The Algorithm to Solve Rubik’s Cube – Cracked and Explained

To the average Joe, an unsolved Rubik’s Cube remains one of the most elusive and difficult conundrums known to man. How in the world are you supposed to get this mangled, jumbled mess back in the right order again?

After a few confident-looking twists this way and that way, most of us throw in the towel (or, rather, throw out the Cube) in frustration before we even come close to solving the thing. But, did you know there’s a simple, relatively easy way to solve Rubik’s Cubes every single time? All it takes is a small algorithm.

The Eight Ways to Rotate a Rubik’s Cube

To understand the following algorithm, it’s necessary to establish the eight basic ways you can actually rotate Rubik’s Cubes. Understanding these moves and their abbreviations is integral to the steps listed below.

Also important to know? You should always hold the Rubik’s Cube with one of the six faces pointed at you. And so, the eight ways to rotate a Rubik’s Cube are as follows:

• R: A clockwise rotation of the right layer.
• R’: A counterclockwise rotation of the right layer.
• L: A clockwise rotation of the left layer.
• L’: A counterclockwise rotation of the left layer.
• U: A clockwise rotation of the top layer.
• U’: A counterclockwise rotation of the top layer.
• F: A clockwise rotation of the front layer.
• F’: A counterclockwise rotation of the front layer.

How to Solve a Rubik’s Cube Every Time Without Fail

Before we dive in, let’s lay out some ground rules. To solve a Rubik’s Cube, you need to understand the basic principles of the hallowed Cube.

For one, the colored square located in the middle of each side cannot change. That’s that particular side’s set color. Additionally, there are eight corners, each with three distinct colors, and 12-edge pieces between these eight corners, each with two distinct colors.

Looking at the steps listed below, it might seem like this process is too convoluted for you to remember off the top of your head. However, once we get into it, you’ll find that it’s just a lot of repetition. That’s all an algorithm is, after all. Simply put, it’s a particular sequence of specific instructions meant to be followed to the exact letter again and again.

The solving of a Rubik’s Cube can be basically summarized as the shuffling of these corner and edge pieces around the six center squares. While the Rubik’s Cube box likes to scare you by boasting that there are 43 quintillion different configurations per Cube, there’s one simple way to solve a Rubik’s Cube every time without fail. Let’s get into it.

Step 1: Make a White Cross

Firstly, turn the Rubik’s Cube so that the white centerpiece is facing you. Then, rotate the Cube so that the white edges make a cross with the white centerpiece. It doesn’t matter what color the corners are at this point in time. Simple, right? You’re already good to move on to the next step.

Step 2: Match Up Centers and Edges

Secondly, look at the color on each edge of the white cross. For our next step, you need to match these colors with their corresponding centerpieces. You can do this by matching the colors of the four corresponding centerpieces with the edges of the white cross. (Make sure to restore the white cross before moving on.)

Step 3: Set the Corners

Thirdly, you need to set your white corners in place. Here, we’ll employ our first algorithm to help make it happen: R U R’ U’ (and repeat). Judging by our eight basic moves outlined above, that’s a clockwise rotation of the right layer, a clockwise rotation of the top layer, a counterclockwise rotation of the right layer, and a counterclockwise rotation of the top layer.

Now, repeat the algorithm for all the remaining corners. When complete, the entire white face of the Rubik’s Cube should be done and all four corresponding centerpieces with edges touching the white side should resemble a Tetris T-block.

Step 4: Complete the Second Layer

Now, we’re going to focus on those T-block shapes on four of these six sides. Our goal for this step is to complete the second layer on all four of these sides to take the T-block shape and make them into rectangles, leaving only the top layer on each of these four lateral sides unsolved. Once again, we’ll be resorting to algorithms.

For the matching color on the right side of the centerpiece, use the algorithm U R U’ R’ U’ F’ U F. For the matching color on the left side of the centerpiece, use the algorithm U’ L’ U L U F U’ F’. Repeat this on all four sides until you have the white side complete and the bottom two layers of the four lateral sides complete.

Step 5: Make a Yellow Cross

Now, it’s time to make another cross. You might have noticed that the yellow side is looking pretty jumbled on the bottom of the Cube. For this step, we’re going to be making a yellow cross — just like we did with the white cross in the first step, only on the opposite side.

Algorithm time: move the Cube using the F R U R’ U’ F’ algorithm. You will likely have to repeat this algorithm two or three times in order to get all the yellow pieces into a cross shape, but be patient and trust the math used to solve Rubik’s Cubes.

Step 6: Match Edges to the Top Layer

We’re getting closer to the end here! A quick reminder of just how important it is to follow these steps to the letter: slipping up or forgetting a move at this point might send you back to square (or should we say cube?) one.

For this step, our goal is to bring all the yellow pieces to the bottom of the Cube so that they match up with the edge. Using the algorithm F R U R’ U’ F’ should make this happen pretty quickly. If you can’t get the corners in the right place, you can simply position the Cube in any way — so long as the unmatched pieces are at the top — and then use the algorithm U R U’ L’ U R’ U’ L a handful of times.

Step 7: Arrange the Corners

Lastly, we’re going to get those yellow corners and edges in place. Starting from any corner you choose, use the algorithm U R’ U’ R, then rotate the top layer until another mismatched corner is on the top right-hand side. Repeat the algorithm U R’ U’ R again, then repeat this process as many times as needed.

After all the corner pieces are in place, you’ll merely need to move the yellow side one or two times to finish the job. (You’ll know exactly what to do when you end up here.) With that, you now know how to solve s Rubik’s Cube like a total pro!

Now, it’s just a matter of mastering that handful of algorithms. After you get those down with continued practice, you’ll have the coolest party trick in the books.

How Algorithms Solve Rubik’s Cube

Since its invention in 1974 by Hungarian architect and sculptor Ernő Rubik, the Rubik’s Cube has been puzzling generations upon generations of kids and adults both young and old. While traditionally marketed and sold as a toy, Rubik’s Cubes are actually just an extension of a few basic mathematic principles. (Unsurprising, considering it was conceived by an architect.)

With six sides, eight corners, 12 edges, and 54 separate squares on a single Rubik’s Cube, it’s not hard to believe that there are more than 43 quintillion different possible layouts. (That’s 18 zeroes!) Thankfully, the basic pillars of these Rubik’s Cube algorithms remain the same — regardless of how many different ways there are to scramble the thing.

Thanks to algorithms, true masters can solve a Rubik’s Cube in as little as 20 moves. However, the above algorithms used are what’s known as the Layer by Layer method. Using what algebraists would call “group theory,” the Rubik’s Cube can be reduced to less than 10 simple routines. More specifically, algorithms solve Rubik’s Cubes through the magic of permutation groups — a branch of group theory.

Without getting too complex, the basic thinking is that each one of the Rubik’s Cube’s movable parts — 48 out of 54, excluding the six centerpieces — can be labeled with numbers 1 through 48. Each scramble of a Rubik’s Cube is a new permutation of those numbers. Once you break it down into numbers, it’s only a matter of repeating particular moves (i.e. algorithms) over and over.

The image featured at the top of this post is ©gd_project/Shutterstock.com.