The Mathematical Marvel Of The Rubik's Cube

This episode delves into the fascinating world of Rubik's Cube and its deep connections with mathematics, as explored through the eyes of a competitive cuber and math enthusiast.

1. The Rubik's Cube can be solved in numerous styles, including unconventional methods like using feet or solving blindfolded.
2. Mathematical strategies akin to algebra are essential for solving the cube efficiently, with sequences of moves termed as algorithms.
3. The cube offers a real-world application of permutations, illustrating complex mathematical concepts in an accessible way.
4. "God's number" is 20, representing the maximum number of moves needed to solve the cube from any configuration.
5. Roman Chavez uses the cube as a tool for education, demonstrating its potential beyond just a puzzle, fostering problem-solving skills and enjoyment in learning.

1: Introduction to the Rubik's Cube

This chapter sets the stage for the 50th anniversary of the Rubik's Cube and introduces Roman Chavez, discussing various styles of competitive cubing. Emily Kwong: "You might have messed around with a Rubik's cube at some point."

2: The Mathematics of Cubing

Explains the mathematical concepts used in solving the Rubik's Cube, likening the process to following a recipe or solving algebraic equations. Roman Chavez: "It's sort of like a recipe. If you apply enough of the algorithms, you get the solve."

3: Permutations and God's Number

Details the complex calculations behind the 43.2 quintillion permutations and discusses "God's number." Roman Chavez: "You have about 15 seconds of inspection time, and then after that 15 seconds is over, it's just like everything just kind of like silences."

4: Educational Impact of the Rubik's Cube

Focuses on Chavez's efforts to teach cubing to youth and his personal connection to the cube. Roman Chavez: "It's just me and the cube. I'm like, the only person I'm competing against."

1. Learn basic algorithms: Start with simple sequences to familiarize yourself with the cube's mechanics.
2. Practice different solving styles: Try various methods like one-handed or blindfolded to improve dexterity and memory.
3. Use the cube to teach math concepts: Employ the cube as a fun tool to explain complex subjects like permutations.
4. Join cubing communities: Engage with other enthusiasts to share strategies and improve skills.
5. Teach others: Share your knowledge of cubing with young learners to inspire interest in mathematics.

The Rubik's Cube was created 50 years ago by Hungarian inventor Ernő Rubik. Since then, over 500 million of them have been sold. We dive into this global phenomenon that's captured the imagination of countless people around the world and inspired all kinds of competitions — even solving with your feet! But no matter the cube, the process of solving one involves math — specifically, algorithms. Roman Chavez loved Rubik's Cubes so much, he founded the Jr. Oakland Cubers in high school. Now a mathematics student at Cornell University, Roman talks to host Emily Kwong about how to solve the cube and what life lessons he's learned from the cube.

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Emily Kwong
You're listening to short wave from NPR.

Hey, short wavers. Emily Kwong here. Okay, so this month, it is the 50th anniversary of the invention of the Rubik's cube, and that has gotten me deep into the world of speed cubic solving these puzzles as quickly as possible.

Roman Chavez
Yes.

Emily Kwong
You might have messed around with a Rubik's cube at some point. The standard one is six colors, one on each side, and each side is made up of nine cubes. And at these competitions, these cubes are everywhere.

Roman Chavez
Some people solve them with their feet, some people solve them with one hand. Some people solve them blindfolded. And then one of the other competitions is least amount of moves.

Emily Kwong
With their feet?

Roman Chavez
Yes, with their feet.

Emily Kwong
Have you been to. Have you seen this in real life?

Roman Chavez
I have seen this in real life, yeah.

Emily Kwong
That's astonishing. So what's your competition?

Roman Chavez
My competition is just standard three by three by three.

Emily Kwong
This is Roman Chavez. He's from Oakland, California. He told me there's many kinds of competitive cubing events. It's like a Rubik's cube Olympics.

And the muscles you're using are mathematical.

Roman Chavez
I often related it to algebra. I would say, well, if we're solving for x, think of one of those pieces on the Rubik's cube as x, and we're trying to get it somewhere.

Emily Kwong
In cube lingo, a series of moves is called an algorithm.

Roman Chavez
It's sort of like a recipe. If you apply enough of the algorithms, if you follow all the recipe, you get the cake or whatever, you get the solve the Rubik's cube.

Emily Kwong
And in a competitive environment, you have to do this as quickly as possible.

Roman Chavez
There is a judge next to you, and when your name is called, you give your cube to this person, who will scramble it, and then they'll put a cup over it, and then they lift up the cup, and then the rivets cube is there on that, like, on that plate. And then that's when your inspection time begins.

Emily Kwong
For some reason, I'm picturing, like, iron chef, you know, when they, like, lift off the COVID and it's like. And the protein of secret is fish.

And then you have to, like, apply all the knowledge you have of fish, which connects to your recipe metaphor from earlier.

