Cuddly puzzle time with Mommy is when I take the concepts we just talked about and demonstrate them on the cube. If you're trying to follow along (even though I'm not qualified to teach you) and you run into one of these, just zoom me and we can try it without the cuddles. I don't know if that works. I only know the cuddling way works.
The Cuddlers
CHAPTER 1: THE FIFTEEN PUZZLE
Hi babies! Come to Mama.Are you ready to learn how to play with Mama's toys?
("Yes!" with lots of hugs. A moment to get comfortable and snuggly - Milli always needs extra time.)
Imagine you have a big bag of marbles in all your favorite colors! Your best friend has a birthday party in an hour, and we forgot to get a present, so you'll have to pick out some of your marbles and put them into a birthday bag to make a birthday present, okay? Did you imagine it? Did you pick them?
In the world of math, you just found a "combination." Any selection of a new group of marbles from your big bag of marbles is a combination.
Now let's pretend that your best friend's birthday party just got cancelled because of covid, and you get to keep all of the marbles after all. (We can get something else for your best friend later.) Let's take all the marbles from the birthday bag and dump them onto the floor and make them into a caterpillar. When we're building a caterpillar, we're making an arrangement instead of a selection.
In the world of math, an arrangement is a "permutation." We could scramble up your caterpillar and then make a new caterpillar from the same marbles!
Would we be making a selection or an arrangement?
An arrangement!
Would we be making another combination or another permutation?
A permutation!!
That's right. In fact, it would be the same combination as before!
A combination is a selection of things where the order/placement/position does not matter
A permutation is an arrangement of things where the order/placement/position does matter
Combination questions usually sound something like, "How many different groups of three marbles can we make make from the big bag of marbles?"
Permutation questions usually sound something like "How many different caterpillars can we make from the caterpillar on the floor?"
All our toys have things to rearrange, so our toys are called permutation puzzles.
Our first toy to play with is the Fifteen Puzzle!
Can you explain why the Fifteen Puzzle is not called a combination puzzle?
CHAPTER 2: THE IVY SKEWB
Now that you know what permutations are, it's time for your first twisty puzzle! The most famous twisty puzzle is the Rubik's Cube, and we'll get to that later. For now, we're going to learn how to solve the Ivy Skewb. It's very fun to twist!When you get a new twisty puzzle, one of the first questions you have to ask yourself is, "What twists when you twist it?" On the Ivy Skewb, if you look carefully, you'll see that every twist rotates a corner of the cube along with 3 ivy petals. See what an ivy petal is?
The next question you have to ask yourself is, "How many different twists are there?" It looks like there are 8, but there are actually only 4! Some of those corners are un-twistable. Just play around with it for a little bit, and don't be afraid to scramble it!
I'm going to teach you how to solve it very soon, but first you have to learn two more fancy words, okay? These are words that adults usually have lots of trouble learning, but you're kids, so you'll have no problem. The first one is "commutator," and the second one is "conjugate." Can you say them with me?
In math, sometimes we use letters to mean different things. Some of the math people's favorite letters are X and Y, and some of their other favorite letters are M and N, so I'm going to use those when I tell you what the new words mean. Ready to learn your new words? Just repeat after me.
A commutator is: X, Y, X-inverse, Y-inverse.
A conjugate is: N, M, N-inverse.
A commutator has 4 syllables and 4 parts.
A conjugate has 3 syllables and 3 parts!
Right. What if I asked you to build a commutator with the letters A and B?
A, B, A-inverse, B-inverse!
What if I asked you to build a conjugate with the letters A and B?
A, B, A-inverse!
Right! It doesn't really matter what letters we choose.
(Drakeson pointed out that they don't even have to be letters.)
Dragon, Snake, Dragon-inverse, Snake-inverse!
(Milli was not far behind.)
Pumpkin, Dragon, Pumpkin-inverse, Dragon-inverse!
(I told you I was only qualified to teach my own children.)
We'll start by practicing commutators! What are they?
X, Y, X-inverse, Y-inverse!
Right. Guess what? X and Y are going to be twists!
You pick them for me.
Which one is X? Which one is Y?
They have to be different.
(They select any two different twists)
If those are X and Y, can you guess what their inverses are?
Show me X. And X-inverse. And Y. And Y-inverse.
Now that you know what those are, do a commutator!
X, Y, X-inverse, Y-inverse.
That's the magic key to solving all of our puzzles!
