Short Wave - The Mathematical Marvel Of The Rubik's Cube

Episode Date: July 31, 2024

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. Interested in more math episodes? Email us at [e-mail] pcm.adswizz.com for information about our collection and use of personal data for sponsorship and to manage your podcast sponsorship preferences.NPR Privacy Policy

You're listening to Shortwave from NPR. Hey, shortwavers, 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. 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. 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. With their feet? Yes, with their feet. Have you seen this in real life? I have seen this in real life, yeah. That's astonishing.

So what's your competition? My competition is just standard three by three by three. 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. 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. In cube lingo, a series of moves is called an algorithm. 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 solved Rubik's Cube. And in a competitive environment, you have to do this as quickly as possible.

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 Rubik's cube is there on that plate. And then that's when your inspection time begins. For some reason I'm picturing like Iron Chef, you know, when they like lift off the cover and it's like, and the protein of secret is fish. And then you have to like apply all the knowledge you have a fish, which connects to your recipe metaphor from earlier. Oh my gosh.

Okay, how many different ways do I know how to cook a fish and how quickly can I cook a fish now? That is exactly what is happening. Yeah. I would have never thought of that. 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.

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? Oh, man, I feel amazing. It's just me in the cube. I'm like the only person I'm competing against. 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 Kwong. You're listening to Shortwave. Science Podcast from NPR. Roman Chavez loves 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. I've taught over 600 youth. Now I think I've taught about over 1,000. Wow. Yeah. And now he's going to 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 going to incorporate it as quickly as I can, at which point you are then using your fingers. Yes, exactly. So you can look at the Rubik's cube, and you 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... Oh my God.

What is a permutation? And how does like playing around with the Rubik's Cube help a person understand that? So think of soda cans. You have three... sodas. You have a sprite, a Dr. Pepper, and a Coke. Okay. And you're going to reorientate the order of the sodas to get, say, Dr. Pepper, Sprite, and Coke. So you switch those first two. You can play around, switch with some others. So say you have Sprite, Coke, Dr. 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. Got it. Okay. So how does this concept then apply to the Rubik's Cube? How do we get to the number of 43.2 quintillion permutation? Let's think about it. You have 12 edges on the Rubik's cube. You have eight corners and you have six center pieces. 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 in the Rubik's cube, we have to do eight factorial because there are eight corners on the Rubik's cube. 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. Yeah. So we have to multiply that by three to the seventh power because there are only three possible ways a corner can be oriented. Oh my gosh. And then you have to multiply that by 12 factorial because there are 12 edges. And then since there are two colors on each edge, that is two to the 11th power because there's 11 other positions. You have to multiply that by six because there are six centerpieces. And then what you do is you divide that all by 12. And when you divide that by 12, you get 43.2 quintillion permutations. Oh my gosh. Those are the amount of permutations that are actually solvable. Yeah.

And if you only calculated that number without dividing by 12, you would get all the possibilities that you can have on the Ruby's Cube. That would be like taking off the stickers, reorientating them around. Which, thank goodness. Can you imagine? Right. That would be so many more permutations. Yeah, it would break the human brain. Exactly.

So going back to competition mindset, let's say you sit down, you lift the cover 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? 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. 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 super computers 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. Oh, yeah. But, like, is that the goal to solve it in as close to 20 moves as possible?

To solve it in 20 moves, you would have to be a superhuman. Oh, okay. Yes. And so, like in a standard solve, for someone solving it in six seconds or seven 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.

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? Right. That makes sense. Okay. So, Roman, you have a watertight, four-step strategy

for quickly solving a Rubik's cube. You are going to teach it to me right now. What is the secret? It's called C-FOP. C-FOP stands for the 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.

What is happening for you as you go through that? Yeah, so I see a scrambled cube when I pick it up. And 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. That's the first step, Z cross. Okay. And then I'm looking for blue corners. So a corner has three colors on it. and I have to match the side colors with the sides of the centerpieces. Essentially, what I'm doing is I'm solving the first layer. Right, which is part of the second step, finishing the first two layers.

Okay. And then I'm just missing four more squares, each of the corners. And then what I have to do is I have to put that correct edges in the second layer, and that develops the second layer. So what's orientating last layer and permutating last layer? Yeah, okay, that's a good question, because the Ruby, cube, it looks like 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 green pieces to be solved. You know those puzzles where it's It's like a jigsaw puzzle and you have to slide pieces into place and you, like, create a picture and there's like one blank space and you shift it all around. Do you know what I'm talking about? This is like a kid's toy. Oh, yes. I think I do know what you're talking about. So the thing about those I always remember as a kid is like, well, if I move this one piece, it's going to mess up this other thing, which will mess up this other thing, which will mess up this other thing. And you can get really like 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. 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 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. They're like, why am I doing this? But the idea is that it's temporary. And you're only breaking it for an instance. Yeah. You have to trust yourself that you're going to fix it later, even though it might look broken right now. 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. Yeah. Absolutely. 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. 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 in their face after they've accomplished solving the Rubik's Cube. I love that part about the Rubik's Cube. That's my favorite part.

I'm so glad you added that. Thank you. You're welcome, Emily. 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 Shortwave from NPR.