## Table of contents:

- Puzzle variations
- What is speedcubing?
- What algorithms exist for solving a 3x3 Rubik's Cube?
- What should the puzzle look like?
- Scheme designations and ways to rotate the cube
- Why collect patterns on the faces of the cube?
- The 3x3 Rubik's Cube Algorithm for Beginners
- Puzzle Solving - Preparatory Work
- Puzzle solution - work on the middle row
- Solving the puzzle - making up the second cross
- Puzzle Solving - Last Spins
- Rubik's Cube and kids

In 1975, sculptor Erne Rubik patented his invention called the "Magic Cube". For more than 40 years, all rights to the puzzle have belonged to the company of a close friend of the inventor - Tom Kroener - called Seven Towns Ltd. The English firm controls the production and sale of the cube around the world. In Hungary, Germany, Portugal and China, the puzzle has retained its original name, in other countries the toy is called the Rubik's Cube.

## Puzzle variations

The classic Rubik's Cube is 3 by 3 squares. Over time, they came up with a huge number of shapes and sizes for toys. No one can surprise anyone with a puzzle in the form of a pyramid or a 17x17 cube. However, humanity never rests on its laurels.

Obviously, there is no assembly scheme for beginners of this cube. The process of assembling and solving the puzzle can take years. Recently, interest in the cube has been growing not only in Asia and Europe, but alsowhere the toy was not very popular, for example, in the USA. One of the fans of the Rubik's Cube filmed the assembly of the 17 by 17 puzzle. The total length of the video is 7.5 hours, the shooting was carried out during the week.

Growing demand creates supply. Sometimes the models for sale are incredible and it is not always clear how they will look when assembled. Every country has its favorite variety of toy.

## What is speedcubing?

Fans of the game arrange real competitions in the speed of solving the cube. On sale there are special "high-speed" puzzles. The mechanism of rotation of such Rubik's cubes is very high quality, and the turns of faces and rows can be done with the movement of one finger.

World Cube Association (WCA) is a non-profit organization supporting the speedcubing movement. The WCA regularly organizes competitions around the world. Almost all countries have representatives of the organization. Anyone can become a participant in a speedcubing event, you just need to register on the site and meet the assembly standard. The most popular discipline in such competitions is the speed assembly of the Rubik's Cube 3x3. The standard for participation is 3 minutes, but even if a person cannot solve the problem in the allotted time, he will still be allowed to the event. You can sign up for any discipline, but you need to come with your own puzzle.

The record for solving a 3x3 Rubik's Cube belongs to Sub1, a robot created by engineer Albert Beer. The machine is able to solve the puzzle for sharesseconds, while it takes 4.7 seconds for a human (an achievement by Mats Valk in 2016). As you can see, the participants in the speedcubing movement have someone to look up to.

## What algorithms exist for solving a 3x3 Rubik's Cube?

There are many ways to solve the famous puzzle. Variants of Rubik's cube assembly schemes 3x3 have been developed for both beginners and advanced people with complicated schemes: 4x4, 6x6 and even 17x17.

The 3x3 puzzle variant is considered a favorite classic by most fans. Therefore, there are much more instructions on how to solve a Rubik's Cube 3x3 than any other.

## What should the puzzle look like?

It is possible to assemble a toy according to the scheme only from a pre-prepared position. If the patterns on the faces of the cube are located incorrectly, then it will not be possible to solve it using the 3x3 Rubik's cube assembly algorithm for beginners. There is a set of such positions for different solutions.

The figure shows a "white cross" or simply "cross" - the starting point of the easiest way to solve a 3x3 Rubik's Cube. It is recommended to disassemble and fold the toy correctly.

## Scheme designations and ways to rotate the cube

Before you start disassembling the formulas of the Rubik's Cube 3x3, you should learn the notation used in speedcubing. All puzzle movements are indicated by capital letters. The absence of an apostrophe above the symbol means that the rotation is clockwise if the symbolis, then rotate in the opposite direction.

The first letters of English (or Russian) words denoting movements are generally accepted:

- front - F or Ф - rotation of the front side;
- back - B or T - backside rotation;
- left - L or L - rotation of the left row;
- right - R or R - right row rotation;
- up - U or B - rotation of the top row;
- down -D or H - rotation of the bottom row.

Also, pointers can be used to change the position of the cube in space - interception movements. Here, too, everything is simple, from the school course of geometry, everyone knows the coordinate axes X, Y and Z. The movement of X means that the cube must be rotated by the face F to the place of the face U, when shifting Y - F, it should take place L, and when rotating Z - F moves to R.

The following group of symbols is rarely used, it is used when drawing up patterns of patterns:

- M - middle row turn, between right (R/R) and left (L/L);
- S - turn of the middle row, between front (F/F) and back (B/T);
- E - turn the middle row, between the top (U/B) and bottom (D/H).

## Why collect patterns on the faces of the cube?

At speedcubing meetings, they compete not only in solving puzzles, but also in the ability to make various patterns on a 3x3 Rubik's Cube. They do this in order to quickly and easily collect the cube in the desired position.

There are a huge number of schemes for assembling a variety of patterns: "dots", "chess", "dots with chess","zigzag", "mason", "cube in a cube in a cube" and many others. Only for the classic puzzle there are more than 46 of them. Speedcubing masters consider it shameful to disassemble the toy. Also, making patterns on a 3x3 Rubik's Cube is a great way to practice and improve your skills.