Now that you know the magic key, we're almost ready to solve the Ivy Skewb for the first time.
Do you see how any twist X and any different twist Y only overlap by one ivy leaf? The overlap is called the "intersection" of X and Y. When the "intersection" of X and Y is only one piece, like this ivy leaf, then the X and Y commutator rotates three ivy leaves around. That's called a "3-cycle." There are lots of 3-cycles in our permutation puzzles!
Let me explain a little more about 3-cycles. Pretend there's a little tea table with three chairs, and Drakeson, Milli, and Mama are all having a tea party, and we're all sitting in the chairs and holding hands. We could keep holding hands, stand up, step over to the next chair, and sit back down. The way we shifted to new seats is called a 3-cycle.
We're going to rotate ivy leaves to different faces of the cube in 3-cycles.
The three leaves that are holding hands in the 3-cycle are:
1. the leaf in the intersection
2. the leaf that X brings to the intersection, and
3. the leaf that Y brings to the intersection.
Make sure you don't bring solved leaves into the intersection!
Otherwise, they'll get unsolved.
The best way to look at 3-cycles on the Ivy Skewb is with 3 ivy leaves that have touching tips. They'll match up on a corner that we can't twist.
(Demonstrations of 3-cycles).
Not only can we control which ivy leaves go into our 3-cycle by choosing which direction our X's and Y's move, but we can also control the direction of our 3-cycle by choosing the order of whether X or Y goes first.
It's time to scramble your Ivy Skewb!
The first step in solving the Ivy Skewb is to twist the corners around until all 6 square ivy leaf outlines match up. We're not moving the corners to different places because they can't even move to different places in the Ivy Skewb. That's pretty easy, right?
Now we have to solve the ivy leaves, and we mostly do that with commutators! Our magic key! If you choose an X that matches an ivy leaf with a corner, then after the commutator you will have already solved at least one ivy leaf! And if you also choose a Y that matches an ivy leaf to the other corner of the intersection face, then after the commutator you will have already solved at least two ivy leaves! It's SO MUCH FUN!!
CHAPTER 3: THE IVY SKEWB & CONJUGATED COMMUTATORS
But.....
If all your ivy leaves are sitting on one twist, we have to fix that with a conjugated magic key! Let's call that a skeleton magic key. Do you know what a skeleton key is? It's a key that can fit in many locks. Like in a hotel, a skeleton key might unlock all the doors in the hotel.
In the whole entire world?
That's not what I said.
Conjugates are sort of like that.
Well, actually, they move all the locks TO our magic key and move the locks back!
Remember, a commutator is: X, Y, X-inverse, Y-inverse.
And a conjugate is: N, M, N-inverse.
What if I took the commutator and used that as the "M" in the conjugate?
To help remember how to make a skeleton magic key, you can remember that "N" is in the word "conjugate" and "M" is in the word "commutator."
Here it is:
N
X, Y, X-inverse, Y-inverse
N-inverse.
Ready to try the skeleton magic key?
We need our N to move one of the ivy leaves off of the twist that has all 3 ivy leaves.
See how N moved one of the ivy leaves off the twist like we wanted? But it also moved 2 other ivy leaves too? Even though those 2 don't look solved, once we do our N-inverse later, they'll be solved again. So we won't worry about them. It's really important to keep track of which 3 ivy leaves we're trying to cycle.
After N, you find your intersection and do your magic key commutator.
Then N-inverse finishes your skeleton magic key!
(Big shiny eyes full of excitement)
I love you.
CHAPTER 4: THE DINO SKEWB
That Ivy Skewb is so easy now, isn't it? It's time for the next level - the Dino Skewb! The Dino Skewb is a lot like the Ivy Skewb, but it's just a little trickier. This time, there are 8 corner twists instead of 4, and all the pieces look the same! Each piece has two colors. But they don't look like dinos, do they? We could call them "triangle edges," but let's just call them "pterodactyls" instead. It's more fun that way.
Want to know why it's called the Dino Skewb?
Yeah!
Because a long time ago, there were pictures of dinos on the sides.
I'll show you what it looked like then.
Anyway, this time, the first step is to solve one side. The sides are called faces, but to finish a side "the standard way," you're going to have to learn what a Rubik's Cube looks like. Ready? There are four rules. Pay attention to the last one because that's the hardest to understand.
