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

by birtanpublished on September 4, 2020

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 to 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 a kind of a solid surface how many faces can you see max when you can 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 do you see is five faces and actually can't 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 start thinking inside

The box now this actually is a view of a rubik's cube simulator so the rubik's cube simulator actually shows it a cube like this so it's a lot better than what you see normally when you look at something like this fall in your hand

Here's a couple of twists there now that one is actually when you turn the rubik's cube and that gets a straight away to our 40 rubik's cube so there 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 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 40 rubik's cube well no it's not the 40 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 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 we want to do okay let's have a look here let's some twists you can see it's a lot more complicated and 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

I 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 harp voice there and something similar is the case was the forty rubik's cube it was the 40 rubik's cube at first at 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 it's first the face cube is there 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 there in the corner here there on the edges here so see those those three cubicle stickers they belong together as you manipulate the cube they will always stay together either wirelessly they can

Never be separated they form one hypercube and then we've got one more type of hyper cutie these are the corner hypercube YZ 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 here 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 this 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 they'll 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 faceless just to show you what I mean by this

Let's just focus on one of those corner twists and so there it is and now I'll undo this corner twist but us doing 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

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 algorithm to solve the whole cube in fact four is enough so you need like one algorithm to recycle three edges of the Rubik's Cube then there's another one here one dead cycles three corners and

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 so 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 what we're actually looking at usually isn't an exploded view is just a rubik's cube but 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 Elgar's and 3d rubik's cube algorithms on it 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

2 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 2 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 algorism into one that actually affects the middle but us 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 now 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 face hypercube each so

What gets cycled here in particular is three face hypercube is and here again every column has one of those face I / Q isn't it these get flipped so what you can do is you can use these algorithms 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 other bits that get pushed around here which is all edge hypercube is the second trick now which makes things very clean okay 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 is this is though so what I want is something like this so this edge

Hypercube me that one and that one just those cycles around with nothing else going on and we do this with commentators and if you watch my other Rubik's Cube video we're familiar with it otherwise maybe watch it so what we

Will do is we'll just twist the top so we'll be 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 wrote it in a way to wait away before okay so let's just do this so this one here in Reverse let's 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 we 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 it's just like this a Rubik's Cube a kind of 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 magically 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 effects 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 raisin for positioning the face hypercube ease and for orienting them

We've got algorithms ford edge hypercube ease and we've got algorithm for the corner hypercube is actually in the middle you see we've got actually lots of algorithms 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 when you create them create both of them ok 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're also fairly easy to locate so

For example if we look at the cell here in the middle there's going to be you know 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 the 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 cycling 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 interface that you're dealing with how

To create lock files how to create macros how to you know create those either isn't it eventually hopefully you get to fixing up all the edges and then well the corners remain and with the corners

A similar kind of surprise waits for you at the end you may have solved a 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

It scramble to you can look at it as long as you want and you put on your blindfold and type in a key no it'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 ungrateful a'somethin that nobody else has been able to do so far blinds of a 40 rubik's cube one person has been

Able to do the two by two by two by two nobody has been able to do this one something slightly less challenging quite a few people have been able to do this to the four by four by four by four 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 five 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 okay here's the real challenge and I really want as many people as possible to go for its 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 last entry on the 27th of May 2016 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

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