!!!

This would be like trying to draw a cube in a line.

16:10 the gniffle when after he said "try to solve it with a blindfold" … priceless.

7:20 that corners permutation is impossible.

Anyone can solve a 4d petaminx?

…

I really should go and learn how to solve the 3x3x3 Rubik's cube.

I simply don't understand why have they not made a 3D "flattening" of a 4D cube and with an addition of an outside cube, because the initial 8th cube would be hidden from the other cubes, instead of this kind of projection.

I see chocolate pieces of different colours. I love chocolates! đ

oh, algorizms

I think your videos are rather different then most ways people think about stuff. I like your explanations they seem original / new ideas. Your on parallel with numberphile website. That solving the cubic using turtle lasers was so freak cool