1. Red is opposite Orange.
2. Yellow is opposite White.
3. Green is opposite Blue.
4. When White is on the top and Red is on the Right, then Blue is on the Back.
If you know that, you can solve any side. Want to see?
Scramble your skewb and try solving just one side!
Did you check that when white was on top and red was on the right, then blue was on the back?
If not, then you have to rebuild your side!
You did it?!?
Did you notice what happened when you went from the third pterodactyl to the fourth one? You needed to use 3 or 4 moves instead of 1, right? And they weren't just any 3 moves! They were a conjugate or a commutator!
Let's scramble the skewb again and solve another side.
Pay attention to the conjugate or commutator you need for the 4th pterodactyl this time.
Now that your side is solved, you have to solve 5 more pterodactyls, all snuggling together in a clump, until there are only 3 left.
You can start using commutators any time, but you definitely need a commutator for the last 3 pterodactyls. Commutators are always your magic key! Just remember to bring the unsolved pterodactyls into the intersection! And if your X and Y don't have an intersection, you'll need your skeleton magic key again.
Just like with the Ivy Skewb, any two different but overlapping twists X and Y have an intersection of 1, so our dino commutators will always cycle 3 pterodactyls. Can you do it? IT'S SO MUCH FUN!! Mommy needs kisses now.
CHAPTER 5: STARTING THE PYRAMINX
The Ivy Skewb taught us about commutators and conjugates! Short commutators are magic keys, and conjugated commutators are skeleton magic keys.
The Dino Skewb taught us how to use short commutators or conjugates in blockbuilding, which is what it's called when you start putting pieces together into a block, and you keep them together while you add more and more solved pieces to your block. It's like when the pterodactyls are snuggling. In blockbuilding, it's okay to break up your block if you can fix it again right away.
Kids that can solve the Ivy Skewb and the Dino Skewb are definitely ready for the Pyraminx!! But I have to warn you, the Pyraminx is even trickier than the Dino Skewb. Do you know what a pyramid is? The Pyraminx is the shape of a 3-layer pyramid.
The corners are little one-layer pyramids, but they don't move into new places, so they're like the corner pieces on the Ivy Skewb. How many corners are there?
4!
That's right. That's also just like the corner pieces on the Ivy Skewb!
The 2-layer pyramids are what move around. How many pieces do those pyramids have?
5!
Mm-hm.
4!
That's right. That's also just like the corner pieces on the Ivy Skewb!
The 2-layer pyramids are what move around. How many pieces do those pyramids have?
5!
Mm-hm.
What can you tell me about the big piece in the 2-layer pyramid?
It's the core of the 2-layer pyramid.
And how many colors does it have?
3!
Just like with the Ivy Skewb and the Dino Skewb, a 2-layer pyramid twist X and another 2-layer pyramid twist Y have a 1-piece intersection, so a Pyraminx commutator will make a 3-cycle.
To solve the Pyraminx, we have to do four steps, but you already know how to do three of them. You still have your magic key, right?
Just like with the Ivy Skewb and the Dino Skewb, a 2-layer pyramid twist X and another 2-layer pyramid twist Y have a 1-piece intersection, so a Pyraminx commutator will make a 3-cycle.
To solve the Pyraminx, we have to do four steps, but you already know how to do three of them. You still have your magic key, right?
What's a commutator?
X, Y, X-inverse, Y-inverse!
Yep!
X, Y, X-inverse, Y-inverse!
Yep!
What's a conjugate?
N, M, N-inverse!
Mm hm! And what's a skeleton magic key?
N, M, N-inverse!
Mm hm! And what's a skeleton magic key?
N, X, Y, X-inverse, Y-inverse, N-inverse!
So smart.
Back to our four steps to solve the Pyraminx.
Back to our four steps to solve the Pyraminx.
We wont' scramble it yet! Just listen.
The first step is to twist the 1-layer pyramid corners so that they match the 2-layer pyramid cores.
(Milli says the solved tips with the 2-layer cores are "diamonds")
The first step is to twist the 1-layer pyramid corners so that they match the 2-layer pyramid cores.
(Milli says the solved tips with the 2-layer cores are "diamonds")
So the first step is to make 4 diamonds.
The second step is to twist the diamonds around until each face has matching diamonds. That's a lot like the first step in solving the Ivy Skewb!
The third step is to use your magic key a little bit, but it's not as easy as it was before. With the Pyraminx, it's possible for a piece to be oriented the wrong way! That didn't happen with the Ivy Skewb or the Dino Skewb!!
