# Invention** of Most Admiring 3×3 Cube**

3×3 Cube invention, in March 1970, Larry D. Nichols invented the 2 × 2 × 2 puzzle “with rotating pieces in groups” 2 × 2 × 2 and filed a Canadian patent for it. Nichols’ cube was held together by magnets. Nichols was granted U.S. Patent 3,655,201 on April 11, 1972,

IN 1970, Frank Fox applied for a patent “fun device”, a type of sliding puzzle. He received his patent in the United Kingdom (1344259) on January 16, 1974.

## Discovery of Fantastic 3×3 Cube

Cube was built as a teaching tool to help students to understand 3D objects, its current goal was to solve the structural problem of moving parts independently, without the whole mechanism disintegrating. He didn’t realize he had created a puzzle until the first time he shuffled his new cube and tried to restore it.

After international appearance, the Cube’s progress on Western toy store was briefly halted so that it could be manufactured to Western packaging. A Cube lighter was produced and Ideal decided to rename it.

## 3×3 Cube craze in 1980

Since most people could only solve one or two sides, several books were published. At one point in 1981, three of the ten best-selling books in the United States were 3×3 Cube resolution books, and the best-selling book of 1981 was James G. Nourse’s The Simple Solution to Rubik’s Cube, which sold over 6 millions of copies. .

In 1981, the Museum of Modern Art in exhibited a cube and at the 1982 World’s Fair in Knoxville, Tennessee, a six-foot cube was also exhibited.

In October 1982, the New York Times reported that “the craze was dead,”. However, in some Communist countries, such as China and the USSR, the craze started later and the demand was still high due to the shortage of cubes.

## Revival of 3×3 Cube in 21st century

The cubes continued to be marketed and sold in the 1980s and 1990s, but it wasn’t until the early 2000s that interest in the cube began to grow again. In the US, sales doubled between 2001 and 2003 and the Boston Globe noted that “it was getting nice to have a 3×3 Cube again.”

The 2003 championship was the first speedcubing tournament since 1982. It took place in Toronto and saw the participation of 83 participants.

### Imitations

Taking advantage of the initial shortage of cubes, numerous imitations and variants emerged, many of which may have infringed one or more patents.

## Mechanics of 3×3 Cube

A standard cube measures 5.6 centimeters on each side. The cube consists of 26 miniature cubes, also known as “cubelets”. Each of them includes a hidden inner extension that fits with the other cubes, allowing them to move to different locations. However, the central hub of each of the six fixed to the central mechanism. They provide the framework in which the other pieces fit and rotate.

So there are 21 pieces: a single centerpiece made up of three axes that intersect and hold the six center squares in place but allow them to rotate, and 20 smaller plastic pieces that snap together to form the assembled puzzle.

Each of the six center pieces rotates on a screw (clamp) held by the center piece, a “3D cross”. A spring between each screw head and its corresponding part tensions the part inward so that, together, the entire assembly remains compact but can still be easily manipulated. The bolt can be tightened or loosened to change the “feel” of the hub.

The 3×3 Cube can be disassembled without too much difficulty, usually by rotating the top layer 45° and then pulling one of its edge cubes away from the other two layers. Consequently, it is a simple process to “resolve” a cube by disassembling and reassembling it in a resolved state.

There are six centerpieces showing a colorful face,

twelve corner pieces showing two colored faces and eight corner pieces showing three colored faces.

Each tile shows a unique color combination, but not all combinations are present (for example, if red and orange are on opposite sides of the solved 3×3 Cube, there is no border with red and orange sides).

The position of these cubes to each other can be changed by rotating an outer third of the cube in 90 degree increments, but the position of the colored sides cannot be changed; is fixed by the relative positions of the central squares

## Mathematics in 3×3 Cube

The puzzle was having “more than 3,000,000,000 combinations, but only one solution”. Depending on how the combinations are counted, the actual number is significantly higher.

## Permutations of 3×3 Cube

The previous figure is limited to the permutations that can be obtained simply by rotating the sides of the 3×3 Cube. If we consider the permutations obtained by disassembling the cube, the number becomes twelve times greater:

There are about 519 quintillions of possible arrangements, but only one in twelve is actually solvable. This is because there is no sequence of moves that will swap a single pair of pieces or rotate a single corner or edge of the cube.

Therefore, there are 12 possible sets of workable configurations, sometimes called “universes” or “orbits”, in which the cube can be positioned by disassembling and reassembling.

The preceding numbers assume that the center faces are in a fixed position. If we assume that we rotate the entire cube with a different permutation, each of the preceding numbers must be multiplied by 24. A chosen color can be on one of the six sides, and therefore one of the adjacent colors can be on one of the four positions; this determines the positions of all other colors.

## Algorithms use in 3×3 Cube

Many algorithms are designed to solve cube only a small part of the cube without interfering with other parts which are already solved, so that they can be repeatedly applied to different parts of the cube until the puzzle is solved. For example, there are well-known algorithms for alternating three corners without changing the rest of the puzzle or reversing the orientation of one pair of edges, leaving the others intact.

Some algorithms have a desired effect on the 3×3 Cube (e.g. swapping two corners), but they can also have the side effect of changing other parts of the 3×3 Cube (like swapping some edges).

