# What's the Fastest Way to Solve Rubik's Cube?

 Areas of Science Pure Mathematics Difficulty Time Required Long (2-4 weeks) Prerequisites To do this project you should enjoy solving puzzles and thinking in three dimensions. Material Availability Readily available Cost Very Low (under \$20) Safety No issues

## Abstract

If you like solving challenging puzzles, this could be a good project for you. In this project you will research different methods for solving a Rubik's cube, and then do an experiment to compare them to each other. Which method works fastest?

## Objective

The goal of this project is to compare different methods for solving Rubik's Cube. Which method provides the fastest solution?

## Credits

Andrew Olson, Ph.D., Science Buddies

General citation information is provided here. Be sure to check the formatting, including capitalization, for the method you are using and update your citation, as needed.

### MLA Style

Science Buddies Staff. "What's the Fastest Way to Solve Rubik's Cube?" Science Buddies, 20 Nov. 2020, https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p023/pure-mathematics/what-is-the-fastest-way-to-solve-rubiks-cube?from=Newsletter. Accessed 7 May 2021.

### APA Style

Science Buddies Staff. (2020, November 20). What's the Fastest Way to Solve Rubik's Cube? Retrieved from https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p023/pure-mathematics/what-is-the-fastest-way-to-solve-rubiks-cube?from=Newsletter

Last edit date: 2020-11-20

## Introduction

Rubik's cube is an interesting 3-dimensional puzzle that challenges your spatial imagination and memory. The goal is to arrange the cube so that each side is a solid color, as shown in Figure 1.

Figure 1. Diagram of a solved Rubik's cube. The six sides are named in pairs—up-down, front-back, and left-right. The up (U), front (F), and right (R) sides are visible. The remaining sides—left (L), back (B), and down (D)—are shown by the projected images.

Figure 1 also shows the labels we will be using when referring to sides of the cube. The six sides are named in pairs—up-down, front-back, and left-right. To refer to a specific side, we'll use the one-letter abbreviations shown in Figure 1 (U, D, F, B, L, R).

The cube is built in such a way that each side, row, and column can rotate (see Figure 2). With a few turns, the colors can be thoroughly mixed up. How can you get all of the squares back to their original positions? It's quite a puzzle to get the colors arranged properly again!

Figure 2. Diagram of the core of a Rubik's cube. The core enables each side, row, and column of the cube to rotate.

In this project you will do background research for at least two different methods of solving a Rubik's cube, and then find out which method works the fastest

Before you start learning Rubik's cube strategies, you need to be familiar with some basic terminology. A Rubik's cube is made of three different types of pieces. We will refer to them as center, corner, and edge pieces. The puzzle has six center pieces, one in the middle of each face. Each center piece has only one visible face. There are eight corner pieces on the puzzle. Each corner piece has three visible faces. The remaining twelve pieces are edge pieces, occupying the middle position along each edge of the cube. Each edge piece has two visible faces.

 Center Piece Corner Piece Edge Piece location # in entire cube 6 8 12 visible faces 1 3 2

For each step in solving the cube, specific sequences of moves come in handy. In order to summarize the move sequences efficiently, we will use a shorthand notation common among Rubik's cube solvers. The shorthand notation is easy to learn. There are just two rules you need to know.
1. When a side is rotated clockwise one quarter turn, the shorthand notation for the move is simply the letter of the side. For example, if you're supposed to rotate the right side one quarter turn clockwise, the shorthand would be R.
2. When a side is rotated counterclockwise one quarter turn, the shorthand notation for the move is the letter + an apostrophe ('). For example, if you're supposed to rotate the right side counterclockwise one quarter turn, the shorthand would be R'.

Now that you are familiar with the basic terminology used to refer to a Rubik's cube, you can start researching different solution methods. You can use the resources in the Bibliography below to get you started, but you should be able to find many more Rubik's cube resources online.

## Terms and Concepts

To do this project, you should do research that enables you to understand the following terms and concepts:
• Rubik's cube:
• How it moves
• Terminology:
• Corner pieces (8)
• Edge pieces (12)
• Center pieces (aka side pieces, 6)

### Questions

• How many visible faces does an edge piece have? A center piece? A corner piece?

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## Materials and Equipment

To do this experiment you will need the following materials and equipment:
• A Rubik's cube
• Timer

## Experimental Procedure

1. Do your background research so that you are familiar with the terms, concepts, and questions, above.
2. If you can already solve Rubik's cube before doing this project, your first step should be to measure your average solution time. Time yourself for each of 5–10 trials, and calculate your average solution time. The cube should be well-randomized for each trial.
3. Do background research to identify a first method for solving a Rubik's cube.
4. Practice using each set of moves on your Rubik's cube.
1. Verify that each sequence works as described.
2. Become familiar enough with each set of moves so that you can step through the sequence in your imagination, without having the cube in your hands.
3. Practice solving the cube using the above moves.
5. Time yourself for 10 or more trials and see how long it takes you, on average, to solve the puzzle. The cube should be well randomized for each trial.
6. If you could solve the puzzle before you started the project, did your average solution time improve?
7. Repeat the process for a second method for solving Rubik's Cube.
1. Study the method and verify that each sequence works as described.
2. Become familiar enough with each set of moves so that you can step through the sequence in your imagination, without having the cube in your hands.
3. Practice solving the cube. Allow yourself the same amount of time practicing as you used with the first method.
8. Time yourself for 10 or more trials and see how long it takes you, on average, to solve the puzzle with the new method. The cube should be well-randomized for each trial.
9. Which method is faster? Why?
.

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