The orientation of a puzzle piece is which direction the colors on the sides are pointing.
So right now, which direction is my nose oriented?
Up!
What about now?
(Pointing and saying a variety of things)
That's right. You need to remember the new word oriented, okay?
K.
Before we go ahead and fully scramble the Pyraminx, let's cycle 3 pterodactyls with a commutator.
How can we re-solve the Pyraminx from here? Well, we can think about this in two ways. One way would be to undo everything we just did. That would be the inverse of the whole commutator. Let me show you.
Now I'll redo the commutator to talk about the second way.
The second way is to forget about how we created that 3-cycle and try to find a magic key that will put the pterodactyls back. Any of the 3 unsolved pterodactyls can be considered the intersection of an X and a Y. In fact, choosing the intersection actually chooses the X and Y! But only ONE of those choices can solve the Pyraminx. Let's try them all and see which one works.
(Cuddly puzzle time with Mommy)
With the Pyraminx, using our magic key without paying attention to any orientations won't necessarily solve everything the way it did in the other skewbs! We can still use our magic key, but sometimes we might want to use a more powerful, bigger key!
The fourth and final step uses big magic keys, and they're pretty fancy.
But you don't get to know about it until you pass your midterm!
You have to get 10 points to pass, and each question is one point. If you don't get 10 points, you can retake the test one time every day, and you'll always get hugs for trying.
You have to get 10 points to pass, and each question is one point. If you don't get 10 points, you can retake the test one time every day, and you'll always get hugs for trying.
1. Explain the words combination, permutation, and orientation.
2. Tell me, in letters or things, what a commutator is.
3. Tell me, in letters or things, what a conjugate is.
4. Tell me, in letters or things, what a skeleton magic key is.
5. Explain what an intersection is and how it relates to a 3-cycle.
6. Tell me the four rules for where the Rubik's Cube colors go.
7. Solve the Ivy Skewb for me.
8. Solve the Dino Skewb for me.
9. Show me a conjugate and its inverse on the Pyraminx.
10. Show me a commutator and its inverse on the Pyraminx.
Extra Credit: Solve one whole face of the Pyraminx!!
7. Solve the Ivy Skewb for me.
8. Solve the Dino Skewb for me.
9. Show me a conjugate and its inverse on the Pyraminx.
10. Show me a commutator and its inverse on the Pyraminx.
Extra Credit: Solve one whole face of the Pyraminx!!
Our first midterm exam required a retake because of question 5, which is the hardest and also most important question. We had to take my cube collection and play the "how many pieces are in the intersection of rotation X and rotation Y" game. Once we were able to identify intersections, it was easier to understand that
"A commutator creates a 3-cycle if the intersection of X and Y is exactly 1."
CHAPTER 6: THE PYRAMINX & LONG COMMUTATORS
Hi Sweethearts!You passed your test!!
Yay!!!
So far, we've been doing short commutators, but now it's time to learn about long commutators. Long commutators are the ones where X or Y have more steps, like X1, X2, X3 or Y1, Y2, Y3.
What do you think the inverse of (X1, X2, X3) would be?
X3-inverse, X2-inverse, X1-inverse!
What do you think the inverse of (Y1, Y2, Y3) would be?
Y3-inverse, Y2-inverse, Y1-inverse!
Great job.
With long commutators, a lot of the time, the X1, X2, X3 are actually conjugates.
Great job.
With long commutators, a lot of the time, the X1, X2, X3 are actually conjugates.
So instead of calling them X1, X2, X3, what could we call them?
N, M, N-inverse!
Right, but what if I wanted to call them all X's? Then what?
X1, X2, X1-inverse?
Yes! That's pretty tricky, huh?
Here's another tricky question.
What if I asked you what the inverse of X1, X2, X1-inverse is?
Could you figure it out?
X1, X2-inverse, X1-inverse!
Isn't that interesting? Look at it. Did you notice that the inverse of a short conjugate only changes the middle? This part is very tricky, and you're doing a great job.
Now come in close. We're about to build our first long commutator, which we'll call our first big magic key. You're going to want to pay attention, because big magic keys help you solve the Rubik's Cube!
If a short commutator, which is a magic key, looks like this:
X
Y
X-inverse
Y-inverse
Then a long commutator, which is a big magic key, looks like this:
X1, X2, X1-inverse
Y
X1, X2-inverse, X1-inverse
Y-inverse
Let's just look at that for a little while.