The picture shows variations of different puzzle patterns. Below are a few more formulas for assembling the most interesting patterns from the position of the cross:

- chess - M
^{2}E^{2}S^{2;} - zigzag - (PLFT)
^{3;} - four z - (PLFT)
^{3}B^{2}N^{2;} - Plummer's cross - TF
^{2}N'P^{2}FNT'FN'VF'N'L^{2}FN^{2B';} - cube in a cube in a cube - V'L
^{2}F^{2}N'L'NV^{2 PV'P'V}2^{P}2^{PF'L'VP'.}

## The 3x3 Rubik's Cube Algorithm for Beginners

Although there are many ways to solve the puzzle, simple and clear schemes for beginners are not so easy to find. With each completed assembly step, the Rubik's 3x3 cube formulas become more difficult. It is necessary not only to change the pattern correctly, but also to save what has been done before. Below is one of the options for how to easily solve a 3x3 Rubik's Cube.

Conventionally, the whole process can be divided into the following stages:

- Assembly of the cross at the top of the cube.
- Correct composition of the entire upper face.
- Working on the middle layers.
- Correct assembly of the ribs of the last row.
- Cross assemblybottom edge.
- Correct orientation of the corners of the last face of the cube.

## Puzzle Solving - Preparatory Work

The first step is the easiest. Beginners can try their hand and practice making cube patterns according to the instructions provided, but this process will take a long time.

You need to select the top face and the color that will be collected first. The 3x3 Rubik's cube assembly algorithm for beginners was developed from the "cross" position. It is not difficult to make it, you need to select the central color, find 4 edge elements of the same shade and raise them to the selected face. The colored arrow in the picture indicates the desired part. The options for the location of the desired element may be different, depending on this, 2 sequences of actions A and B are described. The difficulty lies in continuing the cross along the sides of the cube. You can take a closer look at the final form of the stage in the image posted above.

## Puzzle solution - work on the middle row

At this stage of the 3x3 Rubik's cube for beginners, you need to find and assemble the corner elements of the upper face. The end result should be the complete solution to the cross face and the top row of the puzzle.

The image shows three possible facet patterns. Choosing one of the methods A, B or C, you need to collect all 4 corners of the cube. rememberingrotation algorithms and practicing them, skills and mastery of assembling a puzzle are acquired. It is pointless to consider formulas and imagine the process, it is much easier to take a cube and try all the methods in practice.

The third step seems simple, but it's only an appearance. To solve it, two situations of patterns are described and, accordingly, two rotation formulas are compiled. When applying them, it is worth remembering to preserve the previously achieved results. Masters constantly keep in memory the last 3-4 rotations, so that in case of failure, return the cube to its original state.

To solve the puzzle, you need to rotate it along the coordinate axis in search of the necessary elements and work with them. Such movements are rarely displayed in formulas, only in special cases. It is recommended to start assembling edge faces from the elements of the lower rows, after such rotations all the necessary cubes will descend from the middle row to the lower row.

## Solving the puzzle - making up the second cross

At the fourth stage, the toy is turned upside down. Solving the last face is the most difficult part of the 3x3 Rubik's cube algorithm for beginners. The rotation formulas are long and complex, and their execution will require special care. The purpose of the action is to place the rib elements in their places for further drawing up the cross. The orientation of the rib portions may be incorrect. Cube movement formulathere is only one and it should be applied until the goal of the stage is reached.

Rotations of the fifth stage are aimed at turning the elements to the right side. Its peculiarity lies in the fact that the same rotation formula is used for all three patterns in the figure, the only difference is in the orientation of the cube itself.

The formulas for the movements of the 5th stage are as follows:

- (PS
_{N})^{4}V (PS_{N})^{4 B' – option “A”;} - (PS
_{N})^{4}B' (PS_{N})^{4 C - option "B";} - (PS
_{N})^{4}B^{2}(PS_{N})^{4}B^{2 – B option.}

С_{Н is the rotation of the middle row clockwise, and the exponent above the bracket is the number of repetitions of actions in brackets.}

## Puzzle Solving - Last Spins

At the sixth stage, as well as at the fourth, the necessary cubes are placed in their places, regardless of their orientation. The puzzle should be rotated so that the element that is already in the right place is located in the far left corner at the top of the cube. The options proposed to solve the formula mirror each other. It is necessary to repeat rotations until the desired result is achieved.

The seventh stage is the most solemn and most difficult. When rotating the cube, violations in already assembled rows are inevitable. Would needcompletely focus on the movements, otherwise the result of the assembly may be irretrievably ruined. As in the fifth stage, there is only one sequence of movements, but it is repeated 4 times. First, rotations are performed to orient the element, then reverse rotations are performed to restore broken rows.

One should not forget about recording movements using the characters of the English alphabet. The formulas for the movements of the faces and rows of the cube of this stage are as follows:

- (RF'R'F)
^{2}U (RF'R'F)^{2 – option "a";} - (RF'R'F)
^{2}U' (RF'R'F)^{2– option "b";} - (RF'R'F)
^{2}U^{2}(RF'R'F)^{2– option "in".}

B - rotation of the upper face by 90 degrees, B' - rotation of the same face counterclockwise, and B^{2 - double rotation.}

The complexity of the stage is in the correct assessment of the location of the elements and the choice of the required rotation option. It can be difficult for beginners to immediately identify the pattern correctly and match it with the correct formula.

## Rubik's Cube and kids

Tricky puzzle is interesting not only for adults, but also for children. Teenagers became the world record holders for solving the Rubik's Cube. In 2015, Colin Burns, who was only 15 years old at the time, assembled the toy in 5.2 seconds.

A simple yet captivating toy that has continued to intrigue the younger generation for over 5 decades. Children's hobby often develops into a profession. There are mathematical methods for evaluating the solution to Rubik's cube problems. This branch of mathematics is used fordrawing up and writing solution algorithms for automated computers. Robots that really look for ways to solve the cube, and do not follow a pre-driven algorithm of movements, solve the puzzle in 3 seconds, for example, CubeStormer 3.