Roman Chavez
Oh, my gosh.

Emily Kwong
Okay. How many different ways do I know how to cook a fish. And how quickly can I cook a fish?

Roman Chavez
Now that is exactly what is happening. Yeah, I like, I would have never thought of that. That's. That's incredible. You have about 15 seconds of inspection time, and then after that 15 seconds is over.

It's just like everything just kind of like silences.

Emily Kwong
Nowadays, Roman studies pure math at Cornell University, and he attributes a lot of his early fascination with math to the rubik's cube. How do you feel when you're solving a rubik's cube?

Roman Chavez
Oh, man, I feel amazing.

It's just me and the cube. I'm like, the only person I'm competing against.

Emily Kwong
So today on the show, happy 50th birthday to the Rubik's Cube. We are throwing a party. What can this rainbow colored piece of plastic tell us about math? And, according to Roman, about life? I'm Emily Kwongenhe, science Podcast from NPR.

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Emily Kwong
Roman Chavez loved Rubik's cubes so much that in high school, he founded the junior Oakland Cubers. He went around to tribal centers and community spaces, all these places in Oakland, to teach other students math and the secrets of the Rubik's cube.

Roman Chavez
I've taught over 600 youth. Now I think I've taught about over 1000. Wow. Yeah.

Emily Kwong
And now he's gonna teach me. Okay, Roman, so solving the cube, is it a little like pattern recognition? Like, you look down at the cube, you're like, oh, I know what this is. And this algorithm will solve it, and I'm gonna incorporate it as quickly as I can. At which point you are then using your fingers.

Roman Chavez
Yes, exactly. So you can look at the Rubik's cube, and you'd be like, okay, all right, this color is there, that color is there. This piece is there, and I have that piece there. And so I need to apply this algorithm to get those pieces where I want them to be. And so the more cases that you're met with, by the way, there's like 43.2 quintillion permutations on the Rubik's cube. And so.

Emily Kwong
Oh, my gosh, what is a permutation?

And how does, like, playing around with a Rubik's cube help a person understand that?

Roman Chavez
So think of soda cans.

You have three sodas. You have a sprite, a doctor pepper and a coke.

Emily Kwong
Okay?

Roman Chavez
And you're going to reorientate the order of the sodas to get, say, doctor pepper, sprite and coke. So you switch those first two, you can play around, switch with some others. So say you have sprite, coke, doctor pepper, and that's already three permutations.

And then the way you place the second soda, you have two possibilities depending on where you put the first one. And then where you put the last one, you only have one possibility.

And so that's three times two times one, and that's six. So there's six total possibilities that you can orientate these soda cans.

Emily Kwong
Got it. Okay. So how does this concept then apply to the Rubik's cube? How do we get to the number 43.2 quintus permutations?

Roman Chavez
Let's think about it. You have twelve edges on the Rubik's cube. You have eight corners and you have six centerpieces.

Now, the Rubik's cube is a high step from those three soda cans because there's a lot more interacting with each other.

If we want to find out how many permutations there are on the Rubik's cube, we have to do eight factorial because there are eight corners on the Rubik's cube.

Emily Kwong
Right. Okay. Factorial being when you multiply a number by all the smaller positive whole numbers below it. So like eight times seven times six all the way down to one, that would be eight factorial.

Roman Chavez
Yeah. So you have to multiply that by three to the 7th power because there are only three possible ways a corner can be oriented.

Emily Kwong
Oh, my gosh.

Roman Chavez
And then you have to multiply that by twelve factorial, because there are twelve edges.

And then since there are two colors on each edge, that is two to the 11th power because there's eleven other positions, you have to multiply that by six because there are six center pieces.

And then what you do is you divide that all by twelve and when you divide that by twelve, you get 43.2 quintillion permutations.

Emily Kwong
Oh, my gosh.

Roman Chavez
Those are the amount of permutations that are actually solvable. Yeah.

And if you only calculated that number without dividing by twelve, you would get all the possibilities that you can have on the Rubik's cube. That would be like taking off the stickers, reorientating them around, which, thank goodness, right?

Emily Kwong
Can you imagine?

Roman Chavez
Right. That would be so many more permutations and what?

Emily Kwong
Yeah, it would break the human priority. Exactly.

So, going back to competition mindset, let's say you sit down, you lift the COVID off to reveal the cube that is yours to solve, and you recognize a pattern. Okay, but there are still multiple different ways to solve any single pattern, right?

Roman Chavez
Yes. And that goes down to this idea of God's number, where it has been proven that you can solve a Rubik's cube in 20 moves, and on average, you can solve it in 18 moves.

Emily Kwong
God's number. Okay, I'm looking this up. So it looks like to figure out God's number, mathematicians had to use a bank of supercomputers at Google to run through all the possible solutions and prove that every permutation, like, all 43.2 quintillion, could be solved in just 20 moves.