X
Y
X-inverse
Y-inverse
Then a long commutator, which is a big magic key, looks like this:
X1, X2, X1-inverse
Y
X1, X2-inverse, X1-inverse
Y-inverse
Let's just look at that for a little while.
Ready to move on?
Let's try building a big magic key with a short conjugate in the Y. That would look like this:
X
Y1, Y2, Y1-inverse
X-inverse
Y1, Y2-inverse, Y1-inverse
X
Y1, Y2, Y1-inverse
X-inverse
Y1, Y2-inverse, Y1-inverse
Here's the thing - using the big magic key is step 4 in solving the Pyraminx!
I usually use the big magic keys with the long X parts.
Let me show you.
(Mommy does a skeleton big magic key to set this up)
First we have to find two unsolved edges that are on one face of the Pyraminx.
Also, one of them has to be oriented correctly to that face.
Here we have two unsolved edges on the yellow face, and we're looking for one of them to have the yellow color on the yellow face. Let's figure out a name for those pieces.
The one that matches the face can be called the chameleon, because chameleons can camouflage to match what they're next to. Next, we need to name the other one on the same face. Maybe something a little bit similar because they're on the same face. What's another reptile pet?
A bearded dragon!
Thank you, Drakeson.
Milli, you get to name the third piece.
It's from somewhere else - not the yellow face.
So what's another kind of animal?
A bird.
Okay! What kind of bird? A parrot.
It's finally time to start the Rubik's Cube! I know you want to get started right away.Thank you.
So we have a chameleon, a bearded dragon, and a parrot.
The chameleon and the bearded dragon start off on the same face.
The chameleon camouflages and matches that face.
And the parrot is flying somewhere else, away from that face.
Got it? Now we're ready to use our big magic key to make a 3-cycle!
The chameleon will go to the bearded dragon's spot.
The bearded dragon will go to the parrot's spot.
The parrot will come to the chameleon's spot.
Make sure you know that really well before we go on.
First we use a conjugate, X1, X2, X1-inverse, to get the chameleon out of the yellow plane, replace her with the parrot, and bring the parrot down to where the chameleon was.
First we use a conjugate, X1, X2, X1-inverse, to get the chameleon out of the yellow plane, replace her with the parrot, and bring the parrot down to where the chameleon was.
There's only one way to do that correctly and solve the parrot.
Always think about solving the parrot when you're picking your X1 and X2!!
See how the parrot is now in the yellow plane?
THAT'S THE INTERSECTION OF (X1, X2, X1-inverse) and Y!
It's really really important to understand that.
The next step is Y, and we have to bring the bearded dragon into the intersection.
X conjugate inverse solves the chameleon and also solves the bearded dragon.
Y inverse rotates the yellow plane back into place so that all the diamonds match again.
I know it's complicated, but this is the hardest part of the whole course.
To completely finish solving the Pyraminx, all we have to do is get used to using our big magic keys and skeleton big magic keys!! Without me telling you anything else, can you tell me what that would be?!?
This is a regular big magic key.
X1, X2, X1-inverse
Y
X1, X2-inverse, X1-inverse
Y-inverse
Y
X1, X2-inverse, X1-inverse
Y-inverse
Remember how a conjugate is N, M, N-inverse?
A skeleton big magic key would put all of that into the M of a conjugate!
N
X1, X2, X1-inverse
Y
X1, X2-inverse, X1-inverse
Y-inverse
Y
X1, X2-inverse, X1-inverse
Y-inverse
N-inverse
Let's go through some more examples together, but first, write down your big magic keys and skeleton big magic keys!! We can look at your paper while I solve the Pyraminx a few times!
(Cuddly puzzle time with Mommy)
CHAPTER 7: THE KILOMINX
The Kilominx is one of my very favorite puzzles. Instead of a being in the shape of a cube or a pyramid, it's a dodecahedron. Count the number of sides. How many sides does a dodecahedron have?
12!
Yes, and what's the shape of each side?
A pentagon!!
Good job, Drakeson.
The good news about the Kilominx is that you already know everything you need to know. First you have to do some blockbuilding, and then you have to use some big magic keys and skeleton big magic keys. That's all.
What's a big magic key?
X1, X2, X1-inverse
Y
X1, X2-inverse, X1-inverse
Y-inverse
Y
X1, X2-inverse, X1-inverse
Y-inverse
What's a skeleton big magic key?
