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How Many Possible Rubik’s Cube Combinations Are There?

The Rubik’s cube, although seemingly simple, is a complex mathematical puzzle. It is often used to teach fractions, proportions, and permutation & combination to students. Twisting and turning the cube yields unlimited combinations. In fact, established studies show that there are 43 quintillion possible combinations of the cube.

If that number seems incomprehensible, it sort of is. One quintillion has 18 zeroes, or 1,000,000,000,000,000,000. To put things in perspective, a quintillion is the same as a billion or a million trillion.

Number of Possible Permutations

Although the Rubik’s cube seems easy and straightforward, most people cannot solve it quickly or easily. Solving the Rubik’s cube effortlessly requires a certain degree of mathematical aptitude or at least some knowledge of the different permutations.

Randomly rotating a 3x3x3 cube will lead you to one of the 43 quintillion combinations, but not toward solving the puzzle.  A pocket cube (2x2x2) has 3,674,160 possible permutations, and randomly turning around this innocuous little cube will not help you solve it.

The original 3x3x3 has many likely patterns. According to those who have figured it out, the exact count is 43 quintillion, 252 quadrillions, 3 trillion, 274 billion, 489 million, 856 thousand. To illustrate this, all the permutations and combinations of a large Rubik’s cube of 6 centimeters can cover the Earth’s surface 300 times.

How many combinations are possible among Rubik’s cube adaptations?

Since the time the original Rubik’s cube was launched, there have been many adaptations. Most of these adaptations come in different numbers of cubes within the actual cube. While the original one is 3x3x3, there are also cubes with 2x2x2, 4x4x4, and other amalgamations.

One must be warned that most of these numbers are incomprehensible, and the terms that are used to describe them are mostly unknown to most people. Let us take a look at how many combinations each of these Rubik’s cube adaptations can boast:

  1. Pocket Cube

A Rubik’s cube of 2x2x2 is called a Pocket Cube, and it has 3,674,160 combinations. Although it is “simpler” than the 3x3x3 version the 3,674,160 combinations a 2x2x2 cube possesses are still mind-numbing. If one were to try solving it by pure chance every day full time, one could only solve it 2 or 3 times a year. That is assuming the cube doesn’t break during this time.

  1. 3x3x3 Rubik’s Cube

The classic cube, the 3x3x3 Rubik’s cube has approximately 43 quintillion 43,252,003,274,489,856,000 combinations. It needn’t be said again that this would take years to solve if one were to simply depend on chance or luck. This is why knowledge of combinations and how they work according to mathematics is necessary. Developing strategies, keenly observing the puzzle while trying to solve it, and learning from one’s mistakes (trial and error) will all help one to solve the cube quickly.

  1. 4x4x4 Rubik’s cube

A Rubik’s cube of 4x4x4 amalgamation is called the Master Cube. Some also call it the Rubik’s Revenge. This Master Cube approximately has 7.4 quattuordecillion combinations. The numerical representation looks like this:

7,401,196,841,564,901,869,874,093,974,498,574,336,000,000,000.

  1. 5x5x5 Rubik’s cube

A Rubik’s cube of 5x5x5 is called the Professor’s Cube. It has an approximately 283 trevigintillion combinations. If you have never heard of this term, you probably are not alone. The exact number of combinations possible in this amalgamation is:

282,870,942,277,741,856,536,180,333,107,150,328,293,127,731,985,672,134,721,536,000,000,000,000,000.

  1. 6x6x6 Rubik’s cube

Panagiotis Verdes, a Greek inventor, is famous for inventing the 6x6x6 and the 7x7x7 cubes. The inventor used a special strategy to build these cubes, which were previously believed to be impossible. The 6x6x6 Rubik’s cube is marketed under the brand V-Cube, and the following possible combinations:

157,152,858,401,024,063,281,013,959,519,483,771,508,510,790,313,968,742,344,694,684,829,502,629,887,168,573,442,107,637,760,000,000,000,000,000,000,000,000.

  1. 7x7x7 Rubik’s cube

The 7x7x7x cube has 19.5 duoquinquagintillion combinations. A duoquinquagintillion can be represented as 10159 (10 to the power of 159), or 159 zeroes after the 1. The 7x7x7 Rubik’s cube is marketed under Verdes’ V-Cube brand, and has an exact combination of:

19,500,551,183,731,307,835,329,126,754,019,748,794,904,992,692,043,434,567,152,132,912,323,232,706,135,469,180,065,278,712,755,853,360,682,328,551,719,137,311,299,993,600,000,000,000,000,000,000,000,000,000,000,000.

Don’t just depend on luck or chance

It is clearly impossible to randomly twist and turn the Rubik’s cube and its many adaptations to try and solve them. Since the combinations are limitless, it is necessary to know combination strategies, tips, and tricks. GoCube’s Smart Cube and the associated mobile application can help you learn how to solve the Rubik’s cube on the go. Most importantly, you can learn from those who already excel at it and network with other players.

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