Anecdota

Laughter is the Best Medicine

Cracking the 4D Rubik’s Cube with simple 3D tricks


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 🙂 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

100 thoughts on “Cracking the 4D Rubik’s Cube with simple 3D tricks

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

  2. 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

  3. 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

  4. 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!

  5. 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.

  6. 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.

  7. 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.

  8. 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 N

  9. 3D 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? Wouldn’t it be so boring?
    If so? Then how does a 1D world create games? 0D games?

  10. 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

  11. 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

  12. 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.

  13. 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?

  14. 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.

  15. 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?

  16. 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.

  17. 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?

  18. 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.

  19. 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?

  20. 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?

  21. 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

  22. 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.

  23. 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.).

  24. 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 !

  25. 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.

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

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

  28. 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!!!!!

  29. 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.

  30. 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

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