N
X1, X2, X1-inverse
Y
X1, X2-inverse, X1-inverse
Y-inverse
N-inverse!Y
X1, X2-inverse, X1-inverse
Y-inverse
Watch me solve it once. We'll talk about what we're doing every step of the way, and then you can try. It's even more fun than ANY of the permutation puzzles we've done so far!!
For our skeleton big magic keys, we might need to write down the names of faces for our N's.
R - red
O - orange
Y - yellow
L - leafy green
F - forest green
S - sky blue
C - cobalt blue (neither one of them had ever heard of cobalt)
V - violet
P - pink
W - white
G - grey
T - tan
Do you know about clockwise and counterclockwise?
No.
Sigh.
(Cuddly puzzle time with Mommy)
That's it for this chapter. Now you just get to play with the Kilominx until it's easy.
The Kilominx has 20 pieces and the Pocket Cube, your next puzzle, has only 8. But the Pocket Cube is NO JOKE. In fact, when Daddy first met Mommy, he had a Pocket Cube that neither of us could solve. Mama was determined to learn how to solve it to show Daddy she was smart and win his heart forever! It worked!
CHAPTER 8: THE POCKET CUBE
The Pocket Cube is really hard, and that's because every twist rotates half the pieces. When a puzzle is like that, you have to use your keys and trust them, no matter what you're seeing! Every magic key on the Pocket Cube makes it look really scrambled for a while.
Look at the Pocket Cube. Tell me what you see.
D: It looks like a cube with 8 cubies that is really small.
M: It looks like there has a bunch of pockets. And it's super hard to solve.
D: And it can fit into pockets.
M: And the curved centers look like pockets.
The first step is to choose a color and solve one layer with blockbuilding.
That's the easy part - you just need conjugates for that.
Next, you have to make sure that there are 3 unsolved corners in the unsolved layer.
Sometimes there are only 2, and that's tricky.
If the 2 are in their spots but oriented incorrectly, you need a new tool!!!
It's another big magic key where there are 6 X's instead of 3!!
What should we call it?
M: A 6-X magic key!
D: A 6-edged magic key!
Okay, a 6-edged magic key it is.
It makes 2 corners twist!!!
Let me show you what it looks like.
(Cuddly puzzle time with Mommy)
Sometimes there will be only 2 but they're not in their correct spots. When that happens, you have to change it into 3, because our keys make 3-cycles.
You already have two tools to turn the 2 unsolved corners into 3.
The first is rotating the unsolved face, and the second is your big magic key.
Let's see what this looks like.
(Cuddly puzzle time with Mommy)
Once you have 3 unsolved corners, you just need a big magic key or a skeleton big magic key!
I'm going to have you watch a few solves and I'll explain what's going on the whole time.
You'll tell me if we need big magic keys or skeleton big magic keys.
For our skeleton big magic keys, we might need to write down the names of faces for our N's.
U - up
D - down
R - right
L - left
F - front
B - back
(Cuddly puzzle time with Mommy)
Kiss kiss kiss.
CHAPTER 9: THE RUBIK'S CUBE BLOCKBUILDING
Out of all the puzzles we've done, the Kilominx was the only one that came with solved centers. But guess what? The Rubik's Cube is just like that. It has 6 solved centers, and they follow the rules about where the colors go that we learned when we were doing the Dino Skewb. Usually, people think of the centers as one big 6-part center piece.
The other pieces are either edge pieces or corner pieces.
How many colors does an edge piece have?
2!
Right. And how many edge pieces are there?
12!
How many colors does a corner piece have?
3!
And how many are there?
8!
Right!
And what do you know how to permute - edge pieces or corner pieces?
(Hint - think about the Pocket Cube!)
Corner pieces!
That's right!
Because edge pieces are the hard ones, we have to start our blockbuilding with edge pieces! If we started with corner pieces, then we'd just get stuck when it was time for edges. Nobody wants that.
Most people talk about starting the edge blockbuilding as "building the cross," which is a solved cross shape of 4 edges and 5 centers. That's fine, but let's not worry about that. I want you to build a little cube instead, which might be a little harder. Mommy is so mean!
M: Mommy is so mean that we can't even go to shapeshifters!-----------
D: I don't think Mommy is even being mean at all.
M: No, you have to say something bad.
D: No, I don't have to.