Roman Chavez
Oh, yeah.

Emily Kwong
But, like, is that the goal? To solve it in as close to 20 moves as possible?

Roman Chavez
To solve it in 20 moves, you would have to be a superhuman.

Emily Kwong
Oh, okay.

Roman Chavez
Yes.

Emily Kwong
Okay.

Roman Chavez
And so, like, in a standard solve for someone, solving it in 6 seconds or 7 seconds, usually they're doing like, 50 or 60 moves, but they're doing it so fast with the ways they're manipulating the cube that it might not seem like it's that many moves.

Emily Kwong
Got you. But you're solving for speed. When you're doing competitive cubing, you're not worrying about the number of moves. Is that right?

Roman Chavez
Right.

Emily Kwong
That makes sense. Okay, so, roman, you have a watertight four step strategy for quickly solving a Rubik's cube, and you are going to teach it to me right now.

What is the secret?

Roman Chavez
It's called cfop.

CFOP stands for the c in c. Fop stands for cross the f, and c. Fop stands for finishing the first two layers, and then the o stands for orientating the last layer, and then p stands for permutating the last layer.

Emily Kwong
What is happening for you as you go through that?

Roman Chavez
Yeah, so I see a scrambled cube when I. When I pick it up and.

Emily Kwong
Yep.

Roman Chavez
What I look for immediately is I look for the color that I'm solving with the standard color people solve with is white. I solve with blue because that's the way my professor solved it. And so I'm immediately looking for blue edges around the Rubik's cube. I look for the fastest way with the least amount of moves that I can put these blue edges on the blue center. That develops the cross.

Emily Kwong
That's the first step, z cross. Okay.

Roman Chavez
And then I'm looking for blue corners. So a corner has three colors on it, and, um, I have to match the side colors with the sides of the center pieces. Essentially, what I'm doing is I'm solving the first layer.

Emily Kwong
Right, which is part of the second step, finishing the first two layers. Okay.

Roman Chavez
And then I'm just missing four. Four more squares each of the corners. And then what I have to do is I have to put the correct edges in the second layer, and that develops the second layer.

Emily Kwong
So, what's orientating last layer and permutating last layer?

Roman Chavez
Yeah. Okay. That's a good question, because the Rubik's cube, it looks like it's. It's almost solved. It's not solved yet. You have this mixture in the last layer. So orientating the last layer is just finishing the opposite side that you're solving with. So, I'm solving with blue. The opposite color of blue on the Rubik's cube is green. And so orientating the last layer is orientating those greenhouse pieces to be solved.

Emily Kwong
You know those puzzles where it's like a jigsaw puzzle, and you have to slide pieces into place, and you create a picture, and there's one blank space, and you shift it all around? Do you know what I'm talking about? This is like a kid's toy.

Roman Chavez
Oh, yes. I think I do know what you're talking about.

Emily Kwong
So, the thing about those I always remember as a kid is like, well, if I move this one piece, it's gonna mess up this other thing, which will mess up this other thing, which will mess up this other thing, and you can get really stuck in. Like, if I do this, it'll take it in a direction that I don't want. So, how do you, like, control the forward movement of the solving, knowing you have to kind of mess it up to make it work?

Roman Chavez
When you're solving something like, say, for instance, you solve the first layer, and you're really happy, you're really excited because you solve the first side of the Rubik's cube. But then once you're solving the second layer, you find out that you actually have to break.

Emily Kwong
Right.

Roman Chavez
The bottom layer. You have to break the first layer. You're breaking the work that you just did, and you might think it's counterintuitive, like, why am I doing this? But the idea is that it's temporary and you're only breaking it for an instance.

Emily Kwong
Yeah.

Roman Chavez
You have to trust yourself that you're gonna fix it later, even though it might look broken right now.

Emily Kwong
Roman, there is a beautiful life lesson in there, right, that you have to break what you built in order to get to that next step.

Roman Chavez
Yeah, absolutely.

Emily Kwong
So the Rubik's cube has turned 50 this year, and I guess, you know, this puzzle has been such a big part of your life, and I'm wondering how you see it playing a role in your life moving forward.

Roman Chavez
It's really been the foundation of, really, everything.

I'm not here to be the fastest Rubik's cube solver. I'm here to inspire and teach others.

And I love the joy and excitement that someone gets, even, especially youth.

I love it when they can have this huge smile on their face after they have accomplished solving the Rubik's cube.

I love that part about the Rubik's cube. That's my favorite part.

Emily Kwong
I'm so glad you added that. Thank you.

Roman Chavez
You're welcome, Emily.

Emily Kwong
This episode was produced and fact checked by Hannah Chin. It was edited by our showrunner Rebecca Ramirez. Beth Donovan is our senior director, and Colin Campbell is our senior vice president of podcasting strategy. I'm Emily Kwong. Thank you for listening to short wave from NPRDez.

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