# 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
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