First, instead of 4 edges and 5 centers, I want you to build 2 edges and 3 centers, and then fill in the cube with a corner and another edge. But look, I'll help you. Watch.
First, we build the frame with 2 edges and 3 centers using short conjugates or magic keys. That's like a little part of a cross.
Then we can try to fill in the part that's missing, which is a corner piece and another edge piece.
To do that, we have to figure out which pieces we want.
Then we have to put them together.
Then we have have to put them into our little cube with another conjugate or magic key.
(Cuddly puzzle time with Mommy)
If that's too hard, there's another way.
We can first put the corner into the cube with a conjugate or magic key.
Then we can pull the corner out and put it next to the edge with a magic key.
Then we can put them both back with a magic key.
None of this will be too hard since you can already solve the Kilominx, and you had to do lots of blockbuilding there. I'll show you.
(Cuddly puzzle time with Mommy)
Once we have our little cube, we can solve another leg of the cross and fill it in again.
After that, we'll have a block that's 2x2x3 big!
(Cuddly puzzle time with Mommy)
Once we have our 2x2x3 block, we can solve the last leg of the cross and fill in one more side. I know everybody else likes to fill in all the sides, but I don't! We're going to leave one side unsolved, because that's going to help us with the edges. That's it for today. In your last lesson, we'll finish learning how to solve the Rubik's Cube!
It's time for Mama sandwich kisses!
CHAPTER 10: FINISHING THE RUBIK'S CUBE
Let's take a moment to talk about everything you know!
You know the difference between combinations and permutations.
You know what commutators and conjugates are.
You know what intersections and 3-cycles are.
You know what the orientation of a piece means.
You know what blockbuilding is.
You know that your magic key is a commutator.
And that your skeleton magic key is a commutator inside a conjugate.
And that your big magic key is a commutator with a conjugate in one part.And that your skeleton big magic key is a big magic key inside another conjugate!
And that your 6-edged magic key twists two corners!
And you can solve an Ivy Skewb.
And you can solve a Dino Skewb.
And you can solve a Pyraminx.
And you can solve a Kilominx.
And you can solve a Pocket Cube.
And you can blockbuild a whole bunch of pieces on the Rubik's Cube!
WOW!!
You only have two steps left until you graduate!
Remember how Mommy wanted to leave a path in the first two layers of the Rubik's Cube? That's a really special path that reorients edges without ever using magic keys. We could think of it like a magical path, really. We have to use the magical path to solve the last 5 edges, and this is a really fun puzzle all by itself. Let's call this part the magical path puzzle.
Our first step in the magical path puzzle is to use conjugates with our magical path to orient at least 3 edges on the unsolved layer. Let me show you.
(Cuddly puzzle time with Mommy)
Our second step is to try to make it so that exactly 2 of our 5 edges are solved. That's because we always move things around in 3-cycles, so we need to leave exactly 3 unsolved.
(Cuddly puzzle time with Mommy)
Our last step is to use one more conjugate with our magical path to finish all the edges!
(Cuddly puzzle time with Mommy)
And once the edges are solved, do you know what's left?
What?
Just 5 corners. And you know how to do 5 corners already because you learned everything you need to know about corners with the Pocket Cube! Big magic keys and skeleton big magic keys are all that you need now!
Let's try it together!
(Cuddly puzzle time with Mommy)
Congratulations sweethearts!!
(Shiny eyes & hugs)
(GRADUATION RUBIK'S CUBE PRESENTS!!)
Fifteen Puzzle, Ivy Skewb, Dino Skewb, Pyraminx, Kilominx, Pocket Cube, Rubik's Cube
Materials (QiYi brand, Stickerless)
EPILOGUE
Now that you've graduated, you can play with Mommy's Megaminx! It's like the Kilominx and the Rubik's Cube together, and it's one of my very favorites. There are also a lot of shapeshifters that are based on the Rubik's Cube, so we can also play with those too.
If you want to try to read Mama's adult posts when you're older, the first post teaches more about edge commutators, reorienting-corner commutators, and reorienting-edge commutators. The reorienting commutators are even bigger magic keys, because the X in the commutator has TWO conjugates inside it instead of one! So instead of 3 X's, there are more like 6. The second post talks about why some permutation puzzles seem impossible sometimes, and how to fix that. But like I said, that's for when you're older.
I'm very proud of you.
Beautiful, Lan. Really nice.
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