These algorithms are often simpler than those without side effects and are employed at the beginning of the solution, when most of the puzzle has not yet been solved and the side effects are not important. Most are long and difficult to memorize. At the end of the solution more specific (and often more complicated) algorithms are used.

## How to solve 3×3 Cube

### Shift notation

Many fans of the 3×3 Cube use a notation developed by David Singmaster to indicate a sequence of moves, called “Singmaster notation”.algorithms to be written in such a way that they can be applied regardless of which side is designated at the top or how the colors are arranged in a given cube.

When a prime symbol (′) follows a letter, it indicates a counterclockwise turn of the face; while a letter without a prime symbol indicates a clockwise rotation. These instructions show you how you are looking at the specified face. A letter followed by a 2 (occasionally a superscript 2) indicates two turns, or a 180-degree turn. R is the right side clockwise, but R ′ is the right side counterclockwise.

The letters x, y and z are used to indicate that the entire cube must be rotated around one of its axes, corresponding respectively to R, U and F. When x, y and z are turned on, it is an indication that the cube must be rotated in the opposite direction. When square, the cube must be rotated 180 degrees.

An alternative notation, the Wolstenholme notation, is designed to make it easier for beginners to memorize motion sequences. This notation uses the same letters for the faces, except it replaces U with T (top), so they are all consonants.

The main difference is the use of the vowels O, A and I for clockwise, , which result in word-like sequences such as LOTA RATO LATA ROTI (equivalent to LU ′ R ′ UL ′ U ′ R U2 in Singmaster notation). Adding a C involves the rotation of the entire cube, so ROC is the clockwise rotation of the cube around its right face. The interlayer motions are indicated by adding an M to the corresponding face motion, so RIM means a 180 degree rotation of the interlayer adjacent to the R face.

Another notation appeared in the 1981 book The Simple Solution to 3×3 Cube. Singmaster notation was not well known at the time of publication. The faces were labeled Top (T), Bottom (B), Left (L), Right (R), Front (F) and Back (P), with + clockwise, – counterclockwise and 2 for 180 rotations degrees.

### Optimal solutions of 3×3 Cube

A solution commonly used by speedcubers was developed by Jessica Fridrich. This method is called CFOP, which means “cross, F2L, OLL, PLL”. It is similar to the layer-by-layer method, but employs the use of a large number of algorithms, especially for orienting and permuting the last layer.

The crossing is done first, followed by the corners of the first layer and the edges of the second layer at the same time, with each corner paired with a piece of the edge of the second layer, thus completing the first two layers (F2L). This is followed by last layer orientation and then last layer permutation (OLL and PLL respectively). Fridrich’s solution requires learning about 120 algorithms, but solves the Cube on average in just 55 moves.

A well known method was developed by Lars Petrus. In this method, a 2 × 2 × 2 section is solved first, followed by a 2 × 2 × 3, then the wrong edges are solved using a three-movement algorithm, which eliminates the need for a possible 32-move algorithm afterwards.

The principle behind this is that, layer by layer, you must constantly break and repair the completed layer or layers; the 2 × 2 × 2 and 2 × 2 × 3 sections allow you to record three or two layers (respectively) without hampering your progress. One of the advantages of this method is that it tends to provide solutions in fewer steps. For this reason, the method is also popular for races with the fewest moves.

The Roux method, developed by Gilles Roux, is similar to the Petrus method in that it is based on building blocks rather than layers, but derives from corner-first methods. In Roux, a 3 × 2 × 1 block is solved, followed by another 3 × 2 × 1 on the opposite side. After that, the top level corners are resolved. The cube can then be solved using just the U-layer and M-slice motions.

## Methods for beginners

Most beginner solving methods involve solving the 3×3 Cube one layer at a time, using algorithms that preserve what has already been solved. The simpler layer-by-layer methods require only 3-8 algorithms.

In 1981, 13-year-old Patrick Bossert developed a solution for solving the cube, along with graphical notation, designed to be easily understood by beginners.

In 1997, Denny Dedmore published a solution described using diagrammatic icons representing the moves to be made, instead of the usual notation.

Philip Marshall’s The Ultimate Solution to Rubik’s Cube takes a different approach, averaging just 65 twists but requiring only two algorithms to be memorized. The cross is resolved first, followed by the remaining edges, then by the five corners, and finally by the last three corners.

## Blindfolded resolution of 3×3 Cube

Blindfolded multiple resolution, or “multi-blind”, in which the competitor solves any number of blindfolded cubes in sequence

Solve the 3×3 Cube using only one hand

Solve the cube with the fewest possible moves

In blindfolded solving, the contestant first studies the encrypted cube (i.e., looking at it normally not blind), then is blindfolded before starting to turn the faces of the cube. The time logged for this event includes the time it took to store the cube and the time it took to manipulate it.

In Multiple Blindfolded, all cubes are stored and then all cubes are solved once blindfolded; therefore, the main challenge is to memorize many separate 3×3 Cube, usually ten or more.

The event is scored not based on time, but based on the number of points earned after the one hour limit with the number of unsolved cubes after the end of the attempt, where the greater the number of points, the better. If several competitors get the same number of points, the rankings are evaluated based on the total time of the at3x3 Cube