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Rubik's Cube Combinations - how many?

How Many Possible Rubik’s Cube Combinations Are There?

In the United States, Rubik’s cube is considered one of their bestselling toy. Many people think that it is impossible to solve, even the one who made it, Erno Rubik. They do not know that there was possible combinations of 43,000,000,000,000,000,000 (43 quintillion). How can someone solve this without memorizing?

The answer is an algorithm. There are mathematical equations to get the pieces in their right places without destroying the whole cube.

 

Number of Possible Permutations

When someone is asked to solve a Speed cube, he will answer that it is just so easy as you will only need to rotate the faces to make the color on its right faces. He will think that it just needs to be rotated randomly.

The truth is that playing Rubik’s cube is not simple, especially when one is not familiar with permutations. For instance, there are various possible states that a 3x3x3 Rubik’s cube can have, and one cannot solve it by just randomly rotating. The same with the Pocket Cube (2x2x2), which has possible permutations of 3.674.160. This kind of strategy will not work with the 2x2x2 cube.

The original 3x3x3 has many likely patterns: about 43 quintillion (for the exact count: 43 quintillions, 252 quadrillions, 3 trillion, 274 billion, 489 million, 856 thousand). For the illustration of this number, if there is a large Rubik’s cube of 6 centimeters, one can cover the Earth’s surface 300 times.

Just like with the 7x7x7x cube, this has several 1.95 * 10 raised to 160, which is roughly 19.5 duoquinquagintillion.

 

  • Pocket Cube 

The Rubik’s cube of 2x2x2 is called a Pocket cube, which has 3674160 combinations. In this case, it is still a manageable number. If you find time to randomly fiddle the 2x2x2 cube within 8 hours per day continuously, you can solve it with a pure chance, which is roughly 2 or 3 times a year, when you assume that the cube cannot break during a time. You might solve the 2×2 cube within four months. Yet, it is somewhat slower compared to the world record.

2x2x2 rubiks cube

Taken from https://www.kevingittemeier.com/

 

  • 3x3x3 Rubik’s Cube 

The classic one, which is the 3x3x3 Rubik’s cube, has 43 252 003 274 489 856 000 combinations, which are approximately 43 quintillion. 

 

  • 4x4x4 Rubik’s cube

The Rubik’s cube of 4x4x4 Rubik’s cube is called a Master cube, and others call it the Rubik’s Revenge. This has combinations of approximately 7.4 quattuordecillion (exactly 7 401 196 841 564 901 869 874 093 974 498 574 336 000 000 000)

 

  • 5x5x5 Rubik’s cube

The Rubik’s cube of 5x5x5 is called a Professor’s cube which has an approximate combination of 283 trevigintillion (exactly 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). It is getting closer to the number of atoms that we can find in the entire universe.

 

  • 6x6x6 Rubik’s cube

Panagiotis Verdes, a Greek engineer, has recently figured out to make a 6×6 and the recent 7×7 cubes. The 6x6x6 Rubik’s cube is also called as V-Cube which has an exact combination of 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. This is quite a ridiculous number to memorize.

 

  • 7x7x7 Rubik’s cube

The 7x7x7 Rubik’s cube, also called as the V-cube, has an exact combinations 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. It is amazing to find out that there are still people who are geniuses to solve the 7x7x7 in just a few minutes. This is incredibly amazing!

So, are you still willing to try solving the Rubik’s cube? How many possible Rubik’s cube combinations are you willing to understand? 

Don’t worry, just like the Rubik’s cube, you can learn everything one